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# Retrieve the mean, variance and sample variance from an aggregate
## Covariance
### Online
A stable one-pass algorithm exists, similar to the online algorithm for computing the variance, that computes co-moment $C_n = \sum_{i=1}^n (x_i - \bar x_n)(y_i - \bar y_n)$:
$$\begin{alignat}{2}
\bar x_n &= \bar x_{n-1} &\,+\,& \frac{x_n - \bar x_{n-1}}{n} \\[5pt]
\bar y_n &= \bar y_{n-1} &\,+\,& \frac{y_n - \bar y_{n-1}}{n} \\[5pt]
C_n &= C_{n-1} &\,+\,& (x_n - \bar x_n)(y_n - \bar y_{n-1}) \\[5pt]
&= C_{n-1} &\,+\,& (x_n - \bar x_{n-1})(y_n - \bar y_n)
\end{alignat}$$ The apparent asymmetry in that last equation is due to the fact that $(x_n - \bar x_n) = \frac{n-1}{n}(x_n - \bar x_{n-1})$, so both update terms are equal to $\frac{n-1}{n}(x_n - \bar x_{n-1})(y_n - \bar y_{n-1})$. Even greater accuracy can be achieved by first computing the means, then using the stable one-pass algorithm on the residuals.
Thus the covariance can be computed as
$$\begin{align}
\operatorname{Cov}_N(X,Y) = \frac{C_N}{N} &= \frac{\operatorname{Cov}_{N-1}(X,Y)\cdot(N-1) + (x_n - \bar x_n)(y_n - \bar y_{n-1})}{N}\\
&= \frac{\operatorname{Cov}_{N-1}(X,Y)\cdot(N-1) + (x_n - \bar x_{n-1})(y_n - \bar y_n)}{N}\\
&= \frac{\operatorname{Cov}_{N-1}(X,Y)\cdot(N-1) + \frac{N-1}{N}(x_n - \bar x_{n-1})(y_n - \bar y_{n-1})}{N}\\
&= \frac{\operatorname{Cov}_{N-1}(X,Y)\cdot(N-1) + \frac{N}{N-1}(x_n - \bar x_{n})(y_n - \bar y_{n})}{N}.
\end{align}$$
``` python
def online_covariance(data1, data2):
meanx = meany = C = n = 0
for x, y in zip(data1, data2):
n += 1
dx = x - meanx
meanx += dx / n
meany += (y - meany) / n
C += dx * (y - meany)
population_covar = C / n
# Bessel's correction for sample variance
sample_covar = C / (n - 1)
```
A small modification can also be made to compute the weighted covariance:
``` python
def online_weighted_covariance(data1, data2, data3):
meanx = meany = 0
wsum = wsum2 = 0
C = 0
for x, y, w in zip(data1, data2, data3):
wsum += w
wsum2 += w * w
dx = x - meanx
meanx += (w / wsum) * dx
meany += (w / wsum) * (y - meany)
C += w * dx * (y - meany)
population_covar = C / wsum
# Bessel's correction for sample variance
# Frequency weights
sample_frequency_covar = C / (wsum - 1)
# Reliability weights
sample_reliability_covar = C / (wsum - wsum2 / wsum)
```
Likewise, there is a formula for combining the covariances of two sets that can be used to parallelize the computation:
$$C_X = C_A + C_B + (\bar x_A - \bar x_B)(\bar y_A - \bar y_B)\cdot\frac{n_A n_B}{n_X}
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The **politics of Antigua and Barbuda** takes place in a framework of a unitary parliamentary representative democratic monarchy, wherein the sovereign of Antigua and Barbuda is the head of state, appointing a governor-general to act as vice-regal representative in the nation. A prime minister is appointed by the governor-general as the head of government, and of a multi-party system; the prime minister advises the governor-general on the appointment of a Council of Ministers. Executive power is exercised by the government. Legislative power is vested in both the government and the two chambers of the Parliament. The bicameral Parliament consists of the Senate (seventeen-member body appointed by the governor-general) and the House of Representatives (seventeen seats; members are elected by proportional representation to serve five-year terms).
Antigua and Barbuda has a long history of peaceful changes of government. Since the 1951 general election, the party system has been dominated by the Antigua and Barbuda Labour Party (ABLP), for a long time was dominated by the Bird family, particularly Prime Ministers Vere and Lester Bird. The opposition claimed to be disadvantaged by the ABLP\'s longstanding monopoly on patronage and its control of the media, especially in the 1999 general election. The opposition United Progressive Party (UPP) won the 2004 election, and its leader Winston Baldwin Spencer was prime minister of Antigua and Barbuda from 2004 to 2014.
The elections to the House of Representatives were held on 12 June 2014. The Antigua and Barbuda Labour Party government was elected with fourteen seats. The United Progressive Party had three seats in the House of Representatives. ABLP won 15 of the 17 seats in the 2018 snap election under the leadership of incumbent Prime Minister Gaston Browne.
Constitutional safeguards include freedom of speech, press, worship, movement, and association. Antigua and Barbuda is a member of the eastern Caribbean court system. The Judiciary is independent of the executive and the legislature. Jurisprudence is based on English common law.
## Executive branch {#executive_branch}
### Executive branch leadership {#executive_branch_leadership}
As head of state, King Charles III is represented in Antigua and Barbuda by a governor-general who acts on the advice of the prime minister and the cabinet.
## Legislative branch {#legislative_branch}
Antigua and Barbuda elects on national level a legislature. Parliament has two chambers. The House of Representatives has 19 members: 17 members elected for a five-year term in single-seat constituencies, and 2 ex officio members (president and speaker). The Senate has 17 appointed members. The prime minister is the leader of the majority party in the House and conducts affairs of state with the cabinet. The prime minister and the cabinet are responsible to the Parliament. Elections must be held at least every five years but may be called by the prime minister at any time.
There are special legislative provisions to account for Barbuda\'s low population relative to that of Antigua. Barbuda is guaranteed one member of the House of Representatives and two members of the Senate. In addition, there is a Barbuda Council to govern the internal affairs of the island.
## Political parties and elections {#political_parties_and_elections}
## Administrative divisions {#administrative_divisions}
The country is divided into six parishes, Saint George, John, Mary, Paul, Peter, and Phillip which are all on the island of Antigua. Additionally, the islands of Barbuda and Redonda are considered dependencies.
## Judicial branch {#judicial_branch}
Antigua and Barbuda is a member of the Eastern Caribbean Supreme Court. This court is headquartered in Saint Lucia, but at least one judge of the Supreme Court resides in Antigua and Barbuda, and presides over the High Court. The current High Court judges are Nicola Byer, Ann-Marie Smith, Jan Drysdale, Rene Williams, and Tunde Bakre as of September 2024.
Antigua is also a member of the Caribbean Court of Justice, although it has not yet acceded to Part III of the 2001 Agreement Establishing a Caribbean Court of Justice. Its supreme appellate court therefore remains the British Judicial Committee of the Privy Council. Indeed, of the signatories to the Agreement, as of December 2010, only Barbados has replaced appeals to Her Majesty in Council with the Caribbean Court of Justice.
In addition to the Eastern Caribbean Supreme Court, Antigua and Barbuda has a Magistrates\' Court, which deals with lesser civil and criminal cases
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**Telecommunications in Antigua and Barbuda** are via media in the telecommunications industry.
## Telephone
**Telephones -- main lines in use:** 37,500 (2006)
: *country comparison to the world:* 168
**Telephones -- mobile cellular:** 110,200 (2006) (APUA PCS, Cable & Wireless, Digicel)
: *country comparison to the world:* 177
**Telephone system:**\
*domestic:* good automatic telephone system\
*international:* 3 fiber optic submarine cables (2 to Saint Kitts and 1 to Guadeloupe); satellite earth station -- 1 Intelsat (Atlantic Ocean)
## Radio
**Radio broadcast stations:** AM 4, FM 6, shortwave 0 (2002)
Band / Freq. Call Sign Brand City of license Notes
-------------- -------------------- ------------------------ ------------------------ ----------------------------------------------
AM 620 V2C ABS Radio and TV Saint John\'s, Antigua ABS; 5 kW
AM 1100 ZDK Radio ZDK Saint John\'s, Antigua Owner: Grenville Radio; 20 kW
AM 1160 Unknown Radio Lighthouse Saint John\'s, Antigua 10 kW
AM 1580 Unknown Unknown Judge Bay, Antigua 50 kW
FM 88.5 Unknown Power FM Saint John\'s, Antigua
FM 89.7 Unknown Catholic Radio Saint John\'s, Antigua 2 kW
FM 90.5 V2C-FM ABS Radio and TV Saint John\'s, Antigua repeats AM 620
FM 91.1 Unknown Observer Radio Saint John\'s, Antigua
FM 91.9 Unknown Hitz 91.9 Saint John\'s, Antigua
FM 92.3 Unknown Radio Lighthouse Saint John\'s, Antigua repeats AM 1160
FM 92.9 VYBZ-FM Vybz FM Saint John\'s, Antigua
FM 93.9 Unknown Caribbean SuperStation Saint John\'s, Antigua repeats Caribbean SuperStation from Trinidad
FM 95.7 Unknown Zoom Radio Saint John\'s, Antigua
FM 97.1 ZDK Radio ZDK Saint John\'s, Antigua repeats AM 1100
FM 98.5 Unknown Red Hot Radio Saint John\'s, Antigua
FM 99.1 Unknown Hit Radio Music Power Saint John\'s, Antigua
FM 100.1 Unknown (ZDKR-FM?) Sun FM Saint John\'s, Antigua
FM 101.5 Unknown Second Advent Radio Saint John\'s, Antigua 20 watts
FM 102.3 Unknown Variety Radio Saint John\'s, Antigua
FM 103.1 Unknown Life FM Codrington, Barbuda 1 kW
FM 103.9 Unknown Life FM Saint John\'s, Antigua repeats 103.1 Codrington
FM 104.3 Unknown Nice FM Codrington, Barbuda
FM 107.3 Unknown Crusader Radio Saint John\'s, Antigua
SW 3.255 mHz V2C ABS Radio and TV Saint John\'s, Antigua Repeats AM 620
: Radio Stations of Antigua and Barbuda
**Radios:** 36,000 (1997)
## Television
**Television broadcast stations:** 2 (1997) (including ABS-TV)
**Televisions:** 31,000 (1997)
## Internet
**Internet Service Providers (ISPs):** Cable & Wireless, Antigua Computer Technologies (ACT), Antigua Public Utilities Authority (APUA INET)
**Internet hosts:** 2,215 (2008)
: *country comparison to the world:* 140
**Internet users:** 60,000 (2007)
: *country comparison to the world:* 158
**Country codes:** AG
## Demographics
Q48 Ethnic Q55 Internet Use
------------------------ ------------------
Yes No
African descendent 47.42%
Caucasian/White 83.27%
East Indian/India 58.66%
Mixed (Black/White) 64.34%
Mixed (Other) 61.22%
Hispanic 31.78%
Syrian/Lebanese 60.77%
Other 59.46%
Don\'t know/Not stated 20.58%
Total 48.35%
: Internet Users by Ethnicity
Q48 Ethnic Q25 4 Internet access
------------------------ -----------------------
No Yes
African descendent 51.99%
Caucasian/White 14.56%
East Indian/India 36.63%
Mixed (Black/White) 39.47%
Mixed (Other) 41.76%
Hispanic 67.68%
Syrian/Lebanese 29.48%
Other 34.02%
Don\'t know/Not stated 53.86%
Total 50
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The **Antigua and Barbuda Defence Force** (**ABDF**) is the armed forces of Antigua and Barbuda. The ABDF has responsibility for several different roles: internal security, prevention of drug smuggling, the protection and support of fishing rights, prevention of marine pollution, search and rescue, ceremonial duties, assistance to government programs, provision of relief during natural disasters, assistance in the maintenance of essential services, and support of the police in maintaining law and order. The force entered its current form on 20 December 1995.
The ABDF is one of the world\'s smallest militaries, consisting of 245 personnel. The first militia in Antigua was established in the 1600s, having fought against the French capture of the island in 1666. The governor oversaw the force, and by 1820 the island had a 945-man militia. The island continued to maintain this force for much of the colonial era, and by 1 September 1981 the Antigua Volunteer Defence Force was renamed to the Antigua and Barbuda Defence Force preceding independence. The force has undergone various reforms, and the present force was reestablished on 1 June 1956.
## Organisation
The ABDF consists of five branches:
- Antigua and Barbuda Regiment -- comprises four line companies and is the infantry unit and fighting arm of the defence force.
- Service and Support Unit -- provides administrative, logistic and engineer support to the rest of the defence force.
- Coast Guard -- the maritime element of the defence force.
- Air Wing -- the aerial element of the defence force.
- Cadet Corps -- voluntary youth organisation.
### Defence Board {#defence_board}
The Defence Board is in charge of overseeing the leadership, management, and discipline of the Antigua and Barbuda Defence Force as well as all other matters pertaining to it. The Defence Board has the authority to govern its work, how it will carry out its duties, and the responsibilities of its members. It can also assign any member of the Board any authority or duty, by publishing a notice in the Official Gazette; consult with non-members as appropriate, including officers commanding units of the Force, regarding matters pertaining to their units; and the officers are required to attend the meetings as the Board requests; decide on the protocol to be followed in conducting its business; and provide for any other matter that it deems necessary or desirable for achieving the better performance of its functions.
### Officers
A person cannot be appointed to the force unless they have received a recommendation from a board, known as the Commissions Board in the Defence Act. This board is made up of the chairman, who is appointed by the Chief of Defence Staff; the Chairman of the Public Service Commission, or in his absence, the Vice Chairman of the Public Service Commission; and an individual appointed by the Defence Board for a duration determined by the Board. His Majesty has the authority to appoint people to the Antigua and Barbuda Defence Force, and the Governor-General may act in that capacity. A commission may be awarded for a predetermined amount of time or for an unlimited amount of time.
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## Organisation
### Reserve forces {#reserve_forces}
There are two classes in the Antigua and Barbuda Defence Force Reserve. The soldiers enlisted, deemed to be enlisted, or re-engaged in accordance with this Part for service in that class; the Reserve soldiers of the second class who have, upon written application to the appropriate military authority, been accepted by that authority for service in the first class; and the soldiers transferred to the first class in accordance with section 31 of the Defence Act comprise the first class. The soldiers who are members of the second class by virtue of Part IV of the Defence Act, the officers who are appointed or transferred to that class, and the soldiers who are enlisted, deemed to be enlisted, or re-engaged in accordance with Part IX of the Defence Act for service in that class are all included in the second class.
Each officer and soldier in the first class of the Reserve is required to report for duty at the location and for the duration determined by the Defence Board. They are also required to meet all training-related requirements. Subject to any general directives from the Defence Board, the requirements of the related section may be disregarded in whole or in part with regard to any unit of the first class of the Reserve, as well as with regard to any individual officer or soldier of the first class of the Reserve, by his commanding officer. Nothing stops a Reserve officer or soldier from participating in optional training in addition to any mandated training.
The first class of the Reserve, or as many officers and soldiers of that class as the Board deems necessary, may be called out on temporary duty by the Defence Board when needed. Under section 203, officers and soldiers who are called out for duty are not required to serve for more than ninety days at a time. Because the worker is a Reserve member who is called out in accordance with the section, no employer may fire or give notice of termination to any worker. When an employer violates, they are guilty of a crime and face a maximum fine of \$5,000, a maximum sentence of two (2) years in jail, or both. This applies even in cases of summary conviction.
The Governor-General may, on the advice of the Prime Minister, by proclamation order that the Reserve, or any class thereof, be called out on permanent service in the event of a state of war, insurrection, hostilities, or public emergency; the Defence Board will then take appropriate action. When called out on permanent duty, every Reserve officer and soldier is eligible to stay on permanent duty until told otherwise. Every officer and soldier belonging to such a class, as the case may be, to the part of any class so called out, shall attend in person at the designated location whenever the whole or any part of the first class of the Reserve is called out on temporary or permanent service; or whenever the whole or any part of the second class of the Reserve is called out on permanent service. The Defence Board shall cause every officer or soldier subject to such call-out to be served with a notice requiring him to attend at the time and place specified in the notice in the event that the first class of the Reserve is called out on temporary service or the Reserve is called out on permanent service.
An officer of the Antigua and Barbuda Defence Force may file a summarily complaint against a person who willfully takes away pawns, wrongfully destroys or damages, carelessly loses anything issued to him as an officer or soldier of the Reserve, or willfully refuses or fails to deliver up anything issued to him as an officer or soldier as a debt owed to the Crown. This applies even if the amount exceeds the normal monetary limit on a magistrate\'s jurisdiction.
A Reserve soldier may be released at any point during the duration of their service in the Reserve by the appropriate military authority under the prescribed conditions.
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## Enlistment and terms of service {#enlistment_and_terms_of_service}
A recruiting officer will not enlist anyone in the Force unless they are satisfied that the potential recruit has received, comprehended, and wishes to be enlisted after receiving a notice in the prescribed form from anyone who wants to join the regular Force. A recruiting officer is not allowed to enlist a minor under the age of eighteen into the regular force unless written consent has been obtained from at least one parent, from any parent who may have parental rights and powers over the minor, from any person whose whereabouts are known or can be determined with reasonable effort, or from any person who is in fact or legally responsible for the minor. For the purposes of the Defence Act, an individual who is willing to enlist will be considered to have reached, or not reached, the age of eighteen if the recruiting officer is satisfied---either through the production of a certified copy of an entry in the register of births, or by any other evidence that seems sufficient to them. The period of time that an individual may enlist in the regular force is as follows: in the case of an individual who is 18 years of age or older at the time of enlistment, a term of colour service that does not exceed 12 years as prescribed; in this case, the term of service in the Reserve will apply to the portion of the term that is prescribed as a term of colour service, and the remaining portion will apply to a term of service. In the case of an individual who is younger at the time of enlistment, the period of time that is prescribed will begin on the date that the individual reaches the age of eighteen years or a term not to exceed 12 years, as specified, starting on the day he reaches that age and consisting of the portion of it that is prescribed as a term of colour service and the remaining portion as a term in the reserve.
Any soldier of good character who has served their full term of colour service or who will be serving in the Reserve in two years may, with permission from the appropriate military authority, re-engage for an additional period of colour service and Reserve duty as prescribed; however, the additional period of colour service, when combined with the original period of colour service, may not exceed a total continuous period of 22 years colour service from the date of the soldier\'s original attestation or the date he became eighteen years old, whichever comes first. Any soldier who has completed 22 years of colour service may, if he so chooses and with the consent of the appropriate military authority, continue to serve in all capacities as if his colour service term had not yet expired. However, on the date that he notifies his commanding officer that he wishes to be discharged, he may be eligible for discharge at the end of the three-month period. Any soldier whose term of colour service expires during a public emergency, war, insurrection, hostilities, or other exigency of duty may be kept in the Force and have their service extended for an additional period of time as directed by the Defence Board and the appropriate military authority.
Every regular force soldier who is eligible for discharge will be released as soon as possible, subject to the Defence Act. However, until they are released, they are subject to military law as stipulated by the Act. When a regular force soldier is serving outside of Antigua and Barbuda at the time of his discharge, he has two options: if he wants to be discharged in Antigua and Barbuda, he will be sent there at no cost as soon as possible, and he will be released either when he arrives in Antigua and Barbuda or, if he agrees to a delay in discharge, six months after arriving; else, he will be released where he is currently serving. Releasing a soldier from the regular force requires authorization from the appropriate military authority, unless they are being released in accordance with a court-martial sentence. Upon their release from active duty, all regular force soldiers will receive a certificate of discharge that includes the necessary information. Every regular Force soldier who is scheduled to be transferred to the Reserve may do so in accordance with the Act, but they will remain subject to military law until they are transferred. When a regular Force soldier serving outside of Antigua and Barbuda is scheduled to be transferred to the Reserve, he will be sent there at no cost to him and will be transferred to the Reserve upon arrival, or within six months of his arrival if he agrees to a delay in transfer; he may, however, choose to be transferred to the Reserve without having to return to Antigua and Barbuda. When a regular Force soldier is being transferred to the Reserve, the appropriate military authority has the authority to immediately discharge him without providing a reason.
A court-martial sentence, a Defence Board order, or an order from an officer not lower than Major or a corresponding rank who has been given permission by the commanding officer may be the only ways that a warrant officer or non-commissioned officer\'s rank may be lowered. If a regular force warrant officer is demoted to the ranks, he or she may request to be discharged, barring a state of war, insurrection, hostilities, or public emergency. Anytime during the duration of the soldier\'s term of engagement, the competent military authority may release a regular force soldier for the prescribed reasons. Regular Force soldiers have the right to request their discharge at any point within three months of the date of their first attestation. If they do so, they will be released as soon as possible after paying a sum not to exceed EC\$500. However, they will still be subject to military law until their discharge under the Act. A soldier of the regular Force who was a member of a Commonwealth Force at any point within three months prior to the date of his first attestation is exempt from this.
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## Deployments
- In 1983, fourteen men of the Antigua and Barbuda Defence Force were deployed to Grenada during the Operation Urgent Fury.
- In 1990, twelve soldiers were sent to Trinidad and Tobago after a failed coup attempt by a radical group against the constitutionally elected government headed by Prime Minister A.N.R. Robinson.
- In 1995, members of the Antigua and Barbuda Defence Force were deployed in Haiti as a part of Operation Uphold Democracy
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Azerbaijan is a country in the Caucasus region, situated at the juncture of Eastern Europe and West Asia. Three physical features dominate Azerbaijan: the Caspian Sea, whose shoreline forms a natural boundary to the east; the Greater Caucasus mountain range to the north; and the extensive flatlands at the country\'s center. About the size of Portugal or the US state of Maine, Azerbaijan has a total land area of approximately 86,600 sqkm, less than 1% of the land area of the former Soviet Union. Of the three Transcaucasian states, Azerbaijan has the greatest land area. Special administrative subdivisions are the Nakhchivan Autonomous Republic, which is separated from the rest of Azerbaijan by a strip of Armenian territory, and the Nagorno-Karabakh Autonomous Region, entirely within Azerbaijan. The status of Nagorno-Karabakh is disputed by Armenia, but is internationally recognized as territory of Azerbaijan.
Located in the region of the southern Caucasus Mountains, Azerbaijan borders the Caspian Sea to the east, Georgia and Russia to the north, Iran to the south, and Armenia to the southwest and west. A small part of Nakhchivan also borders Turkey to the northwest. The capital of Azerbaijan is the ancient city of Baku, which has the largest and best harbor on the Caspian Sea and has long been the center of the republic\'s oil industry.
## Topography and drainage {#topography_and_drainage}
The elevation changes over a relatively short distance from lowlands to highlands; nearly half the country is considered mountainous. Notable physical features are the gently undulating hills of the subtropical southeastern coast, which are covered with tea plantations, orange groves, and lemon groves; numerous mud volcanoes and mineral springs in the ravines of Kobustan Mountain near Baku; and coastal terrain that lies as much as twenty-eight meters below sea level.
Except for its eastern Caspian shoreline and some areas bordering Georgia and Iran, Azerbaijan is ringed by mountains. To the northeast, bordering Russia\'s Dagestan Autonomous Republic, is the Greater Caucasus range; to the west, bordering Armenia, is the Lesser Caucasus range. To the extreme southeast, the Talysh Mountains form part of the border with Iran. The highest elevations occur in the Greater Caucasus, where Mount Bazardüzü rises 4,466 meters above sea level. Eight large rivers flow down from the Caucasus ranges into the central Kura-Aras Lowlands, alluvial flatlands and low delta areas along the seacoast designated by the Azerbaijani name for the Mtkvari River (Kura) and its main tributary, the Aras. The Mtkvari, the longest river in the Caucasus region, forms the delta and drains into the Caspian a short distance downstream from the confluence with the Aras. The Mingechaur Reservoir, with an area of 605 square kilometers that makes it the largest body of water in Azerbaijan, was formed by damming the Kura in western Azerbaijan. The waters of the reservoir provide hydroelectric power and irrigation of the Kura--Aras plain. Most of the country\'s rivers are not navigable. About 15% of the land in Azerbaijan is arable.
## Mountains
The country\'s highest peak, Bazardüzü, rises to 4,485 m at the Azerbaijan-Russia border.
## Climate
### Temperature
The climate varies from subtropical and humid in the southeast to subtropical and dry in central and eastern Azerbaijan, continental and humid in the mountains, and continental and dry in Nakhchivan. Baku, on the Caspian, enjoys mild weather that averages 4 °C in January and 25 °C in July.
### Precipitation
Physiographic conditions and different atmosphere circulations admit 8 types of air currents including continental, sea, arctic, tropical currents of air that formulates the climate of the Republic. The maximum annual precipitation falls in Lenkeran (1,600 to) and the minimum in Absheron (200 to). The maximum daily precipitation of 334 mm was observed at the Bilieser Station in 1955.
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## Environmental problems {#environmental_problems}
Air and water pollution are widespread and pose great challenges to economic development. Major sources of pollution include oil refineries and chemical and metallurgical industries, which in the early 1990s continued to operate as inefficiently as they had in the Soviet era. Air quality is extremely poor in Baku, the center of oil refining. Some reports have described Baku\'s air as the most polluted in the former Soviet Union, and other industrial centers suffer similar problems.
The Caspian Sea, including Baku Bay, has been polluted by oil leakages and the dumping of raw or inadequately treated sewage, reducing the yield of caviar and fish. In the Soviet period, Azerbaijan was pressed to use extremely heavy applications of pesticides to improve its output of scarce subtropical crops for the rest of the Soviet Union. The continued regular use of the pesticide DDT in the 1970s and 1980s was an egregious lapse, although that chemical was officially banned in the Soviet Union because of its toxicity to humans. Excessive application of pesticides and chemical fertilizers has caused extensive groundwater pollution and has been linked by Azerbaijani scientists to birth defects and illnesses. Rising water levels in the Caspian Sea, mainly caused by natural factors exacerbated by man-made structures, have reversed the decades-long drying trend and now threaten coastal areas; the average level rose 1.5 meters between 1978 and 1993. Because of the Nagorno-Karabakh conflict, large numbers of trees were felled, roads were built through pristine areas, and large expanses of agricultural land were occupied by military forces.
Like other former Soviet republics, Azerbaijan faces a gigantic environmental cleanup complicated by the economic uncertainties left in the wake of the Moscow-centered planning system. The Committee for the Protection of the Natural Environment is part of the Azerbaijani government, but in the early 1990s it was ineffective at targeting critical applications of limited funds, establishing pollution standards, or monitoring compliance with environmental regulations. Early in 1994, plans called for Azerbaijan to participate in the international Caspian Sea Forum, sponsored by the European Union (EU).
Natural hazards:
: Droughts and floods; some lowland areas threatened by rising levels of the Caspian Sea
Environment -- current issues:
: Local scientists consider the Abseron Yasaqligi (Apsheron Peninsula) (including Baky and Sumqayit) and the Caspian Sea to be the ecologically most devastated area in the world because of severe air, water, and soil pollution; soil pollution results from the use of DDT as a pesticide and also from toxic defoliants used in the production of cotton.
Environment -- international agreements
:\* Party to: Air Pollution, Biodiversity, Climate Change, Desertification, Endangered Species, Hazardous Wastes, Marine Dumping, Ozone Layer Protection, Ship Pollution, Wetlands
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## Area and boundaries {#area_and_boundaries}
Area:
:\* Total: 86,600 sqkm
:\*\**country rank in the world:* 113rd
:\* Land: 82,629 sqkm
:\* Water: 3,971 sqkm
:\* Note: Includes the exclave of Nakhchivan Autonomous Republic and the Nagorno-Karabakh region; the region\'s autonomy was abolished by Azerbaijani Supreme Soviet on November 26, 1991.
Area comparative
:\* Australia comparative: approximately `{{sfrac|2|7}}`{=mediawiki} larger than Tasmania
:\* Canada comparative: approximately `{{sfrac|1|5}}`{=mediawiki} larger than New Brunswick
:\* United Kingdom comparative: slightly larger than Scotland
:\* United States comparative: slightly smaller than Maine
:\* EU comparative: slightly smaller than Portugal
Land boundaries\
\* Total: 2,468 km\
\* Border countries:
:\*\*Armenia (with Azerbaijan-proper) 566 km
:\*\* Armenia (with Azerbaijan-Nakhchivan exclave) 221 km
:\*\* Georgia 428 km
:\*\*Iran (with Azerbaijan-proper) 432 km
:\*\*Iran (with Azerbaijan-Nakhchivan exclave) 700 km
:\*\*Russia 338 km
:\*\*Turkey 17 km
Coastline
:\*0 km
:\*\*Note: Azerbaijan borders the Caspian Sea. Its coastline with the Caspian Sea is 713 km
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Armenia is a landlocked country in the South Caucasus region of the Caucasus. The country is geographically located in West Asia, within the Armenian plateau. Armenia is bordered on the north and east by Georgia and Azerbaijan and on the south and west by Iran, Azerbaijan\'s exclave Nakhchivan, and Turkey.
The terrain is mostly mountainous, with fast flowing rivers and few forests. The climate is highland continental: hot summers and cold winters. The land rises to 4,090 m above sea-level at Mount Aragats.
## Physical environment {#physical_environment}
Armenia is located in the southern Caucasus, the region southwest of Russia between the Black Sea and the Caspian Sea. Modern Armenia occupies part of historical Armenia, whose ancient centers were in the valley of the Araks River and the region around Lake Van in Turkey. Armenia is bordered on the north by Georgia, on the east by Azerbaijan, on the south by Iran, and on the west by Turkey.
In Armenia forest cover is around 12% of the total land area, equivalent to 328,470 hectares (ha) of forest in 2020, down from 334,730 hectares (ha) in 1990. In 2020, naturally regenerating forest covered 310,000 hectares (ha) and planted forest covered 18,470 hectares (ha). Of the naturally regenerating forest 5% was reported to be primary forest (consisting of native tree species with no clearly visible indications of human activity) and around 0% of the forest area was found within protected areas. For the year 2015, 100% of the forest area was reported to be under public ownership.
## Topography and drainage {#topography_and_drainage}
`{{See also|List of rivers of Armenia|List of lakes of Armenia|Mountains of Armenia}}`{=mediawiki}
Twenty-five million years ago, a geological upheaval pushed up the Earth\'s crust to form the Armenian Plateau, creating the complex topography of modern Armenia. The Lesser Caucasus range extends through northern Armenia, runs southeast between Lake Sevan and Azerbaijan, then passes roughly along the Armenian-Azerbaijani border to Iran. Thus situated, the mountains make travel from north to south difficult. Geological turmoil continues in the form of devastating earthquakes, which have plagued Armenia. In December 1988, the second largest city in the republic, Leninakan (now Gyumri), was heavily damaged by a massive quake that killed more than 25,000 people.
About half of Armenia\'s area of approximately 29,743 km2 has an elevation of at least 2000 m, and only 3% of the country lies below 650 m. The lowest points are in the valleys of the Araks River and the Debed River in the far north, which have elevations of 380 and, respectively. Elevations in the Lesser Caucasus vary between 2640 and. To the southwest of the range is the Armenian Plateau, which slopes southwestward toward the Araks River on the Turkish border. The plateau is masked by intermediate mountain ranges and extinct volcanoes. The largest of these, Mount Aragats, 4090 m high, is also the highest point in Armenia. Most of the population lives in the western and northwestern parts of the country, where the two major cities, Yerevan and Gyumri, are located.
The valleys of the Debed and Akstafa rivers form the chief routes into Armenia from the north as they pass through the mountains. Lake Sevan, 72.5 km across at its widest point and 376 km long, is by far the largest lake. It lies 1900 m above sea level on the plateau and is 1279.18 km2 large. Other main lakes are: Arpi, 7.5 km2, Sev, 2 km2, Akna 0.8 km2. Terrain is most rugged in the extreme southeast, which is drained by the Bargushat River, and most moderate in the Araks River valley to the extreme southwest. Most of Armenia is drained by the Araks or its tributary, the Hrazdan, which flows from Lake Sevan. The Araks forms most of Armenia\'s border with Turkey and Iran, while the Zangezur Mountains form the border between Armenia\'s southern province of Syunik and Azerbaijan\'s adjacent Nakhchivan Autonomous Republic.
## Climate
Temperatures in Armenia generally depend upon elevation. Mountain formations block the moderating climatic influences of the Mediterranean Sea and the Black Sea, creating wide seasonal variations with cold snowy winters, and warm to hot summers. On the Armenian Plateau, the mean midwinter temperature is 0 °C to −15 °C, and the mean midsummer temperature is 15 °C to 30 °C. Average precipitation ranges from 250 mm per year in the lower Araks River valley to 800 mm at the highest altitudes. Despite the harshness of winter in most parts (with frosts reaching -40 °C and lower in Shirak region), the fertility of the plateau\'s volcanic soil made Armenia one of the world\'s earliest sites of agricultural activity.
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## Area and boundaries {#area_and_boundaries}
**Area**:\
*total:* 29,743 km^2^
: *country comparison to the world:* 143
*land:* 28,203 km^2^\
*water:* 1,540 km^2^
**Area comparative**
- Australia comparative: about one third (33%) the size of Tasmania
- Canada comparative: greater than half (56%) the size of Nova Scotia
- Turkey comparative: about a quarter (24%) smaller than the size of Konya Province
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The **politics of Armenia** take place in the framework of the parliamentary representative democratic republic of Armenia, whereby the president of Armenia is the head of state and the prime minister of Armenia the head of government, and of a multi-party system. Executive power is exercised by the president and the Government. Legislative power is vested in both the Government and Parliament.
## History
Armenia became independent from the Russian Empire on 28 May 1918 as the *Republic of Armenia*, later referred as First Republic of Armenia. About a month before its independence Armenia was part of short lived Transcaucasian Democratic Federative Republic. Suffering heavy losses during the Turkish invasion of Armenia and after the Soviet invasion of Armenia, the government of the First Republic resigned on 2 December 1920. Soviet Russia reinstalled its control over the country, which later became part of the Transcaucasian SFSR. The TSFSR was dissolved in 1936 and Armenia became a constituent republic of the Soviet Union known as the Armenian SSR, later also referred as the *Second Republic of Armenia*.
During the dissolution of the Soviet Union the population of Armenia voted overwhelmingly for independence following the 1991 Armenian independence referendum. It was followed by a presidential election in October 1991 that gave 83% of the votes to Levon Ter-Petrosyan. Earlier in 1990, when the National Democratic Union party defeated the Armenian Communist Party, he was elected Chairman of the Supreme Council of Armenia. Ter-Petrosyan was re-elected in 1996. Following public discontent and demonstrations against his policies on Nagorno-Karabakh, the President resigned in January 1998 and was replaced by Prime Minister Robert Kocharyan, who was elected as second President in March 1998. Following the assassination of Prime Minister Vazgen Sargsyan, parliament Speaker Karen Demirchyan and six other officials during parliament seating on 27 October 1999, a period of political instability ensued during which an opposition headed by elements of the former Armenian National Movement government attempted unsuccessfully to force Kocharyan to resign. In May 2000, Andranik Margaryan replaced Aram Sargsyan (a brother of assassinated Vazgen Sargsyan) as Prime Minister.
Kocharyan\'s re-election as president in 2003 was followed by widespread allegations of ballot-rigging. He went on to propose controversial constitutional amendments on the role of parliament. These were rejected in a referendum the following May. Concurrent parliamentary elections left Kocharyan\'s party in a very powerful position in the parliament. There were mounting calls for the President\'s resignation in early 2004 with thousands of demonstrators taking to the streets in support of demands for a referendum of confidence in him.
The Government of Armenia\'s stated aim is to build a Western-style parliamentary democracy. However, international observers have questioned the fairness of Armenia\'s parliamentary and presidential elections and constitutional referendum between 1995 and 2018, citing polling deficiencies, lack of cooperation by the Electoral Commission, and poor maintenance of electoral lists and polling places. Armenia is considered one of the most democratic nations of the Commonwealth of Independent States and the most democratic in the Caucasus region.
The observance of human rights in Armenia is uneven and is marked by shortcomings. Police brutality allegedly still goes largely unreported, while observers note that defendants are often beaten to extract confessions and are denied visits from relatives and lawyers. Public demonstrations usually take place without government interference, though one rally in November 2000 by an opposition party was followed by the arrest and imprisonment for a month of its organizer. Freedom of religion is not always protected under existing law. Nontraditional churches, especially the Jehovah\'s Witnesses, have been subjected to harassment, sometimes violently. All churches apart from the Armenian Apostolic Church must register with the government, and proselytizing was forbidden by law, though since 1997 the government has pursued more moderate policies. The government\'s policy toward conscientious objection is in transition, as part of Armenia\'s accession to the Council of Europe.
Armenia boasts a good record on the protection of national minorities, for whose representatives (Assyrians, Kurds, Russians and Yazidis) four seats are reserved in the National Assembly. The government does not restrict internal or international travel.
### Transition to a parliamentary republic {#transition_to_a_parliamentary_republic}
In December 2015, the country held a referendum which approved transformation of Armenia from a semi-presidential to a parliamentary republic.
As a result, the president was stripped of his veto faculty and the presidency was downgraded to a figurehead position elected by parliament every seven years. The president is not allowed to be a member of any political party and re-election is forbidden.
Skeptics saw the constitutional reform as an attempt of third president Serzh Sargsyan to remain in control by becoming Prime Minister after fulfilling his second presidential term in 2018.
In March 2018, the Armenian parliament elected Armen Sarkissian as the new President of Armenia. The controversial constitutional reform to reduce presidential power was implemented, while the authority of the prime minister was strengthened. In May 2018, parliament elected opposition leader Nikol Pashinyan as the new prime minister. His predecessor Serzh Sargsyan resigned two weeks earlier following widespread anti-government demonstrations.
In June 2021, early parliamentary elections were held. Nikol Pashinyan\'s Civil Contract party won 71 seats, while 29 went to the Armenia Alliance headed by former President Robert Kocharyan. The I Have Honor Alliance, which formed around another former president, Serzh Sargsyan, won seven seats. After the election, Armenia\'s acting Prime Minister Nikol Pashinyan was officially appointed to the post of prime minister by the country\'s president Armen Sarkissian. In January 2022, Armenian President Armen Sarkissian resigned from office, stating that the constitution does no longer give the president sufficient powers or influence. On 3 March 2022, Vahagn Khachaturyan was elected as the fifth president of Armenia in the second round of parliamentary vote.
## Government
\|President \|Vahagn Khachaturyan \|Independent \|13 March 2022 \|- \|Prime Minister \|Nikol Pashinyan \|Civil Contract \|8 May 2018 \|}
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## Legislative branch {#legislative_branch}
The unicameral National Assembly of Armenia (*Azgayin Zhoghov*) is the legislative branch of the government of Armenia.
Before the 2015 Armenian constitutional referendum, it was initially made of 131 members, elected for five-year terms: 41 members in single-seat constituencies and 90 by proportional representation. The proportional-representation seats in the National Assembly are assigned on a party-list basis among those parties that receive at least 5% of the total of the number of the votes.
Following the 2015 referendum, the number of MPs was reduced from the original 131 members to 101 and single-seat constituencies were removed.
## Political parties and elections {#political_parties_and_elections}
As of January 2025, there are 123 political parties registered in Armenia. The electoral threshold is currently set at 5% for single parties and 7% for blocs.
### Latest national elections {#latest_national_elections}
### Latest presidential elections {#latest_presidential_elections}
## Independent agencies {#independent_agencies}
Independent of three traditional branches are the following independent agencies, each with separate powers and responsibilities:
- the Constitutional Court of Armenia
- the Central Electoral Commission of Armenia
- the Human Rights Defender of Armenia
- the Central Bank of Armenia
- the Prosecutor General of Armenia
- the Audit Chamber of Armenia
## Corruption
Transparency International\'s 2024 Corruption Perceptions Index ranked Armenia 60th out of 180 in the world with 47 points. This has pushed the country up from being ranked at 60th in 2020 and 58th in 2021. According to Transparency International, Armenia has improved significantly on the Corruption Perception Index since 2012, especially since the 2018 revolution, the country has taken steps to counter corruption. Further mentioning that \"Armenia has taken a gradual approach to reform, resulting in steady and positive improvements in anti-corruption. However, safeguarding judicial independence and ensuring checks and balances remain critical first steps in its anti-corruption efforts. The effectiveness of those efforts is additionally challenged by the current political and economic crisis as a result of the recent Nagorno Karabakh conflict and the subsequent protests against Prime Minister Nikol Pashinyan over a ceasefire deal\".
In 2008, Transparency International reduced its Corruption Perceptions Index for Armenia from 3.0 in 2007 to 2.9 out of 10 (a lower score means more perceived corruption); Armenia slipped from 99th place in 2007 to 109th out of 180 countries surveyed (on a par with Argentina, Belize, Moldova, Solomon Islands, and Vanuatu)
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This article considers **transport in Armenia**.
## Railways
### Total
in common carrier service; does not include industrial lines
### Broad gauge {#broad_gauge}
850 km of `{{RailGauge|1520mm}}`{=mediawiki} gauge (850 km electrified) (1995) There is no service south of Yerevan.
City with metro system: Yerevan
### International links {#international_links}
- Azerbaijan - closed - same gauge
- Georgia - yes - same gauge
- Iran - via Azerbaijan - closed - break of gauge - `{{RailGauge|1520mm}}`{=mediawiki}/`{{RailGauge|sg}}`{=mediawiki}
- Turkey - closed - break of gauge -`{{RailGauge|1520mm}}`{=mediawiki}/`{{RailGauge|sg}}`{=mediawiki}
Most of the cross-border lines are currently closed due to political problems. However, there are daily inbound and outbound trains connecting Tbilisi and Yerevan. Departing from Yerevan railway station trains connect to both Tbilisi and Batumi. From neighboring Georgia, trains depart to Yerevan from Tbilisi railway station. Within Armenia, new electric trains connect passengers from Yerevan to Armenia\'s second-largest city of Gyumri. The new trains run four times a day and the journey takes approximately two hours.
There is also discussion to establish a rail link between Yerevan and Tehran. Armenia is pursuing funding from the Asian Development Bank to launch the construction of this infrastructure project. The completion of the project could establish a major commodities transit corridor and would serve as the shortest transportation route between Europe and the Persian Gulf. In June 2019, Iranian president Hassan Rouhani backed this project and stated that "we want the Persian Gulf and the Gulf of Oman to be connected to the Black Sea, and one of the ways to make this happen is through Iran, Armenia and Georgia."
### Metros
The capital city of Armenia, Yerevan, is serviced by the Yerevan Metro. The system was launched in 1981, and like most former Soviet Metros, its stations are very deep (20--70 meters underground) and intricately decorated with national motifs. The metro runs on a 13.4 kilometers (8.3 mi) line and currently serves 10 active stations. Trains run every five minutes from 6:30 a.m. until 11 p.m. local AMT time. As of 2017, the annual ridership of the metro is 16.2 million passengers. Free Wi-Fi is available at all stations and some trains.
### Trams
Yerevan tram (Armenian: *Երևանի տրամվայ*) was a tram system previously operating in Yerevan, the capital of Armenia. It was opened on 29 September 1906 in the form of a city wagonway. In the second half of the 20th century, the tram system had up to 12 routes, which were served by 3 depots. Trams were operated until 21 January 2004.
#### History
The only city in Armenia where a tram ever existed was Yerevan. On 29 September 1906, the Yerevan horse wagonway was opened. This type of narrow-gauge wagonway existed until August 1918, when the tram was destroyed during World War I.
On 12 January 1933, a wide-gauge electric tram was launched. The number of tram cars increased by 25% on average every five years, in 1933 it was 16, then in 1945 there were 77 cars, and in 1965 - 222 cars. Two types of trams were used, the 71-605 and the RVZ-6M2, both were Soviet made. Since the cost of the tram was 2.4% higher than that of buses, as well as due to expensive electricity and problems arising when the tram crossed the Great Bridge of Hrazdan in Yerevan, route #7 (Erebuni - Zeytun) was closed on 20 June 2003.
Most of the tracks have been removed and the trams have been turned into scrap. The tram depot is used by various private enterprises, and the substation currently serves the Yerevan trolleybus.
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## Buses
### International connections {#international_connections}
Land borders are open with both Georgia and Iran. Yerevan Central Bus Station, also known as Kilikia Bus Station is the main bus terminal in Yerevan with buses connecting to both internal and international destinations. There are daily bus connections between Yerevan and Tbilisi and Yerevan and Tehran. Approximately three times daily, buses depart from Yerevan Central Bus Station to Stepanakert, the capital of the partially recognized state of Artsakh. There are also scheduled bus routes which connect Yerevan with Kyiv, Moscow, Saint Petersburg as well as several other cities across Russia. It is also possible to connect to Chișinău Moldova, Minsk Belarus and other cities in Eastern Europe from Yerevan through connecting bus routes via Georgia and Ukraine. In addition, there is a once a week bus service to Istanbul via Georgia. In June 2019, a new bus route from Baghdad to Yerevan via Iran began.
### Local connections {#local_connections}
The Armenian bus network connects all major cities, towns, and villages throughout the country. In larger cities and towns such as Yerevan, Gyumri, Vanadzor and Armavir, bus stations are equipped with a waiting room and a ticket office, in other towns bus stations may not have shelters. Most of the routes are operated by GAZelle minivans with a capacity of 15 passengers, some routes are operated by soviet bus producer LiAZ (Russia). Yerevan itself has a large integrated bus network, with a newly acquired bus fleet, passengers are able to connect from one end of the city to the other. Wi-Fi is available on most city buses. Despite this, buses often have difficulty meeting the demand for capacity, mainly in Yerevan, where vehicles are typically overcrowded. There are no night services between 11 p.m. and 6 a.m. There is no ticket system in the country, passengers pay in cash to drivers. Passengers on the national bus network pay before boarding, passengers on the Yerevan bus network pay after the ride, while leaving the vehicle. Timetables and fares are published on [Transport for Armenia](https://t-armenia.com/).
From Yeritasardakan metro station in downtown Yerevan, travelers can take the 201 airport shuttle, which goes directly to Zvartnots International Airport, which takes approximately 20 minutes from the city center.
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## Roadways
*Main article: Roads in Armenia* `{{See also|Road signs in Armenia}}`{=mediawiki} Since independence, Armenia has been developing its internal highway network. The \"North-South Road Corridor Investment Program\" is a major infrastructure project which aims at connecting the southern border of Armenia with its northern by means of a 556 km-long Meghri-Yerevan-Bavra highway. It is a major US\$1.5 billion infrastructure project funded by the Asian Development Bank, European Investment Bank and the Eurasian Development Bank. When completed, the highway will provide access to European countries via the Black Sea. It could also eventually interconnect the Black Sea ports of Georgia with the major ports of Iran, thus positioning Armenia in a strategic transport corridor between Europe and Asia. Armenia is pursuing further loans from China as part of the Belt and Road Initiative to complete the north--south highway.
Armenia connects to European road networks via the International E-road network through various routes such as; European route E117, European route E691, European route E001 and European route E60. Armenia also connects to the Asian Highway Network through routes AH81, AH82 and AH83.
The number of insured registered cars in Armenia has grown from 390,457 in 2011 to 457,878 in 2015.
### Total {#total_1}
8,800 km\
World Ranking: 112
### Paved
8,800 km (including 1,561 km of expressways)
### Unpaved
0 km (2006 est.)
## Pipelines
Natural gas 3,838 km (2017)
## Ports and harbors {#ports_and_harbors}
Cargo shipments to landlocked Armenia are routed through ports in Georgia and Turkey.
## Airports
`{{See also| List of airports in Armenia| List of the busiest airports in Armenia| List of airlines of Armenia}}`{=mediawiki}
Air transportation in Armenia is the most convenient and comfortable means of getting into the country. There are large international airports that accept both external and domestic flights throughout the Republic. As of 2020, 11 airports operate in Armenia. However, only Yerevan\'s Zvartnots International Airport and Gyumri\'s Shirak Airport are in use for commercial aviation. There are three additional civil airports currently under reconstruction in Armenia, including Syunik Airport, Stepanavan Airport, and Goris Airport. The leading Armenian airlines in operation are Armenia Aircompany and Armenia Airways.
There are plenty of air connections between Yerevan and other regional cities, including Athens, Barcelona, Beirut, Berlin, Bucharest, Brussels, Damascus, Doha, Dubai, Istanbul, Kyiv, Kuwait City, London, Milan, Minsk, Moscow, Paris, Prague, Riga, Rome, Tehran, Tel-Aviv, Tbilisi, Vienna, Venice, and Warsaw, as well as daily connections to most major cities within the CIS region. Statistics show that the number of tourists arriving in the country by air transportation increases yearly. In 2018, passenger flow at the two main airports of Armenia reached a record high of 2,856,673 million people. In December 2019, yearly passenger flow exceeded 3,000,000 million people for the first time in Armenia\'s history.
In November 2019, the creation of a Free Route Airspace (FRA) between Armenia and Georgia was announced. The process has been carried out through the joint efforts of the General Department of Civil Aviation of Armenia, the Georgian Civil Aviation Administration and Eurocontrol. The Free Route Airspace between the two South Caucasus countries will increase flights to around 40,000 annually.
Country comparison to the world: 153
### Airports - with paved runways {#airports___with_paved_runways}
Total: 10
: Over 3,047 m (9,900 feet): 2
: 1,524 to 2,437 m (7,920 feet): 2
: 914 to 1,523 m (4,950 feet): 4
: Under 914 m: 2 (as of 2008)
### Airports - with unpaved runways {#airports___with_unpaved_runways}
Total: 1
: 1,524 to 2,437 m: 0
: 914 to 1,523 m: 1
: under 914 m: 0 (as of 2008)
## Heliports
Armenia maintains a number of both military and civilian heliports. The main military heliport is located on the premises of Erebuni Airport in Yerevan. Meanwhile, the company Armenian Helicopters, based at Zvartnots Airport in Yerevan, offers charter flights within Armenia and to certain neighboring countries, including Georgia, Russia, and Turkey. Helicopter services are delivered with the US-made Robinson R66 and the European AIRBUS EC130T2 choppers. Flights can be carried out as scheduled or on individual routes.
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## Aerial tramways {#aerial_tramways}
The Wings of Tatev is currently the world\'s longest reversible aerial tramway which holds the record for longest non-stop double-track cable car and is located in the town of Halidzor.
In October 2019, it was announced that investors were interested in creating an aerial tramway in the capital, Yerevan
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**Demographics of American Samoa** include population density, ethnicity, education level, health of the populace, economic status, religious affiliations and other aspects. American Samoa is an unincorporated territory of the United States located in the South Pacific Ocean.
## Population
The statistics from 1900 to 1950 and every decennial census are from the U.S. Census Bureau. There was no census taken in 1910, but a special census taken in 1912. Beginning with the 1930 Census, Swain Island is included in the population count for American Samoa. The remaining statistics are from the World Factbook, unless otherwise indicated.
- Approximately 55,212, but the Factbook states 49,437 (2020 estimate). About 65% of the population are U.S. nationals, of whom at least 10% are U.S. citizens. Of the foreign-born population, 81% are from Samoa, 9% are from other parts of Oceania, and 9% are from Asia.
## Structure of the population {#structure_of_the_population}
Age Group Male Female Total \%
----------- -------- -------- -------- ---------
Total 28 164 27 355 55 519 100
0--4 3 417 3 194 6 611 11.91
5--9 3 470 3 065 6 535 11.77
10--14 3 214 3 065 6 279 11.31
15--19 3 218 3 078 6 296 11.34
20--24 1 944 1 947 3 891 7.01
25--29 1 670 1 654 3 324 5.99
30--34 1 726 1 784 3 510 6.32
35--39 1 845 1 764 3 609 6.50
40--44 1 793 1 807 3 600 6.48
45--49 1 673 1 716 3 389 6.10
50--54 1 335 1 344 2 679 4.83
55--59 1 011 1 038 2 049 3.69
60--64 755 725 1 480 2.67
65--69 500 460 960 1.73
70--74 321 333 654 1.18
75--79 155 182 337 0.61
80--84 76 130 206 0.37
85+ 41 69 110 0.20
Age group Male Female Total Percent
0--14 10 101 9 324 19 425 34.99
15--64 16 970 16 857 33 827 60.93
65+ 1 093 1 174 2 267 4.08
## Vital statistics {#vital_statistics}
### Registered births and deaths {#registered_births_and_deaths}
Year Population Live births Deaths Natural increase Crude birth rate Crude death rate Rate of natural increase Total Fertility Rate
------ ------------ ------------- -------- ------------------ ------------------ ------------------ -------------------------- ----------------------
2001 59,400 1,655 239 1,416 27.9 4.0 23.9 3.50
2002 60,800 1,629 295 1,334 26.8 4.9 21.9 3.86
2003 62,600 1,608 257 1,351 25.7 4.1 21.6 3.85
2004 64,100 1,713 289 1,424 26.7 4.5 22.2 4.14
2005 65,500 1,720 279 1,441 26.3 4.3 22.0 3.92
2006 66,900 1,442 267 1,175 21.6 4.0 17.6 3.52
2007 68,200 1,293 251 1,042 19.0 3.7 15.3 2.87
2008 69,200 1,338 240 1,098 19.3 3.5 15.8 2.91
2009 70,100 1,375 324 1,051 19.6 4.6 15.0 2.86
2010 67,380 1,279 247 1,032 19.0 3.7 15.3 3.11
2011 64,292 1,287 283 1,004 20.0 4.4 15.6 3.10
2012 63,596 1,175 282 893 18.5 4.4 14.1 2.85
2013 62,610 1,161 270 891 18.5 4.3 14.2 2.61
2014 61,811 1,084 259 825 17.5 4.2 13.3 2.60
2015 60,863 1,096 314 782 18.0 5.2 12.8 2.55
2016 60,200 1,013 280 733 16.8 4.7 12.1 2.69
2017 60,300 1,001 310 691 16.6 5.1 11.5 2.59
2018 59,600 921 298 623 15.5 5.0 10.5
2019 58,500 840 278 562 14.4 4.8 9.6
2020 49,841 734 322 412 14.7 6.5 8.2
2021 51,561 706 331 375 13.7 6.4 7.3
2022 51,269 706 399 307 13.8 7.8 6.0
2023 737 356 381 13.8 6.7 7.1
: 21st-century demography of American Samoa
## Ethnic groups {#ethnic_groups}
- Pacific Islander 92.6% (includes Samoan 88.9%, Tongan 2.9%, other 0.8%)
- Asian 3.6% (includes Filipino 2.2%, other 1.4%)
- Mixed 2.7%
- Other 1.2% (2010 est.)
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## Languages
Native languages include:
- Samoan 88.6%
- English 3.9%
- Tongan 2.7%
- Other Pacific islander 3%
- Other 1.8% (2010 est.)
English proficiency is very high.
## Religion
- Christian 98.3%
- Other 1%
- Unaffiliated 0.7% (2010 est.)
Major Christian denominations on the island include the Congregational Christian Church in American Samoa, the Catholic Church, the Church of Jesus Christ of Latter-day Saints and the Methodist Church of Samoa. Collectively, these churches account for the vast majority of the population.
J. Gordon Melton in his book claims that the Methodists, Congregationalists with the London Missionary Society, and Catholics led the first Christian missions to the islands. Other denominations arrived later, beginning in 1895 with the Seventh-day Adventists, various Pentecostals (including the Assemblies of God), Church of the Nazarene, Jehovah\'s Witnesses, and the Church of Jesus Christ of Latter-day Saints.
The World Factbook 2010 estimate shows the religious affiliations of American Samoa as 98.3% Christian, other 1%, unaffiliated 0.7%. World Christian Database 2010 estimate shows the religious affiliations of American Samoa as 98.3% Christian, 0.7% agnostic, 0.4% Chinese Universalist, 0.3% Buddhist, and 0.3% Baháʼí.
According to Pew Research Center, 98.3% of the total population is Christian. Among Christians, 59.5% are Protestant, 19.7% are Catholic and 19.2% are other Christians. A major Protestant church on the island, gathering a substantial part of the local Protestant population, is the Congregational Christian Church in American Samoa, a Reformed denomination in the Congregationalist tradition. `{{As of|2017|8}}`{=mediawiki}, The Church of Jesus Christ of Latter-day Saints website claims membership of 16,180 or one-quarter of the whole population, with 41 congregations, and 4 family history centers in American Samoa. The Jehovah\'s Witnesses claim 210 \"ministers of the word\" and 3 congregations
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**Politics of American Samoa** takes place in a framework of a presidential representative democratic dependency, whereby the governor is the head of government, and of a pluriform multi-party system. American Samoa is an unincorporated and unorganized territory of the United States, administered by the Office of Insular Affairs, U.S. Department of the Interior. Its constitution was ratified in 1966 and came into effect in 1967. Executive power is discharged by the governor and the lieutenant governor. Legislative power is vested in the two chambers of the legislature. The party system is based on the United States party system. The judiciary is independent of the executive and the legislature.
There is also the traditional village politics of the Samoan Islands, the *\[\[fa\'amatai\]\]* and the *\[\[faʻa Sāmoa\]\]*, which continues in American Samoa and in independent Samoa, and which interacts across these current boundaries. The *faʻa Sāmoa* is the language and customs, and the *fa\'amatai* the protocols of the *\[\[fono\]\]* (council) and the chiefly system. The *italic=no* and the *fono* take place at all levels of the Samoan body politic, from the family, to the village, to the region, to national matters. The *matai* (chiefs) are elected by consensus within the *fono* of the extended family and village(s) concerned. The *matai* and the *fono* (which is itself made of *matai*) decide on distribution of family exchanges and tenancy of communal lands. The majority of lands in American Samoa and independent Samoa are communal. A *matai* can represent a small family group or a great extended family that reaches across islands, and to both American Samoa and independent Samoa.
## Government
The government of American Samoa is defined under the Constitution of American Samoa. As an unincorporated territory, the Ratification Act of 1929 vested all civil, judicial, and military powers in the president, who in turn delegated authority to the secretary of the interior in `{{Executive Order|10264}}`{=mediawiki}. The secretary promulgated the Constitution of American Samoa which was approved by a constitutional convention of the people of American Samoa and a majority of the voters of American Samoa voting at the 1966 election, and came into effect in 1967.
The governor of American Samoa is the head of government and along with the lieutenant governor of American Samoa is elected on the same ticket by popular vote for four-year terms.
The legislative power is vested in the American Samoa Fono, which has two chambers. The House of Representatives has 21 members serving two-year terms, being 20 representatives popularly elected from various districts and one delegate from Swains Island elected in a public meeting. The Senate has 18 members, elected for four-year terms by and from the chiefs of the islands.
The judiciary of American Samoa is composed of the High Court of American Samoa, a District Court, and village courts. The High Court is led by a chief justice and an associate justice, appointed by the secretary of the interior. Other judges are appointed by the governor upon the recommendation of the chief justice and confirmed by the Senate
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`{{Modulation techniques}}`{=mediawiki}
**Amplitude modulation** (**AM**) is a signal modulation technique used in electronic communication, most commonly for transmitting messages with a radio wave. In amplitude modulation, the instantaneous amplitude of the wave is varied in proportion to that of the message signal, such as an audio signal. This technique contrasts with angle modulation, in which either the frequency of the carrier wave is varied, as in frequency modulation, or its phase, as in phase modulation.
AM was the earliest modulation method used for transmitting audio in radio broadcasting. It was developed during the first quarter of the 20th century beginning with Roberto Landell de Moura and Reginald Fessenden\'s radiotelephone experiments in 1900. This original form of AM is sometimes called **double-sideband amplitude modulation** (**DSBAM**), because the standard method produces sidebands on either side of the carrier frequency. Single-sideband modulation uses bandpass filters to eliminate one of the sidebands and possibly the carrier signal, which improves the ratio of message power to total transmission power, reduces power handling requirements of line repeaters, and permits better bandwidth utilization of the transmission medium.
AM remains in use in many forms of communication in addition to AM broadcasting: shortwave radio, amateur radio, two-way radios, VHF aircraft radio, citizens band radio, and in computer modems in the form of quadrature amplitude modulation (QAM).
## Foundation
In electronics and telecommunications, modulation is the variation of a property of a continuous wave carrier signal according to an information-bearing signal, such as an audio signal which represents sound, or a video signal which represents images. In this sense, the carrier wave, which has a much higher frequency than the message signal, *carries* the information. At the receiving station, the message signal is extracted from the modulated carrier by demodulation.
In general form, a modulation process of a sinusoidal carrier wave may be described by the following equation:
$$m(t) = A(t) \cdot \cos(\omega t + \phi(t))\,$$.
*A(t)* represents the time-varying amplitude of the sinusoidal carrier wave and the cosine-term is the carrier at its angular frequency $\omega$, and the instantaneous phase deviation $\phi(t)$. This description directly provides the two major groups of modulation, amplitude modulation and angle modulation. In angle modulation, the term *A*(*t*) is constant and the second term of the equation has a functional relationship to the modulating message signal. Angle modulation provides two methods of modulation, frequency modulation and phase modulation.
In amplitude modulation, the angle term is held constant and the first term, *A*(*t*), of the equation has a functional relationship to the modulating message signal.
The modulating message signal may be analog in nature, or it may be a digital signal, in which case the technique is generally called amplitude-shift keying.
For example, in AM radio communication, a continuous wave radio-frequency signal has its amplitude modulated by an audio waveform before transmission. The message signal determines the *envelope* of the transmitted waveform. In the frequency domain, amplitude modulation produces a signal with power concentrated at the carrier frequency and two adjacent sidebands. Each sideband is equal in bandwidth to that of the modulating signal, and is a mirror image of the other. Standard AM is thus sometimes called \"double-sideband amplitude modulation\" (DSBAM).
A disadvantage of all amplitude modulation techniques, not only standard AM, is that the receiver amplifies and detects noise and electromagnetic interference in equal proportion to the signal. Increasing the received signal-to-noise ratio, say, by a factor of 10 (a 10 decibel improvement), thus would require increasing the transmitter power by a factor of 10. This is in contrast to frequency modulation (FM) and digital radio where the effect of such noise following demodulation is strongly reduced so long as the received signal is well above the threshold for reception. For this reason AM broadcast is not favored for music and high fidelity broadcasting, but rather for voice communications and broadcasts (sports, news, talk radio etc.).
AM is inefficient in power usage, as at least two-thirds of the transmitting power is concentrated in the carrier signal. The carrier signal contains none of the transmitted information (voice, video, data, etc.). However, its presence provides a simple means of demodulation using envelope detection, providing a frequency and phase reference for extracting the message signal from the sidebands. In some modulation systems based on AM, a lower transmitter power is required through partial or total elimination of the carrier component, however receivers for these signals are more complex because they must provide a precise carrier frequency reference signal (usually as shifted to the intermediate frequency) from a greatly reduced \"pilot\" carrier (in reduced-carrier transmission or DSB-RC) to use in the demodulation process. Even with the carrier eliminated in double-sideband suppressed-carrier transmission, carrier regeneration is possible using a Costas phase-locked loop. This does not work for single-sideband suppressed-carrier transmission (SSB-SC), leading to the characteristic \"Donald Duck\" sound from such receivers when slightly detuned. Single-sideband AM is nevertheless used widely in amateur radio and other voice communications because it has power and bandwidth efficiency (cutting the RF bandwidth in half compared to standard AM). On the other hand, in medium wave and short wave broadcasting, standard AM with the full carrier allows for reception using inexpensive receivers. The broadcaster absorbs the extra power cost to greatly increase potential audience.
### Shift keying {#shift_keying}
A simple form of digital amplitude modulation which can be used for transmitting binary data is on--off keying, the simplest form of amplitude-shift keying, in which ones and zeros are represented by the presence or absence of a carrier. On--off keying is likewise used by radio amateurs to transmit Morse code where it is known as continuous wave (CW) operation, even though the transmission is not strictly \"continuous\". A more complex form of AM, quadrature amplitude modulation is now more commonly used with digital data, while making more efficient use of the available bandwidth.
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## Foundation
### Analog telephony {#analog_telephony}
A simple form of amplitude modulation is the transmission of speech signals from a traditional analog telephone set using a common battery local loop. The direct current provided by the central office battery is a carrier with a frequency of 0 Hz. It is modulated by a microphone (*transmitter*) in the telephone set according to the acoustic signal from the speaker. The result is a varying amplitude direct current, whose AC-component is the speech signal extracted at the central office for transmission to another subscriber.
### Amplitude reference {#amplitude_reference}
An additional function provided by the carrier in standard AM, but which is lost in either single or double-sideband suppressed-carrier transmission, is that it provides an amplitude reference. In the receiver, the automatic gain control (AGC) responds to the carrier so that the reproduced audio level stays in a fixed proportion to the original modulation. On the other hand, with suppressed-carrier transmissions there is *no* transmitted power during pauses in the modulation, so the AGC must respond to peaks of the transmitted power during peaks in the modulation. This typically involves a so-called *fast attack, slow decay* circuit which holds the AGC level for a second or more following such peaks, in between syllables or short pauses in the program. This is very acceptable for communications radios, where compression of the audio aids intelligibility. However, it is absolutely undesired for music or normal broadcast programming, where a faithful reproduction of the original program, including its varying modulation levels, is expected.
## ITU type designations {#itu_type_designations}
In 1982, the International Telecommunication Union (ITU) designated the types of amplitude modulation:
Designation Description
------------- -----------------------------------------------------------------------------------
A3E double-sideband a full-carrier -- the basic amplitude modulation scheme
R3E single-sideband reduced-carrier
H3E single-sideband full-carrier
J3E single-sideband suppressed-carrier
B8E independent-sideband emission
C3F vestigial-sideband
Lincompex linked compressor and expander (a submode of any of the above ITU Emission Modes)
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## History
Amplitude modulation was used in experiments of multiplex telegraph and telephone transmission in the late 1800s. However, the practical development of this technology is identified with the period between 1900 and 1920 of radiotelephone transmission, that is, the effort to send audio signals by radio waves. The first radio transmitters, called spark gap transmitters, transmitted information by wireless telegraphy, using pulses of the carrier wave to spell out text messages in Morse code. They could not transmit audio because the carrier consisted of strings of damped waves, pulses of radio waves that declined to zero, and sounded like a buzz in receivers. In effect they were already amplitude modulated.
### Continuous waves {#continuous_waves}
The first AM transmission was made by Canadian-born American researcher Reginald Fessenden on December 23, 1900 using a spark gap transmitter with a specially designed high frequency 10 kHz interrupter, over a distance of 1 mi at Cobb Island, Maryland, US. His first transmitted words were, \"Hello. One, two, three, four. Is it snowing where you are, Mr. Thiessen?\". Though his words were \"perfectly intelligible\", the spark created a loud and unpleasant noise.
Fessenden was a significant figure in the development of AM radio. He was one of the first researchers to realize, from experiments like the above, that the existing technology for producing radio waves, the spark transmitter, was not usable for amplitude modulation, and that a new kind of transmitter, one that produced sinusoidal *continuous waves*, was needed. This was a radical idea at the time, because experts believed the impulsive spark was necessary to produce radio frequency waves, and Fessenden was ridiculed. He invented and helped develop one of the first continuous wave transmitters -- the Alexanderson alternator, with which he made what is considered the first AM public entertainment broadcast on Christmas Eve, 1906. He also discovered the principle on which AM is based, heterodyning, and invented one of the first detectors able to rectify and receive AM, the electrolytic detector or \"liquid baretter\", in 1902. Other radio detectors invented for wireless telegraphy, such as the Fleming valve (1904) and the crystal detector (1906) also proved able to rectify AM signals, so the technological hurdle was generating AM waves; receiving them was not a problem.
### Early technologies {#early_technologies}
Early experiments in AM radio transmission, conducted by Fessenden, Valdemar Poulsen, Ernst Ruhmer, Quirino Majorana, Charles Herrold, and Lee de Forest, were hampered by the lack of a technology for amplification. The first practical continuous wave AM transmitters were based on either the huge, expensive Alexanderson alternator, developed 1906--1910, or versions of the Poulsen arc transmitter (arc converter), invented in 1903. The modifications necessary to transmit AM were clumsy and resulted in very low quality audio. Modulation was usually accomplished by a carbon microphone inserted directly in the antenna or ground wire; its varying resistance varied the current to the antenna. The limited power handling ability of the microphone severely limited the power of the first radiotelephones; many of the microphones were water-cooled.
### Vacuum tubes {#vacuum_tubes}
The 1912 discovery of the amplifying ability of the Audion tube, invented in 1906 by Lee de Forest, solved these problems. The vacuum tube feedback oscillator, invented in 1912 by Edwin Armstrong and Alexander Meissner, was a cheap source of continuous waves and could be easily modulated to make an AM transmitter. Modulation did not have to be done at the output but could be applied to the signal before the final amplifier tube, so the microphone or other audio source didn\'t have to modulate a high-power radio signal. Wartime research greatly advanced the art of AM modulation, and after the war the availability of cheap tubes sparked a great increase in the number of radio stations experimenting with AM transmission of news or music. The vacuum tube was responsible for the rise of AM broadcasting around 1920, the first electronic mass communication medium. Amplitude modulation was virtually the only type used for radio broadcasting until FM broadcasting began after World War II.
At the same time as AM radio began, telephone companies such as AT&T were developing the other large application for AM: sending multiple telephone calls through a single wire by modulating them on separate carrier frequencies, called *frequency division multiplexing*.
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## History
### Single-sideband {#single_sideband}
In 1915, John Renshaw Carson formulated the first mathematical description of amplitude modulation, showing that a signal and carrier frequency combined in a nonlinear device creates a sideband on both sides of the carrier frequency. Passing the modulated signal through another nonlinear device can extract the original baseband signal. His analysis also showed that only one sideband was necessary to transmit the audio signal, and Carson patented single-sideband modulation (SSB) on 1 December 1915. This advanced variant of amplitude modulation was adopted by AT&T for longwave transatlantic telephone service beginning 7 January 1927. After WW-II, it was developed for military aircraft communication.
## Analysis
The carrier wave (sine wave) of frequency *f~c~* and amplitude *A* is expressed by
$$c(t) = A \sin(2 \pi f_c t)\,$$.
The message signal, such as an audio signal that is used for modulating the carrier, is *m*(*t*), and has a frequency *f~m~*, much lower than *f~c~*:
$$m(t) = M \cos\left(2\pi f_m t + \phi\right)= Am \cos\left(2\pi f_m t + \phi\right)\,$$,
where *m* is the amplitude sensitivity, *M* is the amplitude of modulation. If *m* \< 1, *(1 + m(t)/A)* is always positive for undermodulation. If *m* \> 1 then overmodulation occurs and reconstruction of message signal from the transmitted signal would lead in loss of original signal. Amplitude modulation results when the carrier *c(t)* is multiplied by the positive quantity *(1 + m(t)/A)*:
$$\begin{align}
y(t) &= \left[1 + \frac{m(t)}{A}\right] c(t) \\
&= \left[1 + m \cos\left(2\pi f_m t + \phi\right)\right] A \sin\left(2\pi f_c t\right)
\end{align}$$
In this simple case *m* is identical to the modulation index, discussed below. With *m* = 0.5 the amplitude modulated signal *y*(*t*) thus corresponds to the top graph (labelled \"50% Modulation\") in figure 4.
Using prosthaphaeresis identities, *y*(*t*) can be shown to be the sum of three sine waves:
$$y(t) = A \sin(2\pi f_c t) + \frac{1}{2}Am\left[\sin\left(2\pi \left[f_c + f_m\right] t + \phi\right) + \sin\left(2\pi \left[f_c - f_m\right] t - \phi\right)\right].\,$$
Therefore, the modulated signal has three components: the carrier wave *c(t)* which is unchanged in frequency, and two sidebands with frequencies slightly above and below the carrier frequency *f~c~*.
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## Spectrum
A useful modulation signal *m(t)* is usually more complex than a single sine wave, as treated above. However, by the principle of Fourier decomposition, *m(t)* can be expressed as the sum of a set of sine waves of various frequencies, amplitudes, and phases. Carrying out the multiplication of *1 + m(t)* with *c(t)* as above, the result consists of a sum of sine waves. Again, the carrier *c(t)* is present unchanged, but each frequency component of *m* at *f~i~* has two sidebands at frequencies *f~c~ + f~i~* and *f~c~ -- f~i~*. The collection of the former frequencies above the carrier frequency is known as the upper sideband, and those below constitute the lower sideband. The modulation *m(t)* may be considered to consist of an equal mix of positive and negative frequency components, as shown in the top of figure 2. One can view the sidebands as that modulation *m(t)* having simply been shifted in frequency by *f~c~* as depicted at the bottom right of figure 2.
The short-term spectrum of modulation, changing as it would for a human voice for instance, the frequency content (horizontal axis) may be plotted as a function of time (vertical axis), as in figure 3. It can again be seen that as the modulation frequency content varies, an upper sideband is generated according to those frequencies shifted *above* the carrier frequency, and the same content mirror-imaged in the lower sideband below the carrier frequency. At all times, the carrier itself remains constant, and of greater power than the total sideband power.
## Power and spectrum efficiency {#power_and_spectrum_efficiency}
The RF bandwidth of an AM transmission (refer to figure 2, but only considering positive frequencies) is twice the bandwidth of the modulating (or \"baseband\") signal, since the upper and lower sidebands around the carrier frequency each have a bandwidth as wide as the highest modulating frequency. Although the bandwidth of an AM signal is narrower than one using frequency modulation (FM), it is twice as wide as single-sideband techniques; it thus may be viewed as spectrally inefficient. Within a frequency band, only half as many transmissions (or \"channels\") can thus be accommodated. For this reason analog television employs a variant of single-sideband (known as vestigial sideband, somewhat of a compromise in terms of bandwidth) in order to reduce the required channel spacing.
Another improvement over standard AM is obtained through reduction or suppression of the carrier component of the modulated spectrum. In figure 2 this is the spike in between the sidebands; even with full (100%) sine wave modulation, the power in the carrier component is twice that in the sidebands, yet it carries no unique information. Thus there is a great advantage in efficiency in reducing or totally suppressing the carrier, either in conjunction with elimination of one sideband (single-sideband suppressed-carrier transmission) or with both sidebands remaining (double sideband suppressed carrier). While these suppressed carrier transmissions are efficient in terms of transmitter power, they require more sophisticated receivers employing synchronous detection and regeneration of the carrier frequency. For that reason, standard AM continues to be widely used, especially in broadcast transmission, to allow for the use of inexpensive receivers using envelope detection. Even (analog) television, with a (largely) suppressed lower sideband, includes sufficient carrier power for use of envelope detection. But for communications systems where both transmitters and receivers can be optimized, suppression of both one sideband and the carrier represent a net advantage and are frequently employed.
A technique used widely in broadcast AM transmitters is an application of the Hapburg carrier, first proposed in the 1930s but impractical with the technology then available. During periods of low modulation the carrier power would be reduced and would return to full power during periods of high modulation levels. This has the effect of reducing the overall power demand of the transmitter and is most effective on speech type programmes. Various trade names are used for its implementation by the transmitter manufacturers from the late 80\'s onwards.
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## Modulation index {#modulation_index}
The AM modulation index is a measure based on the ratio of the modulation excursions of the RF signal to the level of the unmodulated carrier. It is thus defined as:
$$m = \frac{\mathrm{peak\ value\ of\ } m(t)}{A} = \frac{M}{A}$$
where $M\,$ and $A\,$ are the modulation amplitude and carrier amplitude, respectively; the modulation amplitude is the peak (positive or negative) change in the RF amplitude from its unmodulated value. Modulation index is normally expressed as a percentage, and may be displayed on a meter connected to an AM transmitter.
So if $m=0.5$, carrier amplitude varies by 50% above (and below) its unmodulated level, as is shown in the first waveform, below. For $m=1.0$, it varies by 100% as shown in the illustration below it. With 100% modulation the wave amplitude sometimes reaches zero, and this represents full modulation using standard AM and is often a target (in order to obtain the highest possible signal-to-noise ratio) but mustn\'t be exceeded. Increasing the modulating signal beyond that point, known as overmodulation, causes a standard AM modulator (see below) to fail, as the negative excursions of the wave envelope cannot become less than zero, resulting in distortion (\"clipping\") of the received modulation. Transmitters typically incorporate a limiter circuit to avoid overmodulation, and/or a compressor circuit (especially for voice communications) in order to still approach 100% modulation for maximum intelligibility above the noise. Such circuits are sometimes referred to as a vogad.
However it is possible to talk about a modulation index exceeding 100%, without introducing distortion, in the case of double-sideband reduced-carrier transmission. In that case, negative excursions beyond zero entail a reversal of the carrier phase, as shown in the third waveform below. This cannot be produced using the efficient high-level (output stage) modulation techniques (see below) which are widely used especially in high power broadcast transmitters. Rather, a special modulator produces such a waveform at a low level followed by a linear amplifier. What\'s more, a standard AM receiver using an envelope detector is incapable of properly demodulating such a signal. Rather, synchronous detection is required. Thus double-sideband transmission is generally *not* referred to as \"AM\" even though it generates an identical RF waveform as standard AM as long as the modulation index is below 100%. Such systems more often attempt a radical reduction of the carrier level compared to the sidebands (where the useful information is present) to the point of double-sideband suppressed-carrier transmission where the carrier is (ideally) reduced to zero. In all such cases the term \"modulation index\" loses its value as it refers to the ratio of the modulation amplitude to a rather small (or zero) remaining carrier amplitude.
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## `{{anchor|AM modulation methods}}`{=mediawiki}Modulation methods {#modulation_methods}
Modulation circuit designs may be classified as low- or high-level (depending on whether they modulate in a low-power domain---followed by amplification for transmission---or in the high-power domain of the transmitted signal).
### Low-level generation {#low_level_generation}
In modern radio systems, modulated signals are generated via digital signal processing (DSP). With DSP many types of AM are possible with software control (including DSB with carrier, SSB suppressed-carrier and independent sideband, or ISB). Calculated digital samples are converted to voltages with a digital-to-analog converter, typically at a frequency less than the desired RF-output frequency. The analog signal must then be shifted in frequency and linearly amplified to the desired frequency and power level (linear amplification must be used to prevent modulation distortion). This low-level method for AM is used in many Amateur Radio transceivers.
AM may also be generated at a low level, using analog methods described in the next section.
### High-level generation {#high_level_generation}
High-power AM transmitters (such as those used for AM broadcasting) are based on high-efficiency class-D and class-E power amplifier stages, modulated by varying the supply voltage.
Older designs (for broadcast and amateur radio) also generate AM by controlling the gain of the transmitter\'s final amplifier (generally class-C, for efficiency). The following types are for vacuum tube transmitters (but similar options are available with transistors):
Plate modulation: In plate modulation, the plate voltage of the RF amplifier is modulated with the audio signal. The audio power requirement is 50 percent of the RF-carrier power.\
Heising (constant-current) modulation: RF amplifier plate voltage is fed through a choke (high-value inductor). The AM modulation tube plate is fed through the same inductor, so the modulator tube diverts current from the RF amplifier. The choke acts as a constant current source in the audio range. This system has a low power efficiency.\
Control grid modulation: The operating bias and gain of the final RF amplifier can be controlled by varying the voltage of the control grid. This method requires little audio power, but care must be taken to reduce distortion.\
Clamp tube (screen grid) modulation: The screen-grid bias may be controlled through a *clamp tube*, which reduces voltage according to the modulation signal. It is difficult to approach 100-percent modulation while maintaining low distortion with this system.\
Doherty modulation: One tube provides the power under carrier conditions and another operates only for positive modulation peaks. Overall efficiency is good, and distortion is low.\
Outphasing modulation: Two tubes are operated in parallel, but partially out of phase with each other. As they are differentially phase modulated their combined amplitude is greater or smaller. Efficiency is good and distortion low when properly adjusted.\
Pulse-width modulation (PWM) or pulse-duration modulation (PDM): A highly efficient high voltage power supply is applied to the tube plate. The output voltage of this supply is varied at an audio rate to follow the program. This system was pioneered by Hilmer Swanson and has a number of variations, all of which achieve high efficiency and sound quality.\
Digital methods: The Harris Corporation obtained a patent for synthesizing a modulated high-power carrier wave from a set of digitally selected low-power amplifiers, running in phase at the same carrier frequency. The input signal is sampled by a conventional audio analog-to-digital converter (ADC), and fed to a digital exciter, which modulates overall transmitter output power by switching a series of low-power solid-state RF amplifiers on and off. The combined output drives the antenna system.
## `{{anchor|AM demodulation methods}}`{=mediawiki}Demodulation methods {#demodulation_methods}
The simplest form of AM demodulator consists of a diode which is configured to act as envelope detector. Another type of demodulator, the product detector, can provide better-quality demodulation with additional circuit complexity
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An **assembly line**, often called *progressive assembly*, is a manufacturing process where the unfinished product moves in a direct line from workstation to workstation, with parts added in sequence until the final product is completed. By mechanically moving parts to workstations and transferring the unfinished product from one workstation to another, a finished product can be assembled faster and with less labor than having workers carry parts to a stationary product.
Assembly lines are common methods of assembling complex items such as automobiles and other transportation equipment, household appliances and electronic goods.
Workers in charge of the works of assembly line are called **assemblers**.
## Concepts
Assembly lines are designed for the sequential organization of workers, tools or machines, and parts. The motion of workers is minimized to the extent possible. All parts or assemblies are handled either by conveyors or motorized vehicles such as forklifts, or gravity, with no manual trucking. Heavy lifting is done by machines such as overhead cranes or forklifts. Each worker typically performs one simple operation unless job rotation strategies are applied.
According to Henry Ford:
Designing assembly lines is a well-established mathematical challenge, referred to as an assembly line balancing problem. In the simple assembly line balancing problem the aim is to assign a set of tasks that need to be performed on the workpiece to a sequence of workstations. Each task requires a given task duration for completion. The assignment of tasks to stations is typically limited by two constraints: (1) a precedence graph which indicates what other tasks need to be completed before a particular task can be initiated (e.g. not putting in a screw before drilling the hole) and (2) a cycle time which restricts the sum of task processing times which can be completed at each workstation before the work-piece is moved to the next station by the conveyor belt. Major planning problems for operating assembly lines include supply chain integration, inventory control and production scheduling.
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## Simple example {#simple_example}
Consider the assembly of a car: assume that certain steps in the assembly line are to install the engine, install the hood, and install the wheels (in that order, with arbitrary interstitial steps); only one of these steps can be done at a time. In traditional production, only one car would be assembled at a time. If engine installation takes 20 minutes, hood installation takes five minutes, and wheels installation takes 10 minutes, then a car can be produced every 35 minutes.
In an assembly line, car assembly is split between several stations, all working simultaneously. When a station is finished with a car, it passes it on to the next. By having three stations, three cars can be operated on at the same time, each at a different stage of assembly.
After finishing its work on the first car, the engine installation crew can begin working on the second car. While the engine installation crew works on the second car, the first car can be moved to the hood station and fitted with a hood, then to the wheels station and be fitted with wheels. After the engine has been installed on the second car, the second car moves to the hood assembly. At the same time, the third car moves to the engine assembly. When the third car\'s engine has been mounted, it then can be moved to the hood station; meanwhile, subsequent cars (if any) can be moved to the engine installation station.
Assuming no loss of time when moving a car from one station to another, the longest stage on the assembly line determines the throughput (20 minutes for the engine installation) so a car can be produced every 20 minutes, once the first car taking 35 minutes has been produced.
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## History
Before the Industrial Revolution, most manufactured products were made individually by hand. A single craftsman or team of craftsmen would create each part of a product. They would use their skills and tools such as files and knives to create the individual parts. They would then assemble them into the final product, making cut-and-try changes in the parts until they fit and could work together (craft production).
Division of labor was practiced by Ancient Greeks, Chinese and other ancient civilizations. In Ancient Greece it was discussed by Plato and Xenophon. Adam Smith discussed the division of labour in the manufacture of pins at length in his book *The Wealth of Nations* (published in 1776).
The Venetian Arsenal, dating to about 1104, operated similar to a production line. Ships moved down a canal and were fitted by the various shops they passed. At the peak of its efficiency in the early 16th century, the Arsenal employed some 16,000 people who could apparently produce nearly one ship each day and could fit out, arm, and provision a newly built galley with standardized parts on an assembly-line basis. Although the Arsenal lasted until the early Industrial Revolution, production line methods did not become common even then.
### Industrial Revolution {#industrial_revolution}
The Industrial Revolution led to a proliferation of manufacturing and invention. Many industries, notably textiles, firearms, clocks and watches, horse-drawn vehicles, railway locomotives, sewing machines, and bicycles, saw expeditious improvement in materials handling, machining, and assembly during the 19th century, although modern concepts such as industrial engineering and logistics had not yet been named.
The automatic flour mill built by Oliver Evans in 1785 was called the beginning of modern bulk material handling by Roe (1916). Evans\'s mill used a leather belt bucket elevator, screw conveyors, canvas belt conveyors, and other mechanical devices to completely automate the process of making flour. The innovation spread to other mills and breweries.
Probably the earliest industrial example of a linear and continuous assembly process is the Portsmouth Block Mills, built between 1801 and 1803. Marc Isambard Brunel (father of Isambard Kingdom Brunel), with the help of Henry Maudslay and others, designed 22 types of machine tools to make the parts for the rigging blocks used by the Royal Navy. This factory was so successful that it remained in use until the 1960s, with the workshop still visible at HM Dockyard in Portsmouth, and still containing some of the original machinery.
One of the earliest examples of an almost modern factory layout, designed for easy material handling, was the Bridgewater Foundry. The factory grounds were bordered by the Bridgewater Canal and the Liverpool and Manchester Railway. The buildings were arranged in a line with a railway for carrying the work going through the buildings. Cranes were used for lifting the heavy work, which sometimes weighed in the tens of tons. The work passed sequentially through to erection of framework and final assembly.
The first flow assembly line was initiated at the factory of Richard Garrett & Sons, Leiston Works in Leiston in the English county of Suffolk for the manufacture of portable steam engines. The assembly line area was called \'The Long Shop\' on account of its length and was fully operational by early 1853. The boiler was brought up from the foundry and put at the start of the line, and as it progressed through the building it would stop at various stages where new parts would be added. From the upper level, where other parts were made, the lighter parts would be lowered over a balcony and then fixed onto the machine on the ground level. When the machine reached the end of the shop, it would be completed.
### Interchangeable parts {#interchangeable_parts}
During the early 19th century, the development of machine tools such as the screw-cutting lathe, metal planer, and milling machine, and of toolpath control via jigs and fixtures, provided the prerequisites for the modern assembly line by making interchangeable parts a practical reality.
### Late 19th-century steam and electric conveyors {#late_19th_century_steam_and_electric_conveyors}
Steam-powered conveyor lifts began being used for loading and unloading ships some time in the last quarter of the 19th century. Hounshell (1984) shows a c. 1885 sketch of an electric-powered conveyor moving cans through a filling line in a canning factory.
The meatpacking industry of Chicago is believed to be one of the first industrial assembly lines (or disassembly lines) to be utilized in the United States starting in 1867. Workers would stand at fixed stations and a pulley system would bring the meat to each worker and they would complete one task. Henry Ford and others have written about the influence of this slaughterhouse practice on the later developments at Ford Motor Company.
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## History
### 20th century {#th_century}
thumb\|thumbtime=2\|Ford Model T assembly line c. 1919 thumb\|thumbtime=6\|start=6\|end=47\|Ford Model T assembly line c. 1924 thumb\|thumbtime=6\|Ford assembly line c. 1930 thumb\|thumbtime=6\|Ford assembly line c. 1947 According to Domm, the implementation of mass production of an automobile via an assembly line may be credited to Ransom Olds, who used it to build the first mass-produced automobile, the Oldsmobile Curved Dash. Olds patented the assembly line concept, which he put to work in his Olds Motor Vehicle Company factory in 1901.
At Ford Motor Company, the assembly line was introduced by William \"Pa\" Klann upon his return from visiting Swift & Company\'s slaughterhouse in Chicago and viewing what was referred to as the \"disassembly line\", where carcasses were butchered as they moved along a conveyor. The efficiency of one person removing the same piece over and over without moving to another station caught his attention. He reported the idea to Peter E. Martin, soon to be head of Ford production, who was doubtful at the time but encouraged him to proceed. Others at Ford have claimed to have put the idea forth to Henry Ford, but Pa Klann\'s slaughterhouse revelation is well documented in the archives at the Henry Ford Museum and elsewhere, making him an important contributor to the modern automated assembly line concept. Ford was appreciative, having visited the highly automated 40-acre Sears mail order handling facility around 1906. At Ford, the process was an evolution by trial and error of a team consisting primarily of Peter E. Martin, the factory superintendent; Charles E. Sorensen, Martin\'s assistant; Clarence W. Avery; C. Harold Wills, draftsman and toolmaker; Charles Ebender; and József Galamb. Some of the groundwork for such development had recently been laid by the intelligent layout of machine tool placement that Walter Flanders had been doing at Ford up to 1908.
The moving assembly line was developed for the Ford Model T and began operation on October 7, 1913, at the Highland Park Ford Plant, and continued to evolve after that, using time and motion study. The assembly line, driven by conveyor belts, reduced production time for a Model T to just 93 minutes by dividing the process into 45 steps. Producing cars quicker than paint of the day could dry, it had an immense influence on the world.
In 1922, Ford (through his ghostwriter Crowther) said of his 1913 assembly line:
Charles E. Sorensen, in his 1956 memoir *My Forty Years with Ford*, presented a different version of development that was not so much about individual \"inventors\" as a gradual, logical development of industrial engineering:
As a result of these developments in method, Ford\'s cars came off the line in three-minute intervals or six feet per minute. This was much faster than previous methods, increasing production by eight to one (requiring 12.5 man-hours before, 1 hour 33 minutes after), while using less manpower. It was so successful, paint became a bottleneck. Only japan black would dry fast enough, forcing the company to drop the variety of colours available before 1914, until fast-drying Duco lacquer was developed in 1926.
The assembly line technique was an integral part of the diffusion of the automobile into American society. Decreased costs of production allowed the cost of the Model T to fall within the budget of the American middle class. In 1908, the price of a Model T was around \$825, and by 1912 it had decreased to around \$575. This price reduction is comparable to a reduction from \$15,000 to \$10,000 in dollar terms from the year 2000. In 1914, an assembly line worker could buy a Model T with four months\' pay.
Ford\'s complex safety procedures---especially assigning each worker to a specific location instead of allowing them to roam about---dramatically reduced the rate of injury. The combination of high wages and high efficiency is called \"Fordism\", and was copied by most major industries. The efficiency gains from the assembly line also coincided with the take-off of the United States. The assembly line forced workers to work at a certain pace with very repetitive motions which led to more output per worker while other countries were using less productive methods.
In the automotive industry, its success was dominating, and quickly spread worldwide. Ford France and Ford Britain in 1911, Ford Denmark 1923, Ford Germany and Ford Japan 1925; in 1919, Vulcan (Southport, Lancashire) was the first native European manufacturer to adopt it. Soon, companies had to have assembly lines, or risk going broke by not being able to compete; by 1930, 250 companies which did not had disappeared.
The massive demand for military hardware in World War II prompted assembly-line techniques in shipbuilding and aircraft production. Thousands of Liberty ships were built making extensive use of prefabrication, enabling ship assembly to be completed in weeks or even days. After having produced fewer than 3,000 planes for the United States Military in 1939, American aircraft manufacturers built over 300,000 planes in World War II. Vultee pioneered the use of the powered assembly line for aircraft manufacturing. Other companies quickly followed. As William S. Knudsen (having worked at Ford, GM and the National Defense Advisory Commission) observed, \"We won because we smothered the enemy in an avalanche of production, the like of which he had never seen, nor dreamed possible.\"
## Improved working conditions {#improved_working_conditions}
In his 1922 autobiography, Henry Ford mentions several benefits of the assembly line including:
- Workers do not do any heavy lifting.
- No stooping or bending over.
- No special training was required.
- There are jobs that almost anyone can do.
- Provided employment to immigrants.
The gains in productivity allowed Ford to increase worker pay from \$1.50 per day to \$5.00 per day once employees reached three years of service on the assembly line. Ford continued on to reduce the hourly work week while continuously lowering the Model T price. These goals appear altruistic; however, it has been argued that they were implemented by Ford in order to reduce high employee turnover: when the assembly line was introduced in 1913, it was discovered that \"every time the company wanted to add 100 men to its factory personnel, it was necessary to hire 963\" in order to counteract the natural distaste the assembly line seems to have inspired.
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## Sociological problems {#sociological_problems}
Sociological work has explored the social alienation and boredom that many workers feel because of the repetition of doing the same specialized task all day long.
Karl Marx expressed in his theory of alienation the belief that, in order to achieve job satisfaction, workers need to see themselves in the objects they have created, that products should be \"mirrors in which workers see their reflected essential nature\". Marx viewed labour as a chance for people to externalize facets of their personalities. Marxists argue that performing repetitive, specialized tasks causes a feeling of disconnection between what a worker does all day, who they really are, and what they would ideally be able to contribute to society. Furthermore, Marx views these specialised jobs as insecure, since the worker is expendable as soon as costs rise and technology can replace more expensive human labour.
Since workers have to stand in the same place for hours and repeat the same motion hundreds of times per day, repetitive stress injuries are a possible pathology of occupational safety. Industrial noise also proved dangerous. When it was not too high, workers were often prohibited from talking. Charles Piaget, a skilled worker at the LIP factory, recalled that besides being prohibited from speaking, the semi-skilled workers had only 25 centimeters in which to move. Industrial ergonomics later tried to minimize physical trauma
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In mathematics, an **algebraic number** is a number that is a root of a non-zero polynomial in one variable with integer (or, equivalently, rational) coefficients. For example, the golden ratio $(1 + \sqrt{5})/2$ is an algebraic number, because it is a root of the polynomial $X^2 - X - 1$, i.e., a solution of the equation $x^2 - x - 1 = 0$, and the complex number $1 + i$ is algebraic as a root of $X^4 + 4$. Algebraic numbers include all integers, rational numbers, and *n*-th roots of integers.
Algebraic complex numbers are closed under addition, subtraction, multiplication and division, and hence form a field, denoted $\overline{\Q}$. The set of algebraic real numbers $\overline{\Q} \cap \R$ is also a field.
Numbers which are not algebraic are called transcendental and include `{{pi}}`{=mediawiki} and `{{mvar|[[e (mathematical constant)|e]]}}`{=mediawiki}. There are countably many algebraic numbers, hence almost all real (or complex) numbers (in the sense of Lebesgue measure) are transcendental.
## Examples
- All rational numbers are algebraic. Any rational number, expressed as the quotient of an integer `{{mvar|a}}`{=mediawiki} and a (non-zero) natural number `{{mvar|b}}`{=mediawiki}, satisfies the above definition, because `{{math|''x'' {{=}}`{=mediawiki} `{{sfrac|''a''|''b''}}`{=mediawiki}}} is the root of a non-zero polynomial, namely `{{math|''bx'' − ''a''}}`{=mediawiki}.
- Quadratic irrational numbers, irrational solutions of a quadratic polynomial `{{math|''ax''{{sup|2}} + ''bx'' + ''c''}}`{=mediawiki} with integer coefficients `{{mvar|a}}`{=mediawiki}, `{{mvar|b}}`{=mediawiki}, and `{{mvar|c}}`{=mediawiki}, are algebraic numbers. If the quadratic polynomial is monic (`{{math|''a'' {{=}}`{=mediawiki} 1}}), the roots are further qualified as quadratic integers.
- Gaussian integers, complex numbers `{{math|''a'' + ''bi''}}`{=mediawiki} for which both `{{mvar|a}}`{=mediawiki} and `{{mvar|b}}`{=mediawiki} are integers, are also quadratic integers. This is because `{{math|''a'' + ''bi''}}`{=mediawiki} and `{{math|''a'' − ''bi''}}`{=mediawiki} are the two roots of the quadratic `{{math|''x''{{sup|2}} − 2''ax'' + ''a''{{sup|2}} + ''b''{{sup|2}}}}`{=mediawiki}.
- A constructible number can be constructed from a given unit length using a straightedge and compass. It includes all quadratic irrational roots, all rational numbers, and all numbers that can be formed from these using the basic arithmetic operations and the extraction of square roots. (By designating cardinal directions for +1, −1, +`{{mvar|i}}`{=mediawiki}, and −`{{mvar|i}}`{=mediawiki}, complex numbers such as $3+i \sqrt{2}$ are considered constructible.)
- Any expression formed from algebraic numbers using any finite combination of the basic arithmetic operations and extraction of `{{mvar|n}}`{=mediawiki}th roots gives another algebraic number.
- Polynomial roots that cannot be expressed in terms of the basic arithmetic operations and extraction of `{{mvar|n}}`{=mediawiki}th roots (such as the roots of `{{math|''x''<sup>5</sup> − ''x'' + 1}}`{=mediawiki}). That happens with many but not all polynomials of degree 5 or higher.
- Values of trigonometric functions of rational multiples of `{{pi}}`{=mediawiki} (except when undefined): for example, `{{math|cos {{sfrac|{{math|π}}|7}}}}`{=mediawiki}, `{{math|cos {{sfrac|3{{math|π}}|7}}}}`{=mediawiki}, and `{{math|cos {{sfrac|5{{math|π}}|7}}}}`{=mediawiki} satisfy `{{math|8''x''<sup>3</sup> − 4''x''<sup>2</sup> − 4''x'' + 1 {{=}}`{=mediawiki} 0}}. This polynomial is irreducible over the rationals and so the three cosines are *conjugate* algebraic numbers. Likewise, `{{math|tan {{sfrac|3{{math|π}}|16}}}}`{=mediawiki}, `{{math|tan {{sfrac|7{{math|π}}|16}}}}`{=mediawiki}, `{{math|tan {{sfrac|11{{math|π}}|16}}}}`{=mediawiki}, and `{{math|tan {{sfrac|15{{math|π}}|16}}}}`{=mediawiki} satisfy the irreducible polynomial `{{math|''x''<sup>4</sup> − 4''x''<sup>3</sup> − 6''x''<sup>2</sup> + 4''x'' + 1 {{=}}`{=mediawiki} 0}}, and so are conjugate algebraic integers. This is the equivalent of angles which, when measured in degrees, have rational numbers.
- Some but not all irrational numbers are algebraic:
- The numbers $\sqrt{2}$ and $\frac{ \sqrt[3]{3} }{ 2 }$ are algebraic since they are roots of polynomials `{{math|''x''<sup>2</sup> − 2}}`{=mediawiki} and `{{math|8''x''<sup>3</sup> − 3}}`{=mediawiki}, respectively.
- The golden ratio `{{mvar|φ}}`{=mediawiki} is algebraic since it is a root of the polynomial `{{math|''x''<sup>2</sup> − ''x'' − 1}}`{=mediawiki}.
- The numbers `{{pi}}`{=mediawiki} and e are not algebraic numbers (see the Lindemann--Weierstrass theorem).
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## Properties
- If a polynomial with rational coefficients is multiplied through by the least common denominator, the resulting polynomial with integer coefficients has the same roots. This shows that an algebraic number can be equivalently defined as a root of a polynomial with either integer or rational coefficients.
- Given an algebraic number, there is a unique monic polynomial with rational coefficients of least degree that has the number as a root. This polynomial is called its minimal polynomial. If its minimal polynomial has degree `{{mvar|n}}`{=mediawiki}, then the algebraic number is said to be of **degree `{{mvar|n}}`{=mediawiki}**. For example, all rational numbers have degree 1, and an algebraic number of degree 2 is a quadratic irrational.
- The algebraic numbers are dense in the reals. This follows from the fact they contain the rational numbers, which are dense in the reals themselves.
- The set of algebraic numbers is countable, and therefore its Lebesgue measure as a subset of the complex numbers is 0 (essentially, the algebraic numbers take up no space in the complex numbers). That is to say, \"almost all\" real and complex numbers are transcendental.
- All algebraic numbers are computable and therefore definable and arithmetical.
- For real numbers `{{math|''a''}}`{=mediawiki} and `{{math|''b''}}`{=mediawiki}, the complex number `{{math|''a'' + ''bi''}}`{=mediawiki} is algebraic if and only if both `{{math|''a''}}`{=mediawiki} and `{{math|''b''}}`{=mediawiki} are algebraic.
### Degree of simple extensions of the rationals as a criterion to algebraicity {#degree_of_simple_extensions_of_the_rationals_as_a_criterion_to_algebraicity}
For any `{{math|α}}`{=mediawiki}, the simple extension of the rationals by `{{math|α}}`{=mediawiki}, denoted by $\Q(\alpha)$ (whose elements are the $f(\alpha)$ for $f$ a rational function with rational coefficients which is defined at $\alpha$), is of finite degree if and only if `{{math|α}}`{=mediawiki} is an algebraic number.
The condition of finite degree means that there is a finite set $\{a_i | 1\le i\le k\}$ in $\Q(\alpha)$ such that $\Q(\alpha) = \sum_{i=1}^k a_i \Q$; that is, every member in $\Q(\alpha)$ can be written as $\sum_{i=1}^k a_i q_i$ for some rational numbers $\{q_i | 1\le i\le k\}$ (note that the set $\{a_i\}$ is fixed).
Indeed, since the $a_i-s$ are themselves members of $\Q(\alpha)$, each can be expressed as sums of products of rational numbers and powers of `{{math|α}}`{=mediawiki}, and therefore this condition is equivalent to the requirement that for some finite $n$, $\Q(\alpha) = \{\sum_{i=-n}^n \alpha^{i} q_i | q_i\in \Q\}$.
The latter condition is equivalent to $\alpha^{n+1}$, itself a member of $\Q(\alpha)$, being expressible as $\sum_{i=-n}^n \alpha^i q_i$ for some rationals $\{q_i\}$, so $\alpha^{2n+1} = \sum_{i=0}^{2n} \alpha^i q_{i-n}$ or, equivalently, `{{math|α}}`{=mediawiki} is a root of $x^{2n+1}-\sum_{i=0}^{2n} x^i q_{i-n}$; that is, an algebraic number with a minimal polynomial of degree not larger than $2n+1$.
It can similarly be proven that for any finite set of algebraic numbers $\alpha_1$, $\alpha_2$\... $\alpha_n$, the field extension $\Q(\alpha_1, \alpha_2, ... \alpha_n)$ has a finite degree.
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## Field
The sum, difference, product, and quotient (if the denominator is nonzero) of two algebraic numbers is again algebraic:
For any two algebraic numbers `{{math|α}}`{=mediawiki}, `{{math|β}}`{=mediawiki}, this follows directly from the fact that the simple extension $\Q(\gamma)$, for $\gamma$ being either $\alpha+\beta$, $\alpha-\beta$, $\alpha\beta$ or (for $\beta\ne 0$) $\alpha/\beta$, is a linear subspace of the finite-degree field extension $\Q(\alpha,\beta)$, and therefore has a finite degree itself, from which it follows (as shown above) that $\gamma$ is algebraic.
An alternative way of showing this is constructively, by using the resultant.
Algebraic numbers thus form a field $\overline{\mathbb{Q}}$ (sometimes denoted by $\mathbb A$, but that usually denotes the adele ring).
### Algebraic closure {#algebraic_closure}
Every root of a polynomial equation whose coefficients are *algebraic numbers* is again algebraic. That can be rephrased by saying that the field of algebraic numbers is algebraically closed. In fact, it is the smallest algebraically closed field containing the rationals and so it is called the algebraic closure of the rationals.
That the field of algebraic numbers is algebraically closed can be proven as follows: Let `{{math|β}}`{=mediawiki} be a root of a polynomial $\alpha_0 + \alpha_1 x + \alpha_2 x^2 ... +\alpha_n x^n$ with coefficients that are algebraic numbers $\alpha_0$, $\alpha_1$, $\alpha_2$\... $\alpha_n$. The field extension $\Q^\prime \equiv \Q(\alpha_1, \alpha_2, ... \alpha_n)$ then has a finite degree with respect to $\Q$. The simple extension $\Q^\prime(\beta)$ then has a finite degree with respect to $\Q^\prime$ (since all powers of `{{math|β}}`{=mediawiki} can be expressed by powers of up to $\beta^{n-1}$). Therefore, $\Q^\prime(\beta) = \Q(\beta, \alpha_1, \alpha_2, ... \alpha_n)$ also has a finite degree with respect to $\Q$. Since $\Q(\beta)$ is a linear subspace of $\Q^\prime(\beta)$, it must also have a finite degree with respect to $\Q$, so `{{math|β}}`{=mediawiki} must be an algebraic number.
## Related fields {#related_fields}
### Numbers defined by radicals {#numbers_defined_by_radicals}
Any number that can be obtained from the integers using a finite number of additions, subtractions, multiplications, divisions, and taking (possibly complex) `{{mvar|n}}`{=mediawiki}th roots where `{{mvar|n}}`{=mediawiki} is a positive integer are algebraic. The converse, however, is not true: there are algebraic numbers that cannot be obtained in this manner. These numbers are roots of polynomials of degree 5 or higher, a result of Galois theory (see Quintic equations and the Abel--Ruffini theorem). For example, the equation:
$$x^5-x-1=0$$
has a unique real root, ≈ 1.1673, that cannot be expressed in terms of only radicals and arithmetic operations.
### Closed-form number {#closed_form_number}
Algebraic numbers are all numbers that can be defined explicitly or implicitly in terms of polynomials, starting from the rational numbers. One may generalize this to \"closed-form numbers\", which may be defined in various ways. Most broadly, all numbers that can be defined explicitly or implicitly in terms of polynomials, exponentials, and logarithms are called \"elementary numbers\", and these include the algebraic numbers, plus some transcendental numbers. Most narrowly, one may consider numbers *explicitly* defined in terms of polynomials, exponentials, and logarithms -- this does not include all algebraic numbers, but does include some simple transcendental numbers such as `{{mvar|e}}`{=mediawiki} or ln 2.
## Algebraic integers {#algebraic_integers}
*Main article: Algebraic integer* An *algebraic integer* is an algebraic number that is a root of a polynomial with integer coefficients with leading coefficient 1 (a monic polynomial). Examples of algebraic integers are $5 + 13 \sqrt{2},$ $2 - 6i,$ and $\frac{1}{2}(1+i\sqrt{3}).$ Therefore, the algebraic integers constitute a proper superset of the integers, as the latter are the roots of monic polynomials `{{math|''x'' − ''k''}}`{=mediawiki} for all $k \in \mathbb{Z}$. In this sense, algebraic integers are to algebraic numbers what integers are to rational numbers.
The sum, difference and product of algebraic integers are again algebraic integers, which means that the algebraic integers form a ring. The name *algebraic integer* comes from the fact that the only rational numbers that are algebraic integers are the integers, and because the algebraic integers in any number field are in many ways analogous to the integers. If `{{math|''K''}}`{=mediawiki} is a number field, its ring of integers is the subring of algebraic integers in `{{math|''K''}}`{=mediawiki}, and is frequently denoted as `{{math|''O<sub>K</sub>''}}`{=mediawiki}. These are the prototypical examples of Dedekind domains
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**Afro Celt Sound System** are a European and African group who fuse electronic music with traditional Gaelic and West African music. Afro Celt Sound System was formed in 1995 by producer-guitarist Simon Emmerson, and feature a wide range of guest artists. In 2003, they temporarily changed their name to **Afrocelts** before reverting to their original name.
Their albums have been released through Peter Gabriel\'s Real World Records, and they have frequently performed at WOMAD festivals worldwide. Their sales on the label are exceeded only by Gabriel himself. Their recording contract with Real World was for five albums, of which *Volume 5: Anatomic* was the last.
After a number of festival dates in 2007, the band went on hiatus. In 2010, they regrouped to play a number of shows (including a return to WOMAD), and released a remastered retrospective titled *Capture*.
On 20 May 2014, Afro Celt Sound System announced the release of the album *Born*. In January 2016, a posting on their website revealed that due to a dispute with Emmerson, who announced his departure from the band in 2015, there were two active versions of the band, one led by Emmerson and another with a separate line-up headed by James McNally and Martin Russell. Emmerson\'s version of the band released the album *The Source* in 2016. The dispute ended on 21 December 2016, with an announcement on social media.
The band released their seventh studio album, *Flight*, on 23 November 2018.
## Formation
The inspiration behind the project dates back to 1991, when Simon Emmerson, a Grammy Award-nominated British producer and guitarist, collaborated with Afro-pop star Baaba Maal. While making an album with Maal in Senegal, Emmerson was struck by the similarity between one African melody and a traditional Irish air. Back in London, Irish musician Davy Spillane told Emmerson about a belief that nomadic Celts lived in Africa or India before they migrated to Western Europe. Whether or not the theory was true, Emmerson was intrigued by the two regions\' musical affinities.
In an experiment that would prove successful, Emmerson brought two members of Baaba Maal\'s band together with traditional Irish musicians to see what kind of music the two groups would create. Adding a dash of modern sound, Emmerson also brought in English dance mixers for an electronic beat. \"People thought I was mad when I touted the idea,\" Emmerson told Jim Carroll of *The Irish Times*. \"At the time, I was out of favour with the London club scene. I was broke and on income support but the success was extraordinary\".
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## Career
Jamming in the studios at Real World, musician Peter Gabriel\'s recording facilities in Wiltshire, England, the group of musicians recorded the basis of their first album in one week. This album, *Volume 1: Sound Magic*, was released by Real World Records in 1996, and marked the debut of the Afro Celt Sound System.
\"Prior to that first album being made, none of us knew if it would work,\" musician James McNally told Larry Katz of the Boston Herald. \"We were strangers who didn\'t even speak the same language. But we were bowled over by this communication that took place beyond language.\"`{{full citation needed|date=November 2012}}`{=mediawiki} McNally, who grew up second-generation Irish in London, played whistles, keyboards, piano, bodhran, and bamboo flute.
*Sound Magic* has now sold over 300,000 copies. The band performed at festivals, raves, and dance clubs and regularly included two African musicians, Moussa Sissokho on talking drum and djembe and N\'Faly Kouyate on vocals, kora and balafon.
Just as the second album was getting off the ground, one of the group\'s core musicians, 27-year-old keyboardist Jo Bruce, (son of Cream bass player Jack Bruce), died suddenly of an asthma attack. The band was devastated, and the album was put on hold. Sinéad O\'Connor then collaborated with the band and helped them cope with their loss. \"\[O\'Connor\] blew into the studio on a windy November night and blew away again leaving us something incredibly emotional and powerful,\" McNally told Katz. \"We had this track we didn\'t know what to do with. Sinéad scribbled a few lyrics and bang! She left us completely choked up.\"`{{full citation needed|date=November 2012}}`{=mediawiki} The band used the name of O\'Connor\'s song, \"Release\", for the title of their album. *Volume 2: Release* was released in 1999, and by the spring of 2000 it had sold more than half a million copies worldwide. *Release* is also used as one of the GCSE music set works in the UK that students are required to study for their exam.
In 2000, the group was nominated for a Grammy Award in the Best World Music category. The band, composed at the time of eight members from six countries (the UK, Senegal, Guinea, Ireland, France and Kenya), took pride in its ability to bring people together through music. \"We can communicate anywhere at any corner of the planet and feel that we\'re at home,\" McNally told Patrick MacDonald of *The Seattle Times*. \"We\'re breaking down categories of world music and rock music and black music. We leave a door open to communicate with each other\'s traditions. And it\'s changed our lives\".`{{full citation needed|date=November 2012}}`{=mediawiki}
In 2001, the group released *Volume 3: Further in Time*, which climbed to number one on *Billboard*{{\'}}s Top World Music Albums chart. Featuring guest spots by Peter Gabriel and Robert Plant, the album also incorporated a heightened African sound. \"On the first two records, the pendulum swung more toward the Celtic, London club side of the equation,\" Emmerson told *The Irish Times*{{\'}} Carroll. \"For this one, we wanted to have more African vocals and input than we\'d done before.\" Again the Afro Celt Sound System met with success. Chuck Taylor of *Billboard* praised the album as \"a cultural phenomenon that bursts past the traditional boundaries of contemporary music.\"`{{full citation needed|date=November 2012}}`{=mediawiki} The single \"When You\'re Falling\", with vocals by Gabriel, became a radio hit in the United States.
In 2003, for the *Seed* album, they changed their name to Afrocelts. They reverted to the longer band name for their subsequent albums, *Pod*, a compilation of new mixes of songs from the first four albums, *Volume 5: Anatomic* (their fifth studio album), and *Capture (1995--2010)*.
They played a number of shows to promote *Volume 5: Anatomic* in 2006 and summer 2007, ending with a gig in Korea, before taking an extended break to work on side projects, amongst them *The Imagined Village* featuring Simon Emmerson and Johnny Kalsi. Starting in the summer of 2010, the band performed a series of live shows to promote *Capture (1995--2010)*, released on 6 September 2010 on Real World Records. Further performances continue to the present day, and a new album-in-progress titled *Born* was announced on their website in 2014. Following the split (see below), Emmerson\'s version of the band released the album The Source in 2016.
## Split
During 2015, the band had split into two formations, one of them including Simon Emmerson, N\'Faly Kouyate and Johnny Kalsi, the other one James McNally and Martin Russell. The split was announced on the band\'s website in January 2016. The dispute officially ended with an announcement on social media on 21 December 2016. `{{Blockquote |text=Simon Emmerson, James McNally and Martin Russell are pleased to announce that they have been able to set aside their differences and come to an amicable agreement to bring their dispute to an end. Going forward, McNally, Russell and Emmerson have agreed that Emmerson will continue to perform as Afro Celt Sound System and McNally and Russell will work under a new name to be announced in due course. While McNally, Russell and Emmerson will no longer be performing or working together they recognise, and are grateful for each other's contribution to Afro Celt Sound System over the past two decades and will be working with the extensive community of musicians that make up the long standing Afro Celt Sound System family.<ref>{{cite web|url=https://www.facebook.com/officialafroceltsoundsystem/posts/1384670074878165|title=Afro Celt Sound System|via=Facebook|archive-url=https://web.archive.org/web/20200117134949/https://www.facebook.com/officialafroceltsoundsystem/posts/1384670074878165|archive-date=17 January 2020}}</ref><ref>{{cite web |title=Statement about ACSS |url=https://www.afroceltsoundsystem.org.uk/news/statement-about-acss/ |website=Afro Celt Sound System |access-date=15 November 2020 |date=21 December 2016}}</ref>}}`{=mediawiki}
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## Members
When Afro Celt Sound System formed in the mid-1990s during the Real World Recording Week, the difference between a guest artist and a band member was virtually non-existent. However, over time, a combination of people became most often associated with the name Afro Celt Sound System (while *Volume 5: Anatomic* only lists Emmerson, McNally, Ó Lionáird and Russell as regulars). The divided grouping of the band into two versions, both operating under the name Afro Celt Sound System, began in January 2016 and was resolved in December 2016 after McNally and Russell agreed to work under a different name from Emmerson.
- Simon Emmerson who died on 13 March 2023 after falling ill.
- N\'Faly Kouyate
- Johnny Kalsi
- Moussa Sissokho
- Griogair Labhruidh
- Ronan Browne
- Emer Mayock
- Davy Spillane
**Russell/McNally version**
- Martin Russell
- James McNally
- Ian Markin
- Tim Bradshaw
- Babara Bangoura
- Dorothee Munyaneza
- Kadially Kouyaté
- Dav Daheley
Other musicians who have performed or recorded with Afro Celt Sound System include: Jimmy Mahon, Demba Barry, Babara Bangoura, Iarla Ó Lionáird, Peter Gabriel, Robert Plant, Pete Lockett, Sinéad O\'Connor, Pina Kollar, Dorothee Munyaneza, Sevara Nazarkhan, Simon Massey, Jesse Cook, Martin Hayes, Eileen Ivers, Mundy, Mairéad Ní Mhaonaigh and Ciarán Tourish of Altan, Ronan Browne, Michael McGoldrick, Steáfán Hannigan, Myrdhin, Shooglenifty, Mairead Nesbitt, Nigel Eaton, Davy Spillane, Jonas Bruce, Heather Nova, Julie Murphy, Ayub Ogada, Caroline Lavelle, and Ross Ainslie.
## Discography
### Studio albums {#studio_albums}
+--------------------------------------------------------------------------------------------------------------+------+----------------------+
| Title | Year | Peak chart positions |
+==============================================================================================================+======+======================+
| UK\ | AUS\ | FRA\ |
| Peaks in the UK: | | |
| | | |
| - All except noted: full Official Chart history\|publisher=Official Charts\|access-date=5 December 2020}} | | |
| - \"When You\'re Falling\": | | |
+--------------------------------------------------------------------------------------------------------------+------+----------------------+
| *Volume 1: Sound Magic* | 1996 | 59 |
+--------------------------------------------------------------------------------------------------------------+------+----------------------+
| *Volume 2: Release* | 1999 | 38 |
+--------------------------------------------------------------------------------------------------------------+------+----------------------+
| *Volume 3: Further in Time* | 2001 | 77 |
+--------------------------------------------------------------------------------------------------------------+------+----------------------+
| *Seed* | 2003 | --- |
+--------------------------------------------------------------------------------------------------------------+------+----------------------+
| *Volume 5: Anatomic* | 2005 | --- |
+--------------------------------------------------------------------------------------------------------------+------+----------------------+
| *The Source* | 2016 | 86 |
+--------------------------------------------------------------------------------------------------------------+------+----------------------+
| *Flight* | 2018 | --- |
+--------------------------------------------------------------------------------------------------------------+------+----------------------+
| *OVA* | 2024 | --- |
+--------------------------------------------------------------------------------------------------------------+------+----------------------+
: List of studio albums, with selected chart positions
### Other albums {#other_albums}
- *Pod* (remix album) (2004)
- *Capture (1995--2010)* (2010) (compilation) No. 14 NZ
They also recorded the soundtrack for the PC game *Magic and Mayhem*, released in 1998
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This page lists some links to **ancient philosophy**, namely philosophical thought extending as far as early post-classical history (c. 600 CE).
## Overview
Genuine philosophical thought, depending upon original individual insights, arose in many cultures roughly contemporaneously. Karl Jaspers termed the intense period of philosophical development beginning around the 7th century BCE and concluding around the 3rd century BCE an Axial Age in human thought.
In Western philosophy, the spread of Christianity in the Roman Empire marked the ending of Hellenistic philosophy and ushered in the beginnings of medieval philosophy, whereas in the Middle East, the spread of Islam through the Arab Empire marked the end of Old Iranian philosophy and ushered in the beginnings of early Islamic philosophy.
## Ancient Greek and Roman philosophy {#ancient_greek_and_roman_philosophy}
### Philosophers
#### Pre-Socratic philosophers {#pre_socratic_philosophers}
- Milesian School
: Thales (624 -- c 546 BCE)
: Anaximander (610 -- 546 BCE)
: Anaximenes of Miletus (c. 585 -- c. 525 BCE)
- Pythagoreans
: Pythagoras (582 -- 496 BCE)
: Philolaus (470 -- 380 BCE)
: Alcmaeon of Croton
: Archytas (428 -- 347 BCE)
- Heraclitus (535 -- 475 BCE)
- Eleatic School
: Xenophanes (570 -- 470 BCE)
: Parmenides (510 -- 440 BCE)
: Zeno of Elea (490 -- 430 BCE)
: Melissus of Samos (c. 470 BCE -- ?)
- Pluralists
: Empedocles (490 -- 430 BCE)
: Anaxagoras (500 -- 428 BCE)
- Atomists
: Leucippus (first half of 5th century BCE)
: Democritus (460 -- 370 BCE)
: Metrodorus of Chios (4th century BCE)
- Pherecydes of Syros (6th century BCE)
- Sophists
: Protagoras (490 -- 420 BCE)
: Gorgias (487 -- 376 BCE)
: Antiphon (480 -- 411 BCE)
: Prodicus (465/450 -- after 399 BCE)
: Hippias (middle of the 5th century BCE)
: Thrasymachus (459 -- 400 BCE)
: Callicles
: Critias
: Lycophron
- Diogenes of Apollonia (c. 460 BCE -- ?)
#### Classical Greek philosophers {#classical_greek_philosophers}
- Socrates (469 -- 399 BCE)
- Euclid of Megara (450 -- 380 BCE)
- Antisthenes (445 -- 360 BCE)
- Aristippus (435 -- 356 BCE)
- Plato (428 -- 347 BCE)
- Speusippus (407 -- 339 BCE)
- Diogenes of Sinope (400 -- 325 BCE)
- Xenocrates (396 -- 314 BCE)
- Aristotle (384 -- 322 BCE)
- Stilpo (380 -- 300 BCE)
- Theophrastus (370 -- 288 BCE)
#### Hellenistic philosophy {#hellenistic_philosophy}
- Pyrrho (365 -- 275 BCE)
- Epicurus (341 -- 270 BCE)
- Metrodorus of Lampsacus (the younger) (331 -- 278 BCE)
- Zeno of Citium (333 -- 263 BCE)
- Cleanthes (c. 330 -- c. 230 BCE)
- Timon (320 -- 230 BCE)
- Arcesilaus (316 -- 232 BCE)
- Menippus (3rd century BCE)
- Archimedes (c. 287 -- 212 BCE)
- Chrysippus (280 -- 207 BCE)
- Carneades (214 -- 129 BCE)
- Clitomachus (187 -- 109 BCE)
- Metrodorus of Stratonicea (late 2nd century BCE)
- Philo of Larissa (160 -- 80 BCE)
- Posidonius (135 -- 51 BCE)
- Antiochus of Ascalon (130 -- 68 BCE)
- Aenesidemus (1st century BCE)
- Agrippa (1st century CE)
### Hellenistic schools of thought {#hellenistic_schools_of_thought}
- Academic skepticism
- Cynicism
- Cyrenaicism
- Eclecticism
- Epicureanism
- Middle Platonism
- Neo-Platonism
- Neopythagoreanism
- Peripatetic School
- Pyrrhonism
- Stoicism
- Sophism
### Early Roman and Christian philosophy {#early_roman_and_christian_philosophy}
- Neoplatonism in Christianity
- School of the Sextii
### Philosophers during Roman times {#philosophers_during_roman_times}
- Cicero (106 -- 43 BCE)
- Lucretius (94 -- 55 BCE)
- Seneca (4 BCE -- 65 CE)
- Musonius Rufus (30 -- 100 CE)
- Plutarch (45 -- 120 CE)
- Epictetus (55 -- 135 CE)
- Favorinus (c. 80 -- c. 160 CE)
- Marcus Aurelius (121 -- 180 CE)
- Clement of Alexandria (150 -- 215 CE)
- Alcinous (philosopher) (2nd century CE)
- Sextus Empiricus (3rd century CE)
- Alexander of Aphrodisias (3rd century CE)
- Ammonius Saccas (3rd century CE)
- Plotinus (205 -- 270 CE)
- Porphyry (232 -- 304 CE)
- Iamblichus (242 -- 327 CE)
- Themistius (317 -- 388 CE)
- Ambrose (340 -- 397 CE)
- Hypatia of Alexandria (350 -- 415 CE)
- Augustine of Hippo (354 -- 430 CE)
- Proclus (411 -- 485 CE)
- Damascius (462 -- 540 CE)
- Boethius (472 -- 524 CE)
- Simplicius of Cilicia (490 -- 560 CE)
- John Philoponus (490 -- 570 CE)
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## Ancient Iranian philosophy {#ancient_iranian_philosophy}
`{{Main article|Iranian philosophy}}`{=mediawiki} See also: *Dualism, Dualism (philosophy of mind)*
While there are ancient relations between the Indian Vedas and the Iranian Avesta, the two main families of the Indo-Iranian philosophical traditions were characterized by fundamental differences in their implications for the human being\'s position in society and their view of man\'s role in the universe. The first charter of human rights by Cyrus the Great as understood in the Cyrus cylinder is often seen as a reflection of the questions and thoughts expressed by Zarathustra and developed in Zoroastrian schools of thought of the Achaemenid Era of Iranian history.
### Schools of thought {#schools_of_thought}
Ideas and tenets of Zoroastrian schools of Early Persian philosophy are part of many works written in Middle Persian and of the extant scriptures of the Zoroastrian religion in Avestan language. Among these are treatises such as the Shikand-gumanic Vichar by Mardan-Farrux Ohrmazddadan, selections of Denkard, Wizidagīhā-ī Zātspram (\"Selections of Zātspram\") as well as older passages of the book Avesta, the Gathas which are attributed to Zarathustra himself and regarded as his \"direct teachings\".
#### Zoroastrianism
- Zarathustra
- Jamasp
- Ostanes
- Mardan-Farrux Ohrmazddadan
- Adurfarnbag Farroxzadan
- Adurbad Emedan
- *Avesta*
- *Gathas*
Anacharsis
#### Pre-Manichaean thought {#pre_manichaean_thought}
- Bardesanes
#### Manichaeism
- Mani (c. 216 -- 276 CE)
- Ammo
#### Mazdakism
- Mazdak the Elder
- Mazdak (died c. 524 or 528 CE)
#### Zurvanism
- Aesthetic Zurvanism
- Materialist Zurvanism
- Fatalistic Zurvanism
### Philosophy and the Empire {#philosophy_and_the_empire}
- Political philosophy
- Tansar
- University of Gundishapur
- Borzouye
- Bakhtshooa Gondishapuri
- Emperor Khosrau\'s philosophical discourses
- Paul the Persian
### Literature
- Pahlavi literature
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## Ancient Jewish philosophy {#ancient_jewish_philosophy}
- Qohelet (c. 450-180 BCE)
- Pseudo-Aristeas (c. 2nd century BCE)
- Ben Sira (fl. 180--175 BCE)
- Aristobulus of Alexandria (181--124 BCE)
- Philo of Alexandria (30 BCE -- 45 CE)
- Wisdom of Solomon (c. 1st century BCE - 1st century CE)
- 4 Maccabees (c. 1st century CE)
- Rabbi Akiva (c. 40 -- c. 137 CE)
## Ancient Indian philosophy {#ancient_indian_philosophy}
The **ancient Indian philosophy** is a fusion of two ancient traditions: the Vedic tradition and the śramaṇa tradition.
### Vedic philosophy {#vedic_philosophy}
Indian philosophy begins with the *Vedas* wherein questions pertaining to laws of nature, the origin of the universe, and the place of man in it are asked. In the famous Rigvedic *Hymn of Creation* (Nasadiya Sukta) the poet asks:
: \"Whence all creation had its origin,
: he, whether he fashioned it or whether he did not,
: he, who surveys it all from highest heaven,
: he knows---or maybe even he does not know.\"
In the Vedic view, creation is ascribed to the self-consciousness of the primeval being (*Purusha*). This leads to the inquiry into *the one being* that underlies the diversity of empirical phenomena and the origin of all things. Cosmic order is termed *rta* and causal law by *karma*. Nature (*prakriti*) is taken to have three qualities (*sattva*, *rajas*, and *tamas*).
- Vedas
- Upanishads
- Hindu philosophy
### Sramana philosophy {#sramana_philosophy}
Jainism and Buddhism are a continuation of the Sramana school of thought. The Sramanas cultivated a pessimistic worldview of the samsara as full of suffering and advocated renunciation and austerities. They laid stress on philosophical concepts like Ahimsa, Karma, Jnana, Samsara and Moksa. Cārvāka (Sanskrit: चार्वाक) (atheist) philosophy, also known as Lokāyata, it is a system of Hindu philosophy that assumes various forms of philosophical skepticism and religious indifference. It is named after its founder, Cārvāka, author of the Bārhaspatya-sūtras.
### Classical Indian philosophy {#classical_indian_philosophy}
In classical times, these inquiries were systematized in six schools of philosophy. Some of the questions asked were:
- What is the ontological nature of consciousness?
- How is cognition itself experienced?
- Is mind (*chit*) intentional or not?
- Does cognition have its own structure?
The six schools of Indian philosophy are:
- Nyaya
- Vaisheshika
- Samkhya
- Yoga
- Mimamsa (Purva Mimamsa)
- Vedanta (Uttara Mimamsa)
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## Ancient Indian philosophy {#ancient_indian_philosophy}
### Ancient Indian philosophers {#ancient_indian_philosophers}
#### 1st millennium BCE {#st_millennium_bce}
- Parashara -- writer of *Viṣṇu Purāṇa*.
#### Philosophers of Vedic Age (c. 1500 -- c. 600 BCE) {#philosophers_of_vedic_age_c._1500_c._600_bce}
- Rishi Narayana -- seer of the Purusha Sukta of the Rig Veda.
- Seven Rishis -- Atri, Bharadwaja, Gautama, Jamadagni, Kasyapa, Vasishtha, Viswamitra.
- Other Vedic Rishis -- Gritsamada, Sandilya, Kanva etc.
- Rishaba -- Rishi mentioned in Rig Veda and later in several Puranas, and believed by Jains to be the first official religious guru of Jainism, as accredited by later followers.
- Yajnavalkya -- one of the Vedic sages, greatly influenced Buddhistic thought.
- Lopamudra
- Gargi Vachaknavi
- Maitreyi
- Parshvanatha
- Ghosha
- Angiras -- one of the seers of the Atharva Veda and author of Mundaka Upanishad.
- Uddalaka Aruni -- an Upanishadic sage who authored major portions of Chāndogya Upaniṣad.
- Ashvapati -- a King in the Later Vedic age who authored Vaishvanara Vidya of Chāndogya Upaniṣad.
- Ashtavakra -- an Upanishadic Sage mentioned in the Mahabharata, who authored Ashtavakra Gita.
#### Philosophers of Axial Age (600--185 BCE) {#philosophers_of_axial_age_600185_bce}
- Gotama (c. 600 BCE), logician, author of Nyaya Sutra
- Kanada (c. 600 BCE), founded the philosophical school of Vaisheshika, gave theory of atomism
- Mahavira (599--527 BCE) -- heavily influenced Jainism, the 24th Tirthankara of Jainism.
- Purana Kassapa
- Ajita Kesakambali
- Payasi
- *Makkhali Gośāla*
- *Sañjaya Belaṭṭhiputta*
- Mahavira
- Dandamis
- Nagasena
- Lakulisha
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- Pakudha Kaccayana
- Pāṇini (520--460 BCE), grammarian, author of Ashtadhyayi
- Kapila (c. 500 BCE), proponent of the Samkhya system of philosophy.
- Badarayana (lived between 500 BCE and 400 BCE) -- Author of Brahma Sutras.
- Jaimini (c. 400 BCE), author of Purva Mimamsa Sutras.
- Pingala (c. 500 BCE), author of the *Chandas shastra*
- Gautama Buddha (c. 480 -- c. 400 BCE), founder of Buddhist school of thought
- Śāriputra
- Chanakya (c. 350 -- c. 275 BCE), author of Arthashastra, professor (acharya) of political science at the Takshashila University
- Patañjali (c. 200 BCE), developed the philosophy of Raja Yoga in his Yoga Sutras.
- Shvetashvatara -- Author of earliest textual exposition of a systematic philosophy of Shaivism.
#### Philosophers of Golden Age (184 BCE -- 600 CE) {#philosophers_of_golden_age_184_bce_600_ce}
- Aśvaghoṣa, believed to have been the first Sanskrit dramatist, and is considered the greatest Indian poet before Kālidāsa
- Vatsyana, known for \"Kama Sutra\"
- Samantabhadra, a proponent of the Jaina doctrine of Anekantavada
- Isvarakrsna
- Aryadeva, a student of Nagarjuna and contributed significantly to the Madhyamaka
- Dharmakirti
- Haribhadra
- Pujyapada
- Buddhaghosa
- Kamandaka
- Maticandra
- Prashastapada
- Bhāviveka
- Dharmapala
- Udyotakara
- Gaudapada
- Valluvar (c. 5th century CE), wrote the Kural text, a Tamil-language treatise on morality and secular ethics
- Dignāga (c. 500), one of the founders of Buddhist school of Indian logic
- Asanga (c. 300), exponent of the Yogacara
- Bhartrihari (c. 450--510 CE), early figure in Indic linguistic theory
- Bodhidharma (c. 440--528 CE), founder of the Zen school of Buddhism
- Siddhasenadivākarasuri (5th century CE), Jain logician and author of important works in Sanskrit and Prakrit, such as Nyāyāvatāra (on logic) and Sanmatisūtra (dealing with the seven Jaina standpoints, knowledge and the objects of knowledge)
- Vasubandhu (c. 300 CE), one of the main founders of the Indian Yogacara school
- Kundakunda (2nd century CE), exponent of Jain mysticism and Jain nayas dealing with the nature of the soul and its contamination by matter, author of Pañcāstikāyasāra (Essence of the Five Existents), the Pravacanasāra (Essence of the Scripture) and the Samayasāra (Essence of the Doctrine)
- Nagarjuna (c. 150 -- 250 CE), the founder of the Madhyamaka (Middle Path) school of Mahāyāna Buddhism
- Umāsvāti or Umasvami (2nd century CE), author of first Jain work in Sanskrit, Tattvārthasūtra, expounding the Jain philosophy in a most systematized form acceptable to all sects of Jainism
- Adi Shankara -- philosopher and theologian, most renowned exponent of the Advaita Vedanta school of philosophy
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## Ancient Chinese philosophy {#ancient_chinese_philosophy}
Chinese philosophy is the dominant philosophical thought in China and other countries within the East Asian cultural sphere that share a common language, including Japan, Korea, and Vietnam.
### Schools of thought {#schools_of_thought_1}
#### Hundred Schools of Thought {#hundred_schools_of_thought}
The Hundred Schools of Thought were philosophers and schools that flourished from the 6th century to 221 BCE, an era of significant cultural and intellectual expansion in China. Even though this period -- known in its earlier part as the Spring and Autumn period and the Warring States period -- in its latter part was fraught with chaos and bloody battles, it is also known as the Golden Age of Chinese philosophy because a broad range of thoughts and ideas were developed and discussed freely. The thoughts and ideas discussed and refined during this period have profoundly influenced lifestyles and social consciousness up to the present day in East Asian countries. The intellectual society of this era was characterized by itinerant scholars, who were often employed by various state rulers as advisers on the methods of government, war, and diplomacy. This period ended with the rise of the Qin dynasty and the subsequent purge of dissent. The Book of Han lists ten major schools, they are:
- Confucianism, which teaches that human beings are teachable, improvable, and perfectible through personal and communal endeavors, especially including self-cultivation and self-creation. The main idea of Confucianism is the cultivation of virtue and the development of moral perfection. Confucianism holds that one should give up one\'s life, if necessary, either passively or actively, for the sake of upholding the cardinal moral values of *ren* and *yi*.
- Legalism. Often compared with Machiavelli, and foundational for the traditional Chinese bureaucratic empire, the Legalists examined administrative methods, emphasizing a realistic consolidation of the wealth and power of autocrat and state.
- Taoism (also called Daoism), a philosophy which emphasizes the Three Jewels of the Tao: compassion, moderation, and humility, while Taoist thought generally focuses on nature, the relationship between humanity and the cosmos; health and longevity; and wu wei (action through inaction). Harmony with the Universe, or the source thereof (Tao), is the intended result of many Taoist rules and practices.
- Mohism, which advocated the idea of universal love: Mozi believed that \"everyone is equal before heaven\" and that people should seek to imitate heaven by engaging in the practice of collective love. His epistemology can be regarded as primitive materialist empiricism; he believed that human cognition ought to be based on one\'s perceptions -- one\'s sensory experiences, such as sight and hearing -- instead of imagination or internal logic, elements founded on the human capacity for abstraction. Mozi advocated frugality, condemning the Confucian emphasis on ritual and music, which he denounced as extravagant.
- Naturalism, the School of Naturalists or the Yin-yang school, which synthesized the concepts of yin and yang and the Five Elements; Zou Yan is considered the founder of this school.
- Agrarianism, or the School of Agrarianism, which advocated peasant utopian communalism and egalitarianism. The Agrarians believed that Chinese society should be modeled around that of the early sage king Shen Nong, a folk hero which was portrayed in Chinese literature as \"working in the fields, along with everyone else, and consulting with everyone else when any decision had to be reached.\"
- The Logicians or the School of Names, which focused on definition and logic. It is said to have parallels with that of the Ancient Greek sophists or dialecticians. The most notable Logician was Gongsun Longzi.
- The School of Diplomacy or School of Vertical and Horizontal \[Alliances\], which focused on practical matters instead of any moral principle, stressed political and diplomatic tactics, debate, and lobbying skills. Scholars from this school were good orators, debaters, and tacticians.
- The Miscellaneous School, which integrated teachings from different schools; for instance, Lü Buwei found scholars from different schools to write a book called Lüshi Chunqiu cooperatively. This school tried to integrate the merits of various schools and avoid their perceived flaws.
- The School of \"Minor-talks\" was not a unique school of thought but a philosophy constructed of all the thoughts discussed by and originated from ordinary people on the street.
- Another group is the School of the Military that studied strategy and the philosophy of war; Sunzi and Sun Bin were influential leaders. However, this school was not one of the \"Ten Schools\" defined by Hanshu.
#### Early Imperial China {#early_imperial_china}
The founder of the Qin dynasty, who implemented Legalism as the official philosophy, quashed Mohist and Confucianist schools. Legalism remained influential until the emperors of the Han dynasty adopted Daoism and later Confucianism as official doctrine. These latter two became the determining forces of Chinese thought until the introduction of Buddhism.
Confucianism was particularly strong during the Han dynasty, whose greatest thinker was Dong Zhongshu, who integrated Confucianism with the thoughts of the Zhongshu School and the theory of the Five Elements. He also was a promoter of the New Text school, which considered Confucius as a divine figure and a spiritual ruler of China, who foresaw and started the evolution of the world towards the Universal Peace. In contrast, there was an Old Text school that advocated the use of Confucian works written in ancient language (from this comes the denomination *Old Text*) that were so much more reliable. In particular, they refuted the assumption of Confucius as a godlike figure and considered him as the greatest sage, but simply a human and mortal.
The 3rd and 4th centuries saw the rise of the *Xuanxue* (mysterious learning), also called *Neo-Taoism*. The most influential philosophers of this movement were Wang Bi, Xiang Xiu and Guo Xiang. The main question of this school was whether Being came before Not-Being (in Chinese, *ming* and *wuming*). A peculiar feature of these Taoist thinkers, like the Seven Sages of the Bamboo Grove, was the concept of *feng liu* (lit. wind and flow), a sort of romantic spirit which encouraged following the natural and instinctive impulse.
Buddhism arrived in China around the 1st century AD, but it was not until the Northern and Southern, Sui and Tang dynasties that it gained considerable influence and acknowledgement. In the beginning, it was considered a sort of Taoist sect, and there was even a theory about Laozi, founder of Taoism, who went to India and taught his philosophy to Buddha. Mahayana Buddhism was far more successful in China than its rival Hinayana, and both Indian schools and local Chinese sects arose from the 5th century. Two chiefly important monk philosophers were Sengzhao and Daosheng. But probably the most influential and original of these schools was the Chan sect, which had an even stronger impact in Japan as the Zen sect.
### Philosophers {#philosophers_1}
- Taoism
- Laozi (5th--4th century BCE)
- Zhuangzi (4th century BCE)
- Zhang Daoling
- Zhang Jue (died 184 CE)
- Ge Hong (283 -- 343 CE)
- Confucianism
- Confucius
- Mencius
- Xun Zi (c. 312 -- 230 BCE)
- Legalism
- Li Si
- Li Kui
- Han Fei
- Mi Su Yu
- Shang Yang
- Shen Buhai
- Shen Dao
- Mohism
- Mozi
- Song Xing
- Logicians
- Deng Xi
- Hui Shi (380--305 BCE)
- Gongsun Long (c. 325 -- c. 250 BCE)
- Agrarianism
- Xu Xing
- Naturalism
- Zou Yan (305 -- 240 BCE)
- Neotaoism
- Wang Bi
- Guo Xiang
- Xiang Xiu
- School of Diplomacy
- Guiguzi
- Su Qin (380 -- 284 BCE)
- Zhang Yi (bef. 329 -- 309 BCE)
- Yue Yi
- Li Yiji (268 -- 204 BCE)
- Military strategy
- Sunzi (c
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In mathematics, a binary relation $R$ on a set $X$ is **antisymmetric** if there is no pair of *distinct* elements of $X$ each of which is related by $R$ to the other. More formally, $R$ is antisymmetric precisely if for all $a, b \in X,$ $\text{if } \,aRb\, \text{ with } \,a \neq b\, \text{ then } \,bRa\, \text{ must not hold},$ or equivalently, $\text{if } \,aRb\, \text{ and } \,bRa\, \text{ then } \,a = b.$ The definition of antisymmetry says nothing about whether $aRa$ actually holds or not for any $a$. An antisymmetric relation $R$ on a set $X$ may be reflexive (that is, $aRa$ for all $a \in X$), irreflexive (that is, $aRa$ for no $a \in X$), or neither reflexive nor irreflexive. A relation is asymmetric if and only if it is both antisymmetric and irreflexive.
## Examples
The divisibility relation on the natural numbers is an important example of an antisymmetric relation. In this context, antisymmetry means that the only way each of two numbers can be divisible by the other is if the two are, in fact, the same number; equivalently, if $n$ and $m$ are distinct and $n$ is a factor of $m,$ then $m$ cannot be a factor of $n.$ For example, 12 is divisible by 4, but 4 is not divisible by 12.
The usual order relation $\,\leq\,$ on the real numbers is antisymmetric: if for two real numbers $x$ and $y$ both inequalities $x \leq y$ and $y \leq x$ hold, then $x$ and $y$ must be equal. Similarly, the subset order $\,\subseteq\,$ on the subsets of any given set is antisymmetric: given two sets $A$ and $B,$ if every element in $A$ also is in $B$ and every element in $B$ is also in $A,$ then $A$ and $B$ must contain all the same elements and therefore be equal: $A \subseteq B \text{ and } B \subseteq A \text{ implies } A = B$ A real-life example of a relation that is typically antisymmetric is \"paid the restaurant bill of\" (understood as restricted to a given occasion). Typically, some people pay their own bills, while others pay for their spouses or friends. As long as no two people pay each other\'s bills, the relation is antisymmetric.
## Properties
Partial and total orders are antisymmetric by definition. A relation can be both symmetric and antisymmetric (in this case, it must be coreflexive), and there are relations which are neither symmetric nor antisymmetric (for example, the \"preys on\" relation on biological species).
Antisymmetry is different from asymmetry: a relation is asymmetric if and only if it is antisymmetric and irreflexive
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**Astrometry** is a branch of astronomy that involves precise measurements of the positions and movements of stars and other celestial bodies. It provides the kinematics and physical origin of the Solar System and this galaxy, the Milky Way.
## History
The history of astrometry is linked to the history of star catalogues, which gave astronomers reference points for objects in the sky so they could track their movements. This can be dated back to the ancient Greek astronomer Hipparchus, who around 190 BC used the catalogue of his predecessors Timocharis and Aristillus to discover Earth\'s precession. In doing so, he also developed the brightness scale still in use today. Hipparchus compiled a catalogue with at least 850 stars and their positions. Hipparchus\'s successor, Ptolemy, included a catalogue of 1,022 stars in his work the *Almagest*, giving their location, coordinates, and brightness.
In the 10th century, the Iranian astronomer Abd al-Rahman al-Sufi carried out observations on the stars and described their positions, magnitudes and star color; furthermore, he provided drawings for each constellation, which are depicted in his *Book of Fixed Stars*. Egyptian mathematician Ibn Yunus observed more than 10,000 entries for the Sun\'s position for many years using a large astrolabe with a diameter of nearly 1.4 metres. His observations on eclipses were still used centuries later in Canadian--American astronomer Simon Newcomb\'s investigations on the motion of the Moon, while his other observations of the motions of the planets Jupiter and Saturn inspired French scholar Laplace\'s *Obliquity of the Ecliptic* and *Inequalities of Jupiter and Saturn*. In the 15th century, the Timurid astronomer Ulugh Beg compiled the *Zij-i-Sultani*, in which he catalogued 1,019 stars. Like the earlier catalogs of Hipparchus and Ptolemy, Ulugh Beg\'s catalogue is estimated to have been precise to within approximately 20 minutes of arc.
In the 16th century, Danish astronomer Tycho Brahe used improved instruments, including large mural instruments, to measure star positions more accurately than previously, with a precision of 15--35 arcsec. Ottoman scholar Taqi al-Din measured the right ascension of the stars at the Constantinople Observatory of Taqi ad-Din using the \"observational clock\" he invented. When telescopes became commonplace, setting circles sped measurements
English astronomer James Bradley first tried to measure stellar parallaxes in 1729. The stellar movement proved too insignificant for his telescope, but he instead discovered the aberration of light and the nutation of the Earth\'s axis. His cataloguing of 3222 stars was refined in 1807 by German astronomer Friedrich Bessel, the father of modern astrometry. He made the first measurement of stellar parallax: 0.3 arcsec for the binary star 61 Cygni. In 1872, British astronomer William Huggins used spectroscopy to measure the radial velocity of several prominent stars, including Sirius.
Being very difficult to measure, only about 60 stellar parallaxes had been obtained by the end of the 19th century, mostly by use of the filar micrometer. Astrographs using astronomical photographic plates sped the process in the early 20th century. Automated plate-measuring machines and more sophisticated computer technology of the 1960s allowed more efficient compilation of star catalogues. Started in the late 19th century, the project Carte du Ciel to improve star mapping could not be finished but made photography a common technique for astrometry. In the 1980s, charge-coupled devices (CCDs) replaced photographic plates and reduced optical uncertainties to one milliarcsecond. This technology made astrometry less expensive, opening the field to an amateur audience.
In 1989, the European Space Agency\'s Hipparcos satellite took astrometry into orbit, where it could be less affected by mechanical forces of the Earth and optical distortions from its atmosphere. Operated from 1989 to 1993, Hipparcos measured large and small angles on the sky with much greater precision than any previous optical telescopes. During its 4-year run, the positions, parallaxes, and proper motions of 118,218 stars were determined with an unprecedented degree of accuracy. A new \"Tycho catalog\" drew together a database of 1,058,332 stars to within 20-30 mas (milliarcseconds). Additional catalogues were compiled for the 23,882 double and multiple stars and 11,597 variable stars also analyzed during the Hipparcos mission. In 2013, the Gaia satellite was launched and improved the accuracy of Hipparcos. The precision was improved by a factor of 100 and enabled the mapping of a billion stars. Today, the catalogue most often used is USNO-B1.0, an all-sky catalogue that tracks proper motions, positions, magnitudes and other characteristics for over one billion stellar objects. During the past 50 years, 7,435 Schmidt camera plates were used to complete several sky surveys that make the data in USNO-B1.0 accurate to within 0.2 arcsec.
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## Applications
Apart from the fundamental function of providing astronomers with a reference frame to report their observations in, astrometry is also fundamental for fields like celestial mechanics, stellar dynamics and galactic astronomy. In observational astronomy, astrometric techniques help identify stellar objects by their unique motions. It is instrumental for keeping time, in that UTC is essentially the atomic time synchronized to Earth\'s rotation by means of exact astronomical observations. Astrometry is an important step in the cosmic distance ladder because it establishes parallax distance estimates for stars in the Milky Way.
Astrometry has also been used to support claims of extrasolar planet detection by measuring the displacement the proposed planets cause in their parent star\'s apparent position on the sky, due to their mutual orbit around the center of mass of the system. Astrometry is more accurate in space missions that are not affected by the distorting effects of the Earth\'s atmosphere. NASA\'s planned Space Interferometry Mission (SIM PlanetQuest) (now cancelled) was to utilize astrometric techniques to detect terrestrial planets orbiting 200 or so of the nearest solar-type stars. The European Space Agency\'s Gaia Mission, launched in 2013, applies astrometric techniques in its stellar census. In addition to the detection of exoplanets, it can also be used to determine their mass.
Astrometric measurements are used by astrophysicists to constrain certain models in celestial mechanics. By measuring the velocities of pulsars, it is possible to put a limit on the asymmetry of supernova explosions. Also, astrometric results are used to determine the distribution of dark matter in the galaxy.
Astronomers use astrometric techniques for the tracking of near-Earth objects. Astrometry is responsible for the detection of many record-breaking Solar System objects. To find such objects astrometrically, astronomers use telescopes to survey the sky and large-area cameras to take pictures at various determined intervals. By studying these images, they can detect Solar System objects by their movements relative to the background stars, which remain fixed. Once a movement per unit time is observed, astronomers compensate for the parallax caused by Earth\'s motion during this time and the heliocentric distance to this object is calculated. Using this distance and other photographs, more information about the object, including its orbital elements, can be obtained. Asteroid impact avoidance is among the purposes.
Quaoar and Sedna are two trans-Neptunian dwarf planets discovered in this way by Michael E. Brown and others at Caltech using the Palomar Observatory\'s Samuel Oschin telescope of 48 in and the Palomar-Quest large-area CCD camera. The ability of astronomers to track the positions and movements of such celestial bodies is crucial to the understanding of the Solar System and its interrelated past, present, and future with others in the Universe.
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## Statistics
A fundamental aspect of astrometry is error correction. Various factors introduce errors into the measurement of stellar positions, including atmospheric conditions, imperfections in the instruments and errors by the observer or the measuring instruments. Many of these errors can be reduced by various techniques, such as through instrument improvements and compensations to the data. The results are then analyzed using statistical methods to compute data estimates and error ranges.
## Computer programs {#computer_programs}
- [XParallax viu (Free application for Windows)](https://sourceforge.net/projects/xparallaxviu/)
- [Astrometrica (Application for Windows)](http://www.astrometrica.at/)
- [Astrometry.net (Online blind astrometry)](https://web.archive.org/web/20101015122353/http://www.astrometry
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The ***Amber Diceless Roleplaying Game*** is a role-playing game created and written by Erick Wujcik, set in the fictional universe created by author Roger Zelazny for his *Chronicles of Amber*. The game is unusual in that no dice are used in resolving conflicts or player actions; instead a simple diceless system of comparative ability, and narrative description of the action by the players and gamemaster, is used to determine how situations are resolved.
*Amber DRPG* was created in the 1980s, and is much more focused on relationships and roleplaying than most of the roleplaying games of that era. Most *Amber* characters are members of the two ruling classes in the *Amber* multiverse, and are much more advanced in matters of strength, endurance, psyche, warfare and sorcery than ordinary beings. This often means that the only individuals who are capable of opposing a character are from his or her family, a fact that leads to much suspicion and intrigue.
## History
Erick Wujcik wanted to design a role-playing game based on *Amber* for West End Games, and they agreed to look at his work. Wujcik intended to integrate the feel of the *Amber* setting from the novels into a role-playing game, and playtested his system for a few months at the Michigan Gaming Center where he decided to try it out as a diceless game. West End Games was not interested in a diceless role-playing game, so Wujcik acquired the role-playing game rights to *Amber* and offered the game to R. Talsorian Games, until he withdrew over creative differences. Wujcik then founded Phage Press, and published *Amber Diceless Role-playing* in 1991.
The original 256-page game book was published in 1991 by Phage Press, covering material from the first five novels (the \"Corwin Cycle\") and some details -- sorcery and the Logrus -- from the remaining five novels (the \"Merlin Cycle\"), in order to allow players to roleplay characters from the Courts of Chaos. Some details were changed slightly to allow more player choice -- for example, players can be full Trump Artists without having walked the Pattern or the Logrus, which Merlin says is impossible; and players\' psychic abilities are far greater than those shown in the books.
A 256-page companion volume, *Shadow Knight*, was published in 1993. This supplemental rule book includes the remaining elements from the Merlin novels, such as Broken Patterns, and allows players to create Constructs such as Merlin\'s Ghostwheel. The book presents the second series of novels not as additions to the series\' continuity but as an example of a roleplaying campaign with Merlin, Luke, Julia, Jurt and Coral as the PCs. The remainder of the book is a collection of essays on the game, statistics for the new characters and an update of the older ones in light of their appearance in the second series, and (perhaps most usefully for GMs) plot summaries of each of the ten books. The book includes some material from the short story \"The Salesman\'s Tale,\" and some unpublished material cut from *Prince of Chaos*, notably Coral\'s pregnancy by Merlin.
Both books were translated into French and published by Jeux Descartes in 1994 and 1995.
A third book, *Rebma*, was promised. Cover art was commissioned and pre-orders were taken, but it was never published. Wujcik also expressed a desire to create a book giving greater detail to the Courts of Chaos. The publishing rights to the *Amber DRPG* games were acquired in 2004 by Guardians of Order, who took over sales of the game and announced their intention to release a new edition of the game. However, no new edition was released before Guardians of Order went out of business in 2006. The two existing books are now out-of-print, but they have been made available as PDF downloads.
In June 2007 a new publishing company, headed by Edwin Voskamp and Eleanor Todd, was formed with the express purpose of bringing *Amber DRPG* back into print. The new company is named *Diceless by Design*.
In May 2010, *Rite Publishing* secured a license from Diceless by Design to use the rules system with a new setting in the creation of a new product to be written by industry and system veteran Jason Durall. The project **Lords of Gossamer & Shadow (Diceless)** was funded via Kickstarter in May 2013. In Sept 2013 the project was completed, and on in Nov 2013 Lords of Gossamer and Shadow (Diceless) was released publicly in full-color Print and PDF, along with additional supplements and continued support.
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## Setting
The game is set in the multiverse described in Zelazny\'s *Chronicles of Amber*. The first book assumes that gamemasters will set their campaigns after the Patternfall war; that is, after the end of the fifth book in the series, *The Courts of Chaos*, but uses material from the following books to describe those parts of Zelazny\'s cosmology that were featured there in more detail. The *Amber* multiverse consists of **Amber**, a city at one pole of the universe wherein is found the Pattern, the symbol of Order; The **Courts of Chaos**, an assembly of worlds at the other pole where can be found the Logrus, the manifestation of Chaos, and the Abyss, the source or end of all reality; and **Shadow**, the collection of all possible universes (shadows) between and around them. Inhabitants of either pole can use one or both of the Pattern and the Logrus to travel through Shadow.
It is assumed that players will portray the children of the main characters from the books -- the ruling family of Amber, known as the Elder Amberites -- or a resident of the Courts. However, since some feel that being the children of the main characters is too limiting, it is fairly common to either start with King Oberon\'s death *before* the book begins and roleplay the Elder Amberites as they vie for the throne; or to populate Amber from scratch with a different set of Elder Amberites. The former option is one presented in the book; the latter is known in the Amber community as an \"Amethyst\" game. A third option is to have the players portray Corwin\'s children, in an Amber-like city built around Corwin\'s pattern; this is sometimes called an \"Argent\" game, since one of Corwin\'s heraldic colours is Silver.
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## System
### Attributes
Characters in *Amber DRPG* are represented by four attributes: *Psyche*, *Strength*, *Endurance* and *Warfare*.
- **Psyche** is used for feats of willpower or magic
- **Strength** is used for feats of strength or unarmed combat
- **Endurance** is used for feats of endurance
- **Warfare** is used for armed combat, from duelling to commanding armies
The attributes run from −25 (normal human level), through −10 (normal level for a denizen of the Courts of Chaos) and 0 (normal level for an inhabitant of Amber), upwards without limit. Scores above 0 are \"ranked\", with the highest score being ranked 1st, the next-highest 2nd, and so on. The character with 1st rank in each attribute is considered \"superior\" in that attribute, being considered to be substantially better than the character with 2nd rank even if the difference in scores is small. All else being equal, a character with a higher rank in an attribute will always win a contest based on that attribute.
#### The Attribute Auction {#the_attribute_auction}
A character\'s ability scores are purchased during character creation in an auction; players get 100 character points, and bid on each attribute in turn. The character who bids the most for an attribute is \"ranked\" first and is considered superior to all other characters in that attribute. Unlike conventional auctions, bids are non-refundable; if one player bids 65 for psyche and another wins with a bid of 66, then the character with 66 is \"superior\" to the character with 65 even though there is only one bid difference. Instead, lower bidding characters are ranked in ascending order according to how much they have bid, the characters becoming progressively weaker in that attribute as they pay less for it. After the auction, players can secretly pay extra points to raise their ranks, but they can only pay to raise their scores to an existing rank. Further, a character with a bid-for rank is considered to have a slight advantage over character with a bought-up rank.
The Auction simulates a \'history\' of competition between the descendants of Oberon for player characters who have not had dozens of decades to get to know each other. Through the competitive Auction, characters may begin the game vying for standings. The auction serves to introduce some unpredictability into character creation without the need to resort to dice, cards, or other randomizing devices. A player may intend, for example, to create a character who is a strong, mighty warrior, but being \"outplayed\" in the auction may result in lower attribute scores than anticipated, therefore necessitating a change of character concept. Since a player cannot control another player\'s bids, and since all bids are non-refundable, the auction involves a considerable amount of strategizing and prioritization by players. A willingness to spend as many points as possible on an attribute may improve your chances of a high ranking, but too reckless a spending strategy could leave a player with few points to spend on powers and objects. In a hotly contested auction, such as for the important attribute of warfare, the most valuable skill is the ability to force one\'s opponents to back down. With two or more equally determined players, this can result in a \"bidding war,\" in which the attribute is driven up by increments to large sums. An alternative strategy is to try to cow other players into submission with a high opening bid. Most players bid low amounts between one and ten points in an initial bid in order to feel out the competition and to save points for other uses. A high enough opening bid could signal a player\'s determination to be first ranked in that attribute, thereby dissuading others from competing.
#### Psyche in *Amber DRPG* compared to the *Chronicles* {#psyche_in_amber_drpg_compared_to_the_chronicles}
Characters with high psyche are presented as having strong telepathic abilities, being able to hypnotise and even mentally dominate any character with lesser psyche with whom they can make eye-contact. This is likely due to three scenes in the *Chronicles*: first, when Eric paralyzes Corwin with an attack across the Trump and refuses to desist because one or the other would be dominated; second, when Corwin faces the demon Strygalldwir, it is able to wrestle mentally with him when their gazes meet; and third, when Fiona is able to keep Brand immobile in the final battle at the Courts of Chaos. However, in general, the books only feature mental battles when there is some reason for mind-to-mind contact (for example, Trump contact) and magic or Trump is involved in all three of the above conflicts, so it is not clear whether Zelazny intended his characters to have such a power; the combination of Brand\'s \"living trump\" powers and his high Psyche (as presented in the roleplaying game) would have guaranteed him victory over Corwin. *Shadow Knight* does address this inconsistency somewhat, by presenting the \"living trump\" abilities as somewhat limited.
### Powers
Characters in *Amber DRPG* have access to the powers seen in the *Chronicles of Amber*: *Pattern*, *Logrus*, *Shape-shifting*, *Trump*, and *magic*.
- **Pattern:** A character who has walked the pattern can walk in shadow to any possible universe, and while there can manipulate probability.
- **Logrus:** A character who has mastered the Logrus can send out Logrus tendrils and pull themselves or objects through shadow.
- **Shape-shifting:** Shape-shifters can alter their physical form and abilities.
- **Trump:** Trump Artists can create Trumps, a sort of tarot card which allows mental communication and travel. The book features Trump portraits of each of the elder Amberites. The trump picture of Corwin is executed in a subtly different style -- and has features very similar to Roger Zelazny\'s.
- **Magic:** Three types of magic are detailed: **Power Words**, with a quick, small effect; **Sorcery**, with pre-prepared spells as in many other game systems; and **Conjuration**, the creation of small objects.
Each of the first four powers is available in an advanced form.
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## System
### Artifacts, Personal shadows and Constructs {#artifacts_personal_shadows_and_constructs}
While a character with Pattern, Logrus or Conjuration can acquire virtually any object, players can choose to spend character points to obtain objects with particular virtues -- unbreakability, or a mind of their own. Since they have paid points for the items, they are a part of the character\'s legend, and cannot lightly be destroyed. Similarly, a character can find any possible universe, but they can spend character points to know of or inhabit shadows which are (in some sense) \"real\" and therefore useful. The expansion, *Shadow Knight*, adds Constructs -- artifacts with connections to shadows.
### Stuff
Unspent character points become **good stuff** -- a good luck for the character. Players are also allowed to overspend (in moderation), with the points becoming **bad stuff** -- bad luck which the Gamemaster should inflict on the character. Stuff governs how non-player characters perceive and respond to the character: characters with good stuff will often receive friendly or helpful reactions, while characters with bad stuff are often treated with suspicion or hostility.
As well as representing luck, stuff can be seen as representing a character\'s outlook on the universe: characters with good stuff seeing the multiverse as a cheerful place, while characters with bad stuff see it as hostile.
### Conflict resolution {#conflict_resolution}
In any given fair conflict between two characters, the character with the higher score in the relevant attribute will eventually win. The key words here are *fair* and *eventually* -- if characters\' ranks are close, and the weaker character has obtained some advantage, then the weaker character can escape defeat or perhaps prevail. Close ranks result in longer contests while greater difference between ranks result in fast resolution. Alternatively, if characters\' attribute ranks are close, the weaker character can try to change the relevant attribute by changing the nature of the conflict. For example, if two characters are wrestling the relevant attribute is Strength; a character could reveal a weapon, changing it to Warfare; they could try to overcome the other character\'s mind using a power, changing it to Psyche; or they could concentrate their strength on defense, changing it to Endurance. If there is a substantial difference between characters\' ranks, the conflict is generally over before the weaker character can react.
### The \"Golden Rule\" {#the_golden_rule}
*Amber DRPG* advises gamemasters to change rules as they see fit, even to the point of adding or removing powers or attributes.
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## Reception
Steve Crow reviewed *Amber Diceless Roleplaying Game* in *White Wolf* #31 (May/June, 1992), rating it a 4 out of 5 and stated that \"It is undoubtedly a game for experienced gamers. While I would not recommend *Amber* to novices, it is a must buy for experienced gamemasters and players looking for new challenges.\"
In the June 1992 edition of *Dragon* (Issue 182), both Lester Smith and Allen Varney published reviews of this game.
- Smith admired the professional production qualities of the 256-page rulebook, noting that because it was Smyth sewn in 32-page signatures, the book would always lie flat when opened. However, he found the typeface difficult to read, and the lack a coherent hierarchy of rules increased the reading difficulty as well. Smith admired the Attribute Auction and point-buy system for skills, and the focus on roleplaying in place of dice-rolling, but he mused that all of the roleplaying would mean \"GMs have to spend quite a bit of time and creative effort coming up with wide-reaching plots for their players to work through. Canned, linear adventures just won\'t serve.\" He concluded by stating that the diceless system is not for every gamer: \"As impressed as I am with the game, do I think it is the \'end-all\' of role-playing games, or that diceless systems are the wave of the future? I\'ll give a firm "No" on both counts\... However, I certainly do think that the *Amber Diceless Roleplaying Game* is destined for great popularity and a niche among the most respected of role-playing game designs.\"
- Allen Varney thought the \"Attribute Auction\" to be \"brilliant and elegant\", but he wondered if character advancement was perhaps too slow to keep marginal players interested. He also believed that being a gamemaster would be \"tough work. Proceed with caution.\" Varney recommended that players need some familiarity with the first five \"Amber\" novels by Zelazny. He concluded, \"The intensity of the *Amber* game indicates \[game designer Erik \] Wujcik is on to something. When success in every action depends on the role and not the roll, players develop a sense of both control and urgency, along with creativity that borders on mania.\"
In Issue 65 of *Challenge*, Dirk DeJong had a good first impression of the game, especially the information provided about the Amber family members and their various flaws and strengths. However he found that \"The biggest problem with this endeavor, and its downfall, is the nature of the conflict systems. First, they are diceless, really diceless, and don\'t involve any sort of random factors at all, aside from those that you can introduce by roleplaying them out. Thus, if you get involved with a character who\'s better than you at sword-fighting, even if only by one point out of 100, you\'re pretty much dead meat, unless you can act your way out.\" DeJong also disagreed with the suggestion that if the referee and players disagreed with a rule to simply remove it from the game. \"I thought the entire idea of using rules and random results was to prevent the type of arguments that I can see arising from this setup.\" DeJong concluded on an ambivalent note, saying, \"If you love Zelazny and the Amber series, jump on it, as this is the premier sourcebook for running an Amber campaign. \[\...\] Personally, I just can\'t get turned on by a system that expects me to either be content with a simple subtraction of numbers to find out who won, or to describe an entire combat blow by blow, just so that I can attempt some trick to win.\"
Loyd Blankenship reviewed *Amber* in *Pyramid* #2 (July/Aug., 1993), and stated that \"*Amber* is a valuable resource to a GM - even if he isn\'t running an *Amber* game. For gamers who have an aspiring actor or actress lurking within their breast, or for someone running a campaign via electronic mail or message base, *Amber* should be given serious consideration.\"
In his 2023 book *Monsters, Aliens, and Holes in the Ground*, RPG historian Stu Horvath noted, \"There hasn\'t been an RPG quite like *Amber*, before or since. Bold though it was, the game didn\'t do very well commercially. The lack of dice became a flashpoint of controversy, with dice enthusiasts dramatically swearing off the game. That\'s a bit ridiculous, but it does get at a key hurdle *Amber* face: People *like* rolling dice. They\'ve been doing it for thousands of years and a significant part of the appeal of RPGs is giving dice, often in sparkly colours, a toss.\"
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## Community
Despite the game\'s out-of-print status, a thriving convention scene exists supporting the game. Amber conventions, known as *Ambercons*, are held yearly in Massachusetts, Michigan, Portland (United States), Milton Keynes (England), Belfast (Northern Ireland) and Modena, Italy. Additionally, Phage Press published 12 volumes of a dedicated *Amber DRPG* magazine called *Amberzine*. Some *Amberzine* issues are still available from Phage Press
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In computing, an **applet** is any small application that performs one specific task that runs within the scope of a dedicated widget engine or a larger program, often as a plug-in. The term is frequently used to refer to a Java applet, a program written in the Java programming language that is designed to be placed on a web page. Applets are typical examples of transient and auxiliary applications that do not monopolize the user\'s attention. Applets are not full-featured application programs, and are intended to be easily accessible.
## History
The word *applet* was first used in 1990 in *PC Magazine*. However, the concept of an applet, or more broadly a small interpreted program downloaded and executed by the user, dates at least to RFC 5 (1969) by Jeff Rulifson, which described the Decode-Encode Language, which was designed to allow remote use of the oN-Line System over ARPANET, by downloading small programs to enhance the interaction. This has been specifically credited as a forerunner of Java\'s downloadable programs in RFC 2555.
## Applet as an extension of other software {#applet_as_an_extension_of_other_software}
In some cases, an applet does not run independently. These applets must run either in a container provided by a host program, through a plugin, or a variety of other applications including mobile devices that support the applet programming model.
### Web-based applets {#web_based_applets}
Applets were used to provide interactive features to web applications that historically could not be provided by HTML alone. They could capture mouse input and also had controls like buttons or check boxes. In response to the user action, an applet could change the provided graphic content. This made applets well suited for demonstration, visualization, and teaching. There were online applet collections for studying various subjects, from physics to heart physiology. Applets were also used to create online game collections that allowed players to compete against live opponents in real-time.
An applet could also be a text area only, providing, for instance, a cross-platform command-line interface to some remote system. If needed, an applet could leave the dedicated area and run as a separate window. However, applets had very little control over web page content outside the applet dedicated area, so they were less useful for improving the site appearance in general (while applets like news tickers or WYSIWYG editors are also known). Applets could also play media in formats that are not natively supported by the browser.
HTML pages could embed parameters that were passed to the applet. Hence, the same applet could appear differently depending on the parameters that were passed.
Examples of Web-based applets include:
- QuickTime movies
- Flash movies
- Windows Media Player applets, used to display embedded video files in Internet Explorer (and other browsers that supported the plugin)
- 3D modeling display applets, used to rotate and zoom a model
- Browser games that were applet-based, though some developed into fully functional applications that required installation.
### Applet Vs. Subroutine {#applet_vs._subroutine}
A larger application distinguishes its applets through several features:
- Applets execute only on the \"client\" platform environment of a system, as contrasted from \"Servlet\". As such, an applet provides functionality or performance beyond the default capabilities of its container (the browser).
- The container restricts applets\' capabilities.
- Applets are written in a language different from the scripting or HTML language that invokes it. The applet is written in a compiled language, whereas the scripting language of the container is an interpreted language, hence the greater performance or functionality of the applet. Unlike a subroutine, a complete web component can be implemented as an applet.
## Java applets {#java_applets}
A Java applet is a Java program that is launched from HTML and run in a web browser. It takes code from server and run in a web browser. It can provide web applications with interactive features that cannot be provided by HTML. Since Java\'s bytecode is platform-independent, Java applets can be executed by browsers running under many platforms, including Windows, Unix, macOS, and Linux. When a Java technology-enabled web browser processes a page that contains an applet, the applet\'s code is transferred to the client\'s system and executed by the browser\'s Java virtual machine. An HTML page references an applet either via the deprecated `{{tag|applet|o}}`{=mediawiki} tag or via its replacement, the `{{tag|object|o}}`{=mediawiki} tag.
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## Security
Recent developments in the coding of applications, including mobile and embedded systems, have led to the awareness of the security of applets.
### Open platform applets {#open_platform_applets}
Applets in an open platform environment should provide secure interactions between different applications. A compositional approach can be used to provide security for open platform applets. Advanced compositional verification methods have been developed for secure applet interactions.
### Java applets {#java_applets_1}
A Java applet contains different security models: unsigned Java applet security, signed Java applet security, and self-signed Java applet security.
### Web-based applets {#web_based_applets_1}
In an applet-enabled web browser, many methods can be used to provide applet security for malicious applets. A malicious applet can infect a computer system in many ways, including denial of service, invasion of privacy, and annoyance. A typical solution for malicious applets is to make the web browser to monitor applets\' activities. This will result in a web browser that will enable the manual or automatic stopping of malicious applets
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**Area** is the measure of a region\'s size on a surface. The area of a plane region or *plane area* refers to the area of a shape or planar lamina, while *surface area* refers to the area of an open surface or the boundary of a three-dimensional object. Area can be understood as the amount of material with a given thickness that would be necessary to fashion a model of the shape, or the amount of paint necessary to cover the surface with a single coat. It is the two-dimensional analogue of the length of a curve (a one-dimensional concept) or the volume of a solid (a three-dimensional concept). Two different regions may have the same area (as in squaring the circle); by synecdoche, \"area\" sometimes is used to refer to the region, as in a \"polygonal area\".
The area of a shape can be measured by comparing the shape to squares of a fixed size. In the International System of Units (SI), the standard unit of area is the square metre (written as m^2^), which is the area of a square whose sides are one metre long. A shape with an area of three square metres would have the same area as three such squares. In mathematics, the unit square is defined to have area one, and the area of any other shape or surface is a dimensionless real number.
There are several well-known formulas for the areas of simple shapes such as triangles, rectangles, and circles. Using these formulas, the area of any polygon can be found by dividing the polygon into triangles. For shapes with curved boundary, calculus is usually required to compute the area. Indeed, the problem of determining the area of plane figures was a major motivation for the historical development of calculus.
For a solid shape such as a sphere, cone, or cylinder, the area of its boundary surface is called the surface area. Formulas for the surface areas of simple shapes were computed by the ancient Greeks, but computing the surface area of a more complicated shape usually requires multivariable calculus.
Area plays an important role in modern mathematics. In addition to its obvious importance in geometry and calculus, area is related to the definition of determinants in linear algebra, and is a basic property of surfaces in differential geometry. In analysis, the area of a subset of the plane is defined using Lebesgue measure, though not every subset is measurable if one supposes the axiom of choice. In general, area in higher mathematics is seen as a special case of volume for two-dimensional regions.
Area can be defined through the use of axioms, defining it as a function of a collection of certain plane figures to the set of real numbers. It can be proved that such a function exists.
## Formal definition {#formal_definition}
An approach to defining what is meant by \"area\" is through axioms. \"Area\" can be defined as a function from a collection M of a special kinds of plane figures (termed measurable sets) to the set of real numbers, which satisfies the following properties:
- For all *S* in *M*, `{{nowrap|''a''(''S'') ≥ 0}}`{=mediawiki}.
- If *S* and *T* are in *M* then so are `{{nowrap|''S'' ∪ ''T''}}`{=mediawiki} and `{{nowrap|''S'' ∩ ''T''}}`{=mediawiki}, and also `{{nowrap|1=''a''(''S''∪''T'') = ''a''(''S'') + ''a''(''T'') − ''a''(''S'' ∩ ''T'')}}`{=mediawiki}.
- If *S* and *T* are in *M* with `{{nowrap|''S'' ⊆ ''T''}}`{=mediawiki} then `{{nowrap|''T'' − ''S''}}`{=mediawiki} is in *M* and `{{nowrap|1=''a''(''T''−''S'') = ''a''(''T'') − ''a''(''S'')}}`{=mediawiki}.
- If a set *S* is in *M* and *S* is congruent to *T* then *T* is also in *M* and `{{nowrap|1=''a''(''S'') = ''a''(''T'')}}`{=mediawiki}.
- Every rectangle *R* is in *M*. If the rectangle has length *h* and breadth *k* then `{{nowrap|1=''a''(''R'') = ''hk''}}`{=mediawiki}.
- Let *Q* be a set enclosed between two step regions *S* and *T*. A step region is formed from a finite union of adjacent rectangles resting on a common base, i.e. `{{nowrap|''S'' ⊆ ''Q'' ⊆ ''T''}}`{=mediawiki}. If there is a unique number *c* such that `{{nowrap|''a''(''S'') ≤ c ≤ ''a''(''T'')}}`{=mediawiki} for all such step regions *S* and *T*, then `{{nowrap|1=''a''(''Q'') = ''c''}}`{=mediawiki}.
It can be proved that such an area function actually exists.
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## Units
Every unit of length has a corresponding unit of area, namely the area of a square with the given side length. Thus areas can be measured in square metres (m^2^), square centimetres (cm^2^), square millimetres (mm^2^), square kilometres (km^2^), square feet (ft^2^), square yards (yd^2^), square miles (mi^2^), and so forth. Algebraically, these units can be thought of as the squares of the corresponding length units.
The SI unit of area is the square metre, which is considered an SI derived unit.
### Conversions
Calculation of the area of a square whose length and width are 1 metre would be:
1 metre × 1 metre = 1 m^2^
and so, a rectangle with different sides (say length of 3 metres and width of 2 metres) would have an area in square units that can be calculated as:
3 metres × 2 metres = 6 m^2^. This is equivalent to 6 million square millimetres. Other useful conversions are:
- 1 square kilometre = 1,000,000 square metres
- 1 square metre = 10,000 square centimetres = 1,000,000 square millimetres
- 1 square centimetre = 100 square millimetres.
#### Non-metric units {#non_metric_units}
In non-metric units, the conversion between two square units is the square of the conversion between the corresponding length units.
: 1 foot = 12 inches,
the relationship between square feet and square inches is
: 1 square foot = 144 square inches,
where 144 = 12^2^ = 12 × 12. Similarly:
- 1 square yard = 9 square feet
- 1 square mile = 3,097,600 square yards = 27,878,400 square feet
In addition, conversion factors include:
- 1 square inch = 6.4516 square centimetres
- 1 square foot = `{{gaps|0.092|903|04}}`{=mediawiki} square metres
- 1 square yard = `{{gaps|0.836|127|36}}`{=mediawiki} square metres
- 1 square mile = `{{gaps|2.589|988|110|336}}`{=mediawiki} square kilometres
### Other units including historical {#other_units_including_historical}
There are several other common units for area. The are was the original unit of area in the metric system, with:
- 1 are = 100 square metres
Though the are has fallen out of use, the hectare is still commonly used to measure land:
- 1 hectare = 100 ares = 10,000 square metres = 0.01 square kilometres
Other uncommon metric units of area include the tetrad, the hectad, and the myriad.
The acre is also commonly used to measure land areas, where
- 1 acre = 4,840 square yards = 43,560 square feet.
An acre is approximately 40% of a hectare.
On the atomic scale, area is measured in units of barns, such that:
- 1 barn = 10^−28^ square meters.
The barn is commonly used in describing the cross-sectional area of interaction in nuclear physics.
In South Asia (mainly Indians), although the countries use SI units as official, many South Asians still use traditional units. Each administrative division has its own area unit, some of them have same names, but with different values. There\'s no official consensus about the traditional units values. Thus, the conversions between the SI units and the traditional units may have different results, depending on what reference that has been used.
Some traditional South Asian units that have fixed value:
- 1 Killa = 1 acre
- 1 Ghumaon = 1 acre
- 1 Kanal = 0.125 acre (1 acre = 8 kanal)
- 1 Decimal = 48.4 square yards
- 1 Chatak = 180 square feet
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## History
### Circle area {#circle_area}
In the 5th century BCE, Hippocrates of Chios was the first to show that the area of a disk (the region enclosed by a circle) is proportional to the square of its diameter, as part of his quadrature of the lune of Hippocrates, but did not identify the constant of proportionality. Eudoxus of Cnidus, also in the 5th century BCE, also found that the area of a disk is proportional to its radius squared.
Subsequently, Book I of Euclid\'s *Elements* dealt with equality of areas between two-dimensional figures. The mathematician Archimedes used the tools of Euclidean geometry to show that the area inside a circle is equal to that of a right triangle whose base has the length of the circle\'s circumference and whose height equals the circle\'s radius, in his book *Measurement of a Circle*. (The circumference is 2`{{pi}}`{=mediawiki}*r*, and the area of a triangle is half the base times the height, yielding the area `{{pi}}`{=mediawiki}*r*^2^ for the disk.) Archimedes approximated the value of `{{pi}}`{=mediawiki} (and hence the area of a unit-radius circle) with his doubling method, in which he inscribed a regular triangle in a circle and noted its area, then doubled the number of sides to give a regular hexagon, then repeatedly doubled the number of sides as the polygon\'s area got closer and closer to that of the circle (and did the same with circumscribed polygons).
### Triangle area {#triangle_area}
### Quadrilateral area {#quadrilateral_area}
In the 7th century CE, Brahmagupta developed a formula, now known as Brahmagupta\'s formula, for the area of a cyclic quadrilateral (a quadrilateral inscribed in a circle) in terms of its sides. In 1842, the German mathematicians Carl Anton Bretschneider and Karl Georg Christian von Staudt independently found a formula, known as Bretschneider\'s formula, for the area of any quadrilateral.
### General polygon area {#general_polygon_area}
The development of Cartesian coordinates by René Descartes in the 17th century allowed the development of the surveyor\'s formula for the area of any polygon with known vertex locations by Gauss in the 19th century.
### Areas determined using calculus {#areas_determined_using_calculus}
The development of integral calculus in the late 17th century provided tools that could subsequently be used for computing more complicated areas, such as the area of an ellipse and the surface areas of various curved three-dimensional objects.
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## Area formulas {#area_formulas}
### Polygon formulas {#polygon_formulas}
For a non-self-intersecting (simple) polygon, the Cartesian coordinates $(x_i, y_i)$ (*i*=0, 1, \..., *n*-1) of whose *n* vertices are known, the area is given by the surveyor\'s formula:
$$A = \frac{1}{2} \Biggl\vert \sum_{i = 0}^{n - 1}( x_i y_{i + 1} - x_{i + 1} y_i) \Biggr\vert$$
where when *i*=*n*-1, then *i*+1 is expressed as modulus *n* and so refers to 0.
#### Rectangles
The most basic area formula is the formula for the area of a rectangle. Given a rectangle with length `{{mvar|l}}`{=mediawiki} and width `{{mvar|w}}`{=mediawiki}, the formula for the area is:
: *lw*}} (rectangle).
That is, the area of the rectangle is the length multiplied by the width. As a special case, as `{{math|''l'' {{=}}`{=mediawiki} *w*}} in the case of a square, the area of a square with side length `{{mvar|s}}`{=mediawiki} is given by the formula:
: *s*^2^}} (square).
The formula for the area of a rectangle follows directly from the basic properties of area, and is sometimes taken as a definition or axiom. On the other hand, if geometry is developed before arithmetic, this formula can be used to define multiplication of real numbers.
#### Dissection, parallelograms, and triangles {#dissection_parallelograms_and_triangles}
Most other simple formulas for area follow from the method of dissection. This involves cutting a shape into pieces, whose areas must sum to the area of the original shape. For an example, any parallelogram can be subdivided into a trapezoid and a right triangle, as shown in figure to the left. If the triangle is moved to the other side of the trapezoid, then the resulting figure is a rectangle. It follows that the area of the parallelogram is the same as the area of the rectangle:
: *bh*}} (parallelogram).
However, the same parallelogram can also be cut along a diagonal into two congruent triangles, as shown in the figure to the right. It follows that the area of each triangle is half the area of the parallelogram:
$$A = \frac{1}{2}bh$$ (triangle). Similar arguments can be used to find area formulas for the trapezoid as well as more complicated polygons.
### Area of curved shapes {#area_of_curved_shapes}
#### Circles
`{{main article|Area of a circle}}`{=mediawiki} The formula for the area of a circle (more properly called the area enclosed by a circle or the area of a disk) is based on a similar method. Given a circle of radius `{{math|''r''}}`{=mediawiki}, it is possible to partition the circle into sectors, as shown in the figure to the right. Each sector is approximately triangular in shape, and the sectors can be rearranged to form an approximate parallelogram. The height of this parallelogram is `{{math|''r''}}`{=mediawiki}, and the width is half the circumference of the circle, or `{{math|π''r''}}`{=mediawiki}. Thus, the total area of the circle is `{{math|π''r''<sup>2</sup>}}`{=mediawiki}:
: π*r*^2^}} (circle).
Though the dissection used in this formula is only approximate, the error becomes smaller and smaller as the circle is partitioned into more and more sectors. The limit of the areas of the approximate parallelograms is exactly `{{math|π''r''<sup>2</sup>}}`{=mediawiki}, which is the area of the circle.
This argument is actually a simple application of the ideas of calculus. In ancient times, the method of exhaustion was used in a similar way to find the area of the circle, and this method is now recognized as a precursor to integral calculus. Using modern methods, the area of a circle can be computed using a definite integral:
$$A \;=\;2\int_{-r}^r \sqrt{r^2 - x^2}\,dx \;=\; \pi r^2.$$
#### Ellipses
The formula for the area enclosed by an ellipse is related to the formula of a circle; for an ellipse with semi-major and semi-minor axes `{{math|''x''}}`{=mediawiki} and `{{math|''y''}}`{=mediawiki} the formula is:
$$A = \pi xy .$$
### Non-planar surface area {#non_planar_surface_area}
Most basic formulas for surface area can be obtained by cutting surfaces and flattening them out (see: developable surfaces). For example, if the side surface of a cylinder (or any prism) is cut lengthwise, the surface can be flattened out into a rectangle. Similarly, if a cut is made along the side of a cone, the side surface can be flattened out into a sector of a circle, and the resulting area computed.
The formula for the surface area of a sphere is more difficult to derive: because a sphere has nonzero Gaussian curvature, it cannot be flattened out. The formula for the surface area of a sphere was first obtained by Archimedes in his work *On the Sphere and Cylinder*. The formula is:
: 4*πr*^2^}} (sphere),
where `{{math|''r''}}`{=mediawiki} is the radius of the sphere. As with the formula for the area of a circle, any derivation of this formula inherently uses methods similar to calculus.
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## Area formulas {#area_formulas}
### General formulas {#general_formulas}
#### Areas of 2-dimensional figures {#areas_of_2_dimensional_figures}
- A triangle: $\tfrac12Bh$ (where *B* is any side, and *h* is the distance from the line on which *B* lies to the other vertex of the triangle). This formula can be used if the height *h* is known. If the lengths of the three sides are known then *Heron\'s formula* can be used: $\sqrt{s(s-a)(s-b)(s-c)}$ where *a*, *b*, *c* are the sides of the triangle, and $s = \tfrac12(a + b + c)$ is half of its perimeter. If an angle and its two included sides are given, the area is $\tfrac12 a b \sin(C)$ where `{{math|''C''}}`{=mediawiki} is the given angle and `{{math|''a''}}`{=mediawiki} and `{{math|''b''}}`{=mediawiki} are its included sides. If the triangle is graphed on a coordinate plane, a matrix can be used and is simplified to the absolute value of $\tfrac12(x_1 y_2 + x_2 y_3 + x_3 y_1 - x_2 y_1 - x_3 y_2 - x_1 y_3)$. This formula is also known as the shoelace formula and is an easy way to solve for the area of a coordinate triangle by substituting the 3 points *(x~1~,y~1~)*, *(x~2~,y~2~)*, and *(x~3~,y~3~)*. The shoelace formula can also be used to find the areas of other polygons when their vertices are known. Another approach for a coordinate triangle is to use calculus to find the area.
- A simple polygon constructed on a grid of equal-distanced points (i.e., points with integer coordinates) such that all the polygon\'s vertices are grid points: $i + \frac{b}{2} - 1$, where *i* is the number of grid points inside the polygon and *b* is the number of boundary points. This result is known as Pick\'s theorem.
#### Area in calculus {#area_in_calculus}
- The area between a positive-valued curve and the horizontal axis, measured between two values *a* and *b* (b is defined as the larger of the two values) on the horizontal axis, is given by the integral from *a* to *b* of the function that represents the curve:
$$A = \int_a^{b} f(x) \, dx.$$
- The area between the graphs of two functions is equal to the integral of one function, *f*(*x*), minus the integral of the other function, *g*(*x*):
$$A = \int_a^{b} ( f(x) - g(x) ) \, dx,$$ where $f(x)$ is the curve with the greater y-value.
- An area bounded by a function $r = r(\theta)$ expressed in polar coordinates is:
$$A = {1 \over 2} \int r^2 \, d\theta.$$
- The area enclosed by a parametric curve $\vec u(t) = (x(t), y(t))$ with endpoints $\vec u(t_0) = \vec u(t_1)$ is given by the line integrals:
$$\oint_{t_0}^{t_1} x \dot y \, dt = - \oint_{t_0}^{t_1} y \dot x \, dt = {1 \over 2} \oint_{t_0}^{t_1} (x \dot y - y \dot x) \, dt$$
: or the *z*-component of
$${1 \over 2} \oint_{t_0}^{t_1} \vec u \times \dot{\vec u} \, dt.$$
: (For details, see `{{slink|Green's theorem|Area calculation}}`{=mediawiki}.) This is the principle of the planimeter mechanical device.
#### Bounded area between two quadratic functions {#bounded_area_between_two_quadratic_functions}
To find the bounded area between two quadratic functions, we first subtract one from the other, writing the difference as $f(x)-g(x)=ax^2+bx+c=a(x-\alpha)(x-\beta)$ where *f*(*x*) is the quadratic upper bound and *g*(*x*) is the quadratic lower bound. By the area integral formulas above and Vieta\'s formula, we can obtain that $A=\frac{(b^2-4ac)^{3/2}}{6a^2}=\frac{a}{6}(\beta-\alpha)^3,\qquad a\neq0.$ The above remains valid if one of the bounding functions is linear instead of quadratic.
#### Surface area of 3-dimensional figures {#surface_area_of_3_dimensional_figures}
- Cone: $\pi r\left(r + \sqrt{r^2 + h^2}\right)$, where *r* is the radius of the circular base, and *h* is the height. That can also be rewritten as $\pi r^2 + \pi r l$ or $\pi r (r + l) \,\!$ where *r* is the radius and *l* is the slant height of the cone. $\pi r^2$ is the base area while $\pi r l$ is the lateral surface area of the cone.
- Cube: $6s^2$, where *s* is the length of an edge.
- Cylinder: $2\pi r(r + h)$, where *r* is the radius of a base and *h* is the height. The $2\pi r$ can also be rewritten as $\pi d$, where *d* is the diameter.
- Prism: $2B + Ph$, where *B* is the area of a base, *P* is the perimeter of a base, and *h* is the height of the prism.
- pyramid: $B + \frac{PL}{2}$, where *B* is the area of the base, *P* is the perimeter of the base, and *L* is the length of the slant.
- Rectangular prism: $2 (\ell w + \ell h + w h)$, where $\ell$ is the length, *w* is the width, and *h* is the height.
#### General formula for surface area {#general_formula_for_surface_area}
The general formula for the surface area of the graph of a continuously differentiable function $z=f(x,y),$ where $(x,y)\in D\subset\mathbb{R}^2$ and $D$ is a region in the xy-plane with the smooth boundary:
: $A=\iint_D\sqrt{\left(\frac{\partial f}{\partial x}\right)^2+\left(\frac{\partial f}{\partial y}\right)^2+1}\,dx\,dy.$
An even more general formula for the area of the graph of a parametric surface in the vector form $\mathbf{r}=\mathbf{r}(u,v),$ where $\mathbf{r}$ is a continuously differentiable vector function of $(u,v)\in D\subset\mathbb{R}^2$ is:
: $A=\iint_D \left|\frac{\partial\mathbf{r}}{\partial u}\times\frac{\partial\mathbf{r}}{\partial v}\right|\,du\,dv.$
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## Area formulas {#area_formulas}
### List of formulas {#list_of_formulas}
+------------------------+--------------------------------------------------------------------+--------------------------------------------------------+
| Shape | Formula | Variables |
+========================+====================================================================+========================================================+
| Square | $A=s^2$ | |
+------------------------+--------------------------------------------------------------------+--------------------------------------------------------+
| Rectangle | $A=ab$ | |
+------------------------+--------------------------------------------------------------------+--------------------------------------------------------+
| Triangle | $A=\frac12bh \,\!$ | |
+------------------------+--------------------------------------------------------------------+--------------------------------------------------------+
| Triangle | $A=\frac12 a b \sin(\gamma)\,\!$ | |
+------------------------+--------------------------------------------------------------------+--------------------------------------------------------+
| Triangle\ | $A=\sqrt{s(s-a)(s-b)(s-c)}\,\!$ | $s =\tfrac 1 2 (a+b+c)$ |
| (Heron\'s formula) | | |
+------------------------+--------------------------------------------------------------------+--------------------------------------------------------+
| Isosceles triangle | $A=\frac{c}{4}\sqrt{4a^2-c^2}$ | |
+------------------------+--------------------------------------------------------------------+--------------------------------------------------------+
| Regular triangle\ | $A=\frac{\sqrt{3}}{4}a^2\,\!$ | |
| (equilateral triangle) | | |
+------------------------+--------------------------------------------------------------------+--------------------------------------------------------+
| Rhombus/Kite | $A=\frac12de$ | |
+------------------------+--------------------------------------------------------------------+--------------------------------------------------------+
| Parallelogram | $A=ah_a\,\!$ | |
+------------------------+--------------------------------------------------------------------+--------------------------------------------------------+
| Trapezoid | $A=\frac{(a+c)h}{2} \,\!$ | |
+------------------------+--------------------------------------------------------------------+--------------------------------------------------------+
| Regular hexagon | $A=\frac{3}{2} \sqrt{3}a^2\,\!$ | |
+------------------------+--------------------------------------------------------------------+--------------------------------------------------------+
| Regular octagon | $A=2(1+\sqrt{2})a^2\,\!$ | |
+------------------------+--------------------------------------------------------------------+--------------------------------------------------------+
| Regular polygon\ | $A=n\frac{ar}{2}=\frac{pr}{2}$\ | $p=na\$ (perimeter)\ |
| ($n$ sides) | $\quad =\tfrac 1 4 na^2\cot(\tfrac \pi n)$\ | $r=\tfrac a 2 \cot(\tfrac \pi n),$\ |
| | $\quad = nr^2 \tan(\tfrac \pi n)$\ | $\tfrac a 2= r\tan(\tfrac \pi n)=R\sin(\tfrac \pi n)$\ |
| | $\quad =\tfrac{1}{4n}p^2\cot(\tfrac \pi n)$\ | $r:$ incircle radius\ |
| | $\quad =\tfrac{1}{2}nR^2 \sin(\tfrac{2\pi}{n}) \,\!$ | $R:$ circumcircle radius |
+------------------------+--------------------------------------------------------------------+--------------------------------------------------------+
| Circle | $A=\pi r^2=\frac{\pi d^2}{4}$\ | 100px |
| | ($d=2r:$ diameter) | |
+------------------------+--------------------------------------------------------------------+--------------------------------------------------------+
| Circular sector | $A=\frac{\theta}{2}r^2=\frac{L \cdot r}{2}\,\!$ | |
+------------------------+--------------------------------------------------------------------+--------------------------------------------------------+
| Ellipse | $A=\pi ab \,\!$ | |
+------------------------+--------------------------------------------------------------------+--------------------------------------------------------+
| Integral | $A=\int_a^b f(x)\mathrm{d}x ,\ f(x)\ge 0$ | |
+------------------------+--------------------------------------------------------------------+--------------------------------------------------------+
| | **Surface area** | |
+------------------------+--------------------------------------------------------------------+--------------------------------------------------------+
| Sphere\ | $A = 4\pi r^2 = \pi d^2$ | |
+------------------------+--------------------------------------------------------------------+--------------------------------------------------------+
| Cuboid | $A = 2(ab+ac+bc)$ | |
+------------------------+--------------------------------------------------------------------+--------------------------------------------------------+
| Cylinder\ | $A = 2 \pi r (r + h)$ | |
| (incl. bottom and top) | | |
+------------------------+--------------------------------------------------------------------+--------------------------------------------------------+
| Cone\ | $A = \pi r (r + \sqrt{r^2+h^2})$ | |
| (incl. bottom) | | |
+------------------------+--------------------------------------------------------------------+--------------------------------------------------------+
| Torus | $A = 4\pi^2 \cdot R \cdot r$ | |
+------------------------+--------------------------------------------------------------------+--------------------------------------------------------+
| Surface of revolution | $A = 2\pi\int_a^b\! f(x)\sqrt{1+\left[f'(x)\right]^2}\mathrm{d}x$\ | |
| | (rotation around the x-axis) | |
+------------------------+--------------------------------------------------------------------+--------------------------------------------------------+
| | | |
+------------------------+--------------------------------------------------------------------+--------------------------------------------------------+
: Additional common formulas for area:
The above calculations show how to find the areas of many common shapes.
The areas of irregular (and thus arbitrary) polygons can be calculated using the \"Surveyor\'s formula\" (shoelace formula).
### Relation of area to perimeter {#relation_of_area_to_perimeter}
The isoperimetric inequality states that, for a closed curve of length *L* (so the region it encloses has perimeter *L*) and for area *A* of the region that it encloses,
$$4\pi A \le L^2,$$
and equality holds if and only if the curve is a circle. Thus a circle has the largest area of any closed figure with a given perimeter.
At the other extreme, a figure with given perimeter *L* could have an arbitrarily small area, as illustrated by a rhombus that is \"tipped over\" arbitrarily far so that two of its angles are arbitrarily close to 0° and the other two are arbitrarily close to 180°.
For a circle, the ratio of the area to the circumference (the term for the perimeter of a circle) equals half the radius *r*. This can be seen from the area formula *πr*^2^ and the circumference formula 2*πr*.
The area of a regular polygon is half its perimeter times the apothem (where the apothem is the distance from the center to the nearest point on any side).
### Fractals
Doubling the edge lengths of a polygon multiplies its area by four, which is two (the ratio of the new to the old side length) raised to the power of two (the dimension of the space the polygon resides in). But if the one-dimensional lengths of a fractal drawn in two dimensions are all doubled, the spatial content of the fractal scales by a power of two that is not necessarily an integer. This power is called the fractal dimension of the fractal.
## Area bisectors {#area_bisectors}
There are an infinitude of lines that bisect the area of a triangle. Three of them are the medians of the triangle (which connect the sides\' midpoints with the opposite vertices), and these are concurrent at the triangle\'s centroid; indeed, they are the only area bisectors that go through the centroid. Any line through a triangle that splits both the triangle\'s area and its perimeter in half goes through the triangle\'s incenter (the center of its incircle). There are either one, two, or three of these for any given triangle.
Any line through the midpoint of a parallelogram bisects the area.
All area bisectors of a circle or other ellipse go through the center, and any chords through the center bisect the area. In the case of a circle they are the diameters of the circle.
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## Optimization
Given a wire contour, the surface of least area spanning (\"filling\") it is a minimal surface. Familiar examples include soap bubbles.
The question of the filling area of the Riemannian circle remains open.
The circle has the largest area of any two-dimensional object having the same perimeter.
A cyclic polygon (one inscribed in a circle) has the largest area of any polygon with a given number of sides of the same lengths.
A version of the isoperimetric inequality for triangles states that the triangle of greatest area among all those with a given perimeter is equilateral.
The triangle of largest area of all those inscribed in a given circle is equilateral; and the triangle of smallest area of all those circumscribed around a given circle is equilateral.
The ratio of the area of the incircle to the area of an equilateral triangle, $\frac{\pi}{3\sqrt{3}}$, is larger than that of any non-equilateral triangle.
The ratio of the area to the square of the perimeter of an equilateral triangle, $\frac{1}{12\sqrt{3}},$ is larger than that for any other triangle
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In Greek mythology, **Actaeon** (`{{IPAc-en|æ|k|ˈ|t|iː|ə|n}}`{=mediawiki}; *Ἀκταίων\]\]* *Aktaiōn*) was the son of the priestly herdsman Aristaeus and Autonoe in Boeotia, and a famous Theban hero. Through his mother he was a member of the ruling House of Cadmus. Like Achilles, in a later generation, he was trained by the centaur Chiron.
He fell to the fatal wrath of Artemis (later his myth was attached to her Roman counterpart Diana), but the surviving details of his transgression vary: \"the only certainty is in what Aktaion suffered, his pathos, and what Artemis did: the hunter became the hunted; he was transformed into a stag, and his raging hounds, struck with a \'wolf\'s frenzy\' (Lyssa), tore him apart as they would a stag.\"
The many depictions both in ancient art and in the Renaissance and post-Renaissance art normally show either the moment of transgression and transformation, or his death by his own hounds.
## Story
Among others, John Heath has observed, \"The unalterable kernel of the tale was a hunter\'s transformation into a deer and his death in the jaws of his hunting dogs. But authors were free to suggest different motives for his death.\" In the version that was offered by the Hellenistic poet Callimachus, which has become the standard setting, Artemis was bathing in the woods when the hunter Actaeon stumbled across her, thus seeing her naked. He stopped and stared, amazed at her ravishing beauty. Once seen, Artemis got revenge on Actaeon: she forbade him speech -- if he tried to speak, he would be changed into a stag -- for the unlucky profanation of her virginity\'s mystery.
\[\[<File:Jean> Mignon - The Transformation of Actaeon - Google Art Project.jpg\|thumb\|*The Transformation of Actaeon*, etching by Jean Mignon, 430 x 574 mm, 1550s?, without its very elaborate frame. Actaeon is shown three times, finally being killed by his hounds.
with frame\]\]
Upon hearing the call of his hunting party, he cried out to them and immediately transformed. At this, he fled deep into the woods, and doing so he came upon a pond and, seeing his reflection, groaned. His own hounds then turned upon him and pursued him, not recognizing him. In an endeavour to save himself, he raised his eyes (and would have raised his arms, had he had them) toward Mount Olympus. The gods did not heed his desperation, and he was torn to pieces. An element of the earlier myth made Actaeon the familiar hunting companion of Artemis, no stranger. In an embroidered extension of the myth, the hounds were so upset with their master\'s death, that Chiron made a statue so lifelike that the hounds thought it was Actaeon.
There are various other versions of his transgression: The Hesiodic *Catalogue of Women* and pseudo-Apollodoran *Bibliotheke* state that his offense was that he was a rival of Zeus for Semele, his mother\'s sister, whereas in Euripides\' *Bacchae* he has boasted that he is a better hunter than Artemis:
+------+--------------------------------------------------------+
| : | : Look at Actaeon\'s wretched fate |
| | : who by the man-eating hounds he had raised, |
| : | : was torn apart, better at hunting |
| | : than Artemis he had boasted to be, in the meadows. |
| : | |
| | |
| : | |
+------+--------------------------------------------------------+
Further materials, including fragments that belong with the Hesiodic *Catalogue of Women* and at least four Attic tragedies, including a *Toxotides* of Aeschylus, have been lost. Diodorus Siculus (4.81.4), in a variant of Actaeon\'s *hubris* that has been largely ignored, has it that Actaeon wanted to marry Artemis. Other authors say the hounds were Artemis\' own; some lost elaborations of the myth seem to have given them all names and narrated their wanderings after his loss. A number of ancient Greek vases depicting the metamorphosis and death of Actaeon include the goddess Lyssa in the scene, infecting his dogs with rabies and setting them against him.
According to the Latin version of the story told by the Roman Ovid having accidentally seen Diana (Artemis) on Mount Cithaeron while she was bathing, he was changed by her into a stag, and pursued and killed by his fifty hounds. This version also appears in Callimachus\' Fifth Hymn, as a mythical parallel to the blinding of Tiresias after he sees Athena bathing. The literary testimony of Actaeon\'s myth is largely lost, but Lamar Ronald Lacy, deconstructing the myth elements in what survives and supplementing it by iconographic evidence in late vase-painting, made a plausible reconstruction of an ancient Actaeon myth that Greek poets may have inherited and subjected to expansion and dismemberment. His reconstruction opposes a too-pat consensus that has an archaic Actaeon aspiring to Semele, a classical Actaeon boasting of his hunting prowess and a Hellenistic Actaeon glimpsing Artemis\' bath. Lacy identifies the site of Actaeon\'s transgression as a spring sacred to Artemis at Plataea where Actaeon was a *hero archegetes* (\"hero-founder\") The righteous hunter, the companion of Artemis, seeing her bathing naked in the spring, was moved to try to make himself her consort, as Diodorus Siculus noted, and was punished, in part for transgressing the hunter\'s \"ritually enforced deference to Artemis\" (Lacy 1990:42).
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## Names of dogs {#names_of_dogs}
Dogs Source
------------------------ -------- --------- ----------------
*Apollodorus* *Ovid* Hyginus
*Ovid* *Other author*
Acamas
Aethon
Agrius
Amarynthus ✓
Arcas ?
Argiodus (Towser) ✓ ✓
Asbolos (Sooty) ✓ ✓
Balius (Dappled) ✓
Borax
Bores ✓
Boreas
Charops
Corus
Cyllopodes
Cyprius ?
Dorceus (Quicksight) ✓ ✓
Draco
Dromas (Racer) ✓ ✓
Dromius
Echnobas ?
Elion ?
Gnosius ?
Eudromus
Haemon
Harpalicus
Harpalos (Snap) ✓ ✓
Hylactor (Babbler) ✓ ✓
Hylaeus (Woodranger) ✓ ✓
Ichneus
Ichnobates (Tracer) ✓ ✓
Labros (Wildtooth) ✓ ✓
Lacon ✓ ✓
Ladon ✓ ✓
Laelaps (Hunter) ✓ ✓
Lampus
Leon
Leucon (Blanche) ✓ ✓
Lynceus ✓
Machimus
Melampus (Blackfoot) ✓ ✓
Melaneus (Blackcoat) ✓ ✓
Obrimus
Ocydromus
Ocythous
Omargus ✓
Nebrophonos (Killbuck) ✓ ✓
Oribasos (Surefoot) ✓ ✓
Pachylus
Pamphagos (Glutton) ✓ ✓
Pterelas (Wingfoot) ✓ ✓
Spartus ✓
Stilbon
Syrus
Theron (Tempest) ✓ ✓
Thoos (Quickfoot) ✓ ✓
Tigris (Tiger) ✓ ✓
Zephyrus
Number 6 22 27
: List of Actaeon\'s dogs
Notes:
- Names of dogs were verified to correspond to the list given in Ovid\'s text where the names were already transliterated.
- ? = Seven listed names of dogs in Hyginus\' *Fabulae*, was probably misread or misinterpreted by later authors because it does not correspond to the exact numbers and names given by Ovid:
- *Arcas* signifies Arcadia, place of origin of three dogs namely Pamphagos, Dorceus and Oribasus
- *Cyprius* means Cyprus, where the dogs Lysisca and Harpalos originated
- *Gnosius* can be read as Knossus in Crete, which signify that Ichnobates was a Knossian breed of dog
- *Echnobas*, *Elion*, *Aura* and *Therodanapis* were probably place names or adjectives defining the characteristics of dogs
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## The \"bed of Actaeon\" {#the_bed_of_actaeon}
In the second century AD, the traveller Pausanias was shown a spring on the road in Attica leading to Plataea from Eleutherae, just beyond Megara \"and a little farther on a rock. It is called the bed of Actaeon, for it is said that he slept thereon when weary with hunting and that into this spring he looked while Artemis was bathing in it.\"
\"As to Actæon there is a tradition at Orchomenus, that a spectre which sat on a stone injured their land. And when they consulted the oracle at Delphi, the god bade them bury in the ground whatever remains they could find of Actæon: he also bade them to make a brazen copy of the spectre and fasten it with iron to the stone. This I have myself seen, and they annually offer funeral rites to Actæon.\"
## Parallels in Akkadian and Ugarit poems {#parallels_in_akkadian_and_ugarit_poems}
In the standard version of the *Epic of Gilgamesh* (tablet vi) there is a parallel, in the series of examples Gilgamesh gives Ishtar of her mistreatment of her serial lovers:
> You loved the herdsman, shepherd and chief shepherd\
> Who was always heaping up the glowing ashes for you,\
> And cooked ewe-lambs for you every day.\
> But you hit him and turned him into a wolf,\
> His own herd-boys hunt him down\
> And his dogs tear at his haunches.
Actaeon, torn apart by dogs incited by Artemis, finds another Near Eastern parallel in the Ugaritic hero Aqht, torn apart by eagles incited by Anath who wanted his hunting bow.
The virginal Artemis of classical times is not directly comparable to Ishtar of the many lovers, but the mytheme of Artemis shooting Orion, was linked to her punishment of Actaeon by T.C.W. Stinton; the Greek context of the mortal\'s reproach to the amorous goddess is translated to the episode of Anchises and Aphrodite. Daphnis too was a herdsman loved by a goddess and punished by her: see Theocritus\' First Idyll.
## Symbolism regarding Actaeon {#symbolism_regarding_actaeon}
In Greek Mythology, Actaeon is widely thought to symbolize ritual human sacrifice in attempt to please a God or Goddess: the dogs symbolize the sacrificers and Actaeon symbolizes the sacrifice.
Actaeon may symbolize human curiosity or irreverence.
The myth is seen by Jungian psychologist Wolfgang Giegerich as a symbol of spiritual transformation and/or enlightenment.
Actaeon often symbolizes a cuckold, as when he is turned into a stag, he becomes \"horned\". This is alluded to in Shakespeare\'s *Merry Wives*, Robert Burton\'s *Anatomy of Melancholy*, and others.
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## Cultural depictions {#cultural_depictions}
The two main scenes are Actaeon surprising Artemis/Diana, and his death. In classical art Actaeon is normally shown as fully human, even as his hounds are killing him (sometimes he has small horns), but in Renaissance art he is often given a deer\'s head with antlers even in the scene with Diana, and by the time he is killed he has at the least this head, and has often completely transformed into the shape of a deer.
- Aeschylus and other tragic poets made use of the story, which was a favourite subject in ancient works of art.
- There is a well-known small marble group in the British Museum illustrative of the story, in gallery 83/84.
- Two paintings by the 16th century painter Titian (*Death of Actaeon* and *Diana and Actaeon*).
- *Actéon*, an operatic pastorale by Marc-Antoine Charpentier.
- Percy Bysshe Shelley suggests a parallel between his alter-ego and Actaeon in his elegy for John Keats, *Adonais*, stanza 31 (\'\[he\] had gazed on Nature\'s naked loveliness/ Actaeon-like, and now he fled astray/ \.../ And his own thoughts, along that rugged way,/ Pursued, like raging hounds, their father and their prey.\')
- The aria \"Oft she visits this lone mountain\" from Purcell\'s *Dido and Aeneas*, first performed in 1689 or earlier.
- Giordano Bruno, *Gli Eroici Furori*.
- In canto V of Giambattista Marino\'s poem Adone the protagonist goes to theater to see a tragedy representing the myth of Actaeon. This episode foreshadows the protagonist\'s violent death at the end of the book.
- In Act I Scene 2 of Jacques Offenbach\'s *Orpheus in the Underworld*, Actaeon is Diana (Artemis)\'s lover, and it is Jupiter who turns him into a stag, which puts Diana off hunting. His story is relinquished at this point, in favour of the other plots.
- Ted Hughes wrote a version of the story in his *Tales from Ovid*.
- Diane and Actéon Pas de Deux from Marius Petipa\'s ballet, *Le Roi Candaule*, to the music by Riccardo Drigo and Cesare Pugni, later incorporated into the second act of *La Esmeralda (ballet)*.
- In *Twelfth Night* by William Shakespeare, Orsino compares his unrequited love for Olivia to the fate of Actaeon. \"O, when mine eyes did see Olivia first, Methought she purged the air of pestilence, That instant was I turned into a hart, and my desires like fell and cruel hounds e\'er since pursue me.\" Act 1 Scene 1.
- In Christopher Marlowe\'s play *Edward II*, courtier Piers Gaveston seeks to entertain his lover, King Edward II of England, by presenting a play based on the Actaeon myth. In Gaveston\'s version, Diane is played by a naked boy holding an olive branch to hide his loins, and it is the boy-Diane who transforms Actaeon into a hart and lets him be devoured by the hounds. Thus, Gaveston\'s (and Marlowe\'s) interpretation adds a strong element of homoeroticism, absent from the original myth.
- Paul Manship in 1925 created a set of copper statute of Diane and Actaeon, which in the Luce Lunder Smithsonian Institution.
- French based collective LFKs and his film/theatre director, writer and visual artist Jean Michel Bruyere produced a series of 600 shorts and \"medium\" films, an interactive 360° installation, *Si poteris narrare licet* (\"if you are able to speak of it, then you may do so\") in 2002, a 3D 360° installation *La Dispersion du Fils* (from 2008 to 2016) and an outdoor performance, *Une Brutalité pastorale* (2000) all about the myth of Diana and Actaeon.
- In Matthew Barney\'s 2019 movie *Redoubt* set in the Sawtooth Mountains of the U.S. state of Idaho and an accompanying traveling art exhibition originating at the Yale University Art Gallery the myth is retold by the visual artist and filmmaker via avenues of his own design.
- Seamus Heaney\'s collection *North* contains an aisling concerning the myth of Diana and Actaeon
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This article is about communications systems in Anguilla.
## Telephone
**Telephones -- main lines in use:** 6,200 (2002)
: *country comparison to the world:* 212
**Telephones -- mobile cellular:** 1,800 (2002)
: *country comparison to the world:* 211
**Telephone system:**\
*Domestic:* Modern internal telephone system\
*International:* EAST CARIBBEAN FIBRE SYSTEM ECFS (cable system)\
*microwave radio relay to island of Saint Martin (Guadeloupe and Netherlands Antilles)*
## Mobile phone (GSM) {#mobile_phone_gsm}
**Mobile phone operators:\
** FLOW (Anguilla) Ltd. -- GSM and UMTS 850 and 1900 MHz, LTE 700 MHz with Island-wide coverage \
Digicel (Anguilla) Ltd. -- GSM and UMTS 850 to 1900 MHz, LTE 700 MHz
**Mobiles:** ? (2007)
## Radio
**Radio broadcast stations:** AM 3, FM 7, shortwave 0 (2007)
Band / Freq. Call Sign Brand City of licence Notes
-------------- ----------- --------------------------------------- ----------------- ----------------------------------------
AM 690 kHz Unknown Caribbean Beacon The Valley Religious broadcaster
AM 1500 kHz Unknown Caribbean Beacon The Valley 2.5 kW repeater
AM 1610 kHz Unknown Caribbean Beacon The Valley 200 kW repeater
FM 92.9 MHz Unknown Klass 92.9 The Valley
FM 93.3 MHz Unknown Rainbow FM The Valley Caribbean Music, News
FM 95.5 MHz Unknown Radio Anguilla The Valley Public broadcaster
FM 97.7 MHz Unknown Heart Beat Radio/Up Beat Radio The Valley 30 kW, Caribbean Music, News
FM 99.3 MHz ZNBR-FM NBR -- New Beginning Radio / Grace FM The Valley 5 kW, Religious broadcaster
FM 100.1 MHz Unknown Caribbean Beacon The Valley Religious broadcaster
FM 100.9 MHz Unknown CBN -- Country Broadcast Network The Valley 3 kW
FM 103.3 MHz Unknown Kool FM The Valley Religious broadcaster, Urban Caribbean
FM 105.1 MHz ZRON-FM Tradewinds Radio The Valley 5 kW, Caribbean Music, News
FM 106.7 MHz unknown VOC -- Voice Of Creation Sachasses Religious broadcaster
FM 107.9 MHz unknown GEM Radio Network The Valley Repeater (Trinidad)
SW 6090 kHz Unknown Caribbean Beacon The Valley Religious
SW 11775 kHz Unknown Caribbean Beacon The Valley Religious
: Radio Stations of Anguilla
**Radios:** 3,000 (1997)
## Television
**Television broadcast stations:** 1 (1997)
**Televisions:** 1,000 (1997)
## Internet
**Internet country code:** .ai (Top level domain)
**Internet Service Providers (ISPs):** 2 (FLOW -- [1](https://archive.today/20200404133519/https://discoverflow.co/anguilla/), Digicel Anguilla -- [2](https://www.digicelgroup.com/ai/en
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**Acoustic theory** is a scientific field that relates to the description of sound waves. It derives from fluid dynamics. See acoustics for the engineering approach.
For sound waves of any magnitude of a disturbance in velocity, pressure, and density we have
:
` \begin{align}`\
` \frac{\partial \rho'}{\partial t} +\rho_0\nabla\cdot \mathbf{v} + \nabla\cdot(\rho'\mathbf{v}) & = 0 \qquad \text{(Conservation of Mass)} \\`\
` (\rho_0+\rho')\frac{\partial \mathbf{v}}{\partial t} + (\rho_0+\rho')(\mathbf{v}\cdot\nabla)\mathbf{v} + \nabla p' & = 0 \qquad \text{(Equation of Motion)}`\
` \end{align}`
In the case that the fluctuations in velocity, density, and pressure are small, we can approximate these as
:
` \begin{align}`\
` \frac{\partial \rho'}{\partial t} +\rho_0\nabla\cdot \mathbf{v} & = 0 \\`\
` \frac{\partial \mathbf{v}}{\partial t} + \frac{1}{\rho_0}\nabla p'& = 0`\
` \end{align}`
Where $\mathbf{v}(\mathbf{x},t)$ is the perturbed velocity of the fluid, $p_0$ is the pressure of the fluid at rest, $p'(\mathbf{x},t)$ is the perturbed pressure of the system as a function of space and time, $\rho_0$ is the density of the fluid at rest, and $\rho'(\mathbf{x}, t)$ is the variance in the density of the fluid over space and time.
In the case that the velocity is irrotational ($\nabla\times \mathbf{v} = 0$), we then have the acoustic wave equation that describes the system:
$$\frac{1}{c^2}\frac{\partial^2 \phi}{\partial t^2} - \nabla^2\phi = 0$$
Where we have
$$\begin{align}
\mathbf{v} & = -\nabla \phi \\
c^2 & = (\frac{\partial p}{\partial \rho})_s\\
p' & = \rho_0\frac{\partial \phi}{\partial t}\\
\rho' & = \frac{\rho_0}{c^2}\frac{\partial \phi}{\partial t}
\end{align}$$
## Derivation for a medium at rest {#derivation_for_a_medium_at_rest}
Starting with the Continuity Equation and the Euler Equation:
:
` \begin{align}`\
` \frac{\partial \rho}{\partial t} +\nabla\cdot \rho\mathbf{v} & = 0 \\`\
` \rho\frac{\partial \mathbf{v}}{\partial t} + \rho(\mathbf{v}\cdot\nabla)\mathbf{v} + \nabla p & = 0`\
` \end{align}`
If we take small perturbations of a constant pressure and density:
:
` \begin{align}`\
` \rho & = \rho_0+\rho' \\`\
` p & = p_0 + p'`\
` \end{align}`
Then the equations of the system are
:
` \begin{align}`\
` \frac{\partial}{\partial t}(\rho_0+\rho') +\nabla\cdot (\rho_0+\rho')\mathbf{v} & = 0 \\`\
` (\rho_0+\rho')\frac{\partial \mathbf{v}}{\partial t} + (\rho_0+\rho')(\mathbf{v}\cdot\nabla)\mathbf{v} + \nabla (p_0+p') & = 0`\
` \end{align}`
Noting that the equilibrium pressures and densities are constant, this simplifies to
:
` \begin{align}`\
` \frac{\partial \rho'}{\partial t} +\rho_0\nabla\cdot\mathbf{v}+\nabla\cdot \rho'\mathbf{v} & = 0 \\`\
` (\rho_0+\rho')\frac{\partial \mathbf{v}}{\partial t} + (\rho_0+\rho')(\mathbf{v}\cdot\nabla)\mathbf{v} + \nabla p' & = 0`\
` \end{align}`
### A Moving Medium {#a_moving_medium}
Starting with
:
` \begin{align}`\
` \frac{\partial \rho'}{\partial t} +\rho_0\nabla\cdot\mathbf{w}+\nabla\cdot \rho'\mathbf{w} & = 0 \\`\
` (\rho_0+\rho')\frac{\partial \mathbf{w}}{\partial t} + (\rho_0+\rho')(\mathbf{w}\cdot\nabla)\mathbf{w} + \nabla p' & = 0`\
` \end{align}`
We can have these equations work for a moving medium by setting $\mathbf{w} = \mathbf{u} + \mathbf{v}$, where $\mathbf{u}$ is the constant velocity that the whole fluid is moving at before being disturbed (equivalent to a moving observer) and $\mathbf{v}$ is the fluid velocity.
In this case the equations look very similar:
:
` \begin{align}`\
` \frac{\partial \rho'}{\partial t} +\rho_0\nabla\cdot\mathbf{v}+\mathbf{u}\cdot\nabla\rho' + \nabla\cdot \rho'\mathbf{v} & = 0 \\`\
` (\rho_0+\rho')\frac{\partial \mathbf{v}}{\partial t} + (\rho_0+\rho')(\mathbf{u}\cdot\nabla)\mathbf{v} + (\rho_0+\rho')(\mathbf{v}\cdot\nabla)\mathbf{v} + \nabla p' & = 0`\
` \end{align}`
Note that setting $\mathbf{u} = 0$ returns the equations at rest.
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## Linearized Waves {#linearized_waves}
Starting with the above given equations of motion for a medium at rest:
:
` \begin{align}`\
` \frac{\partial \rho'}{\partial t} +\rho_0\nabla\cdot\mathbf{v}+\nabla\cdot \rho'\mathbf{v} & = 0 \\`\
` (\rho_0+\rho')\frac{\partial \mathbf{v}}{\partial t} + (\rho_0+\rho')(\mathbf{v}\cdot\nabla)\mathbf{v} + \nabla p' & = 0`\
` \end{align}`
Let us now take $\mathbf{v},\rho',p'$ to all be small quantities.
In the case that we keep terms to first order, for the continuity equation, we have the $\rho'\mathbf{v}$ term going to 0. This similarly applies for the density perturbation times the time derivative of the velocity. Moreover, the spatial components of the material derivative go to 0. We thus have, upon rearranging the equilibrium density:
:
` \begin{align}`\
` \frac{\partial \rho'}{\partial t} +\rho_0\nabla\cdot \mathbf{v} & = 0 \\`\
` \frac{\partial \mathbf{v}}{\partial t} + \frac{1}{\rho_0}\nabla p' & = 0`\
` \end{align}`
Next, given that our sound wave occurs in an ideal fluid, the motion is adiabatic, and then we can relate the small change in the pressure to the small change in the density by
:
` p' = \left(\frac{\partial p}{\partial \rho_{0}}\right)_{s}\rho'`
Under this condition, we see that we now have
:
` \begin{align}`\
` \frac{\partial p'}{\partial t} +\rho_{0}\left(\frac{\partial p}{\partial \rho_0}\right)_{s}\nabla\cdot \mathbf{v} & = 0 \\`\
` \frac{\partial \mathbf{v}}{\partial t} + \frac{1}{\rho_0}\nabla p' & = 0`\
` \end{align}`
Defining the speed of sound of the system:
:
c \\equiv \\sqrt{\\left(\\frac{\\partial p}{\\partial \\rho\_{0}}\\right)\_{s}}
Everything becomes
:
` \begin{align}`\
` \frac{\partial p'}{\partial t} +\rho_0c^2\nabla\cdot \mathbf{v} & = 0 \\`\
` \frac{\partial \mathbf{v}}{\partial t} + \frac{1}{\rho_0}\nabla p' & = 0`\
` \end{align}`
### For Irrotational Fluids {#for_irrotational_fluids}
In the case that the fluid is irrotational, that is $\nabla\times\mathbf{v} = 0$, we can then write $\mathbf{v} = -\nabla\phi$ and thus write our equations of motion as
:
` \begin{align}`\
` \frac{\partial p'}{\partial t} -\rho_0c^2\nabla^2\phi & = 0 \\`\
` -\nabla\frac{\partial\phi}{\partial t} + \frac{1}{\rho_0}\nabla p' & = 0`\
` \end{align}`
The second equation tells us that
:
` p' = \rho_0 \frac{\partial \phi}{\partial t}`
And the use of this equation in the continuity equation tells us that
:
` \rho_0\frac{\partial^2 \phi}{\partial t} -\rho_0c^2\nabla^2\phi = 0`
This simplifies to
:
` \frac{1}{c^2}\frac{\partial^2 \phi}{\partial t^2} -\nabla^2\phi = 0`
Thus the velocity potential $\phi$ obeys the wave equation in the limit of small disturbances. The boundary conditions required to solve for the potential come from the fact that the velocity of the fluid must be 0 normal to the fixed surfaces of the system.
Taking the time derivative of this wave equation and multiplying all sides by the unperturbed density, and then using the fact that $p' = \rho_0 \frac{\partial \phi}{\partial t}$ tells us that
:
` \frac{1}{c^2}\frac{\partial^2 p'}{\partial t^2} -\nabla^2p' = 0`
Similarly, we saw that $p' = \left(\frac{\partial p}{\partial \rho_{0}}\right)_{s}\rho' = c^{2}\rho'$. Thus we can multiply the above equation appropriately and see that
:
` \frac{1}{c^2}\frac{\partial^2 \rho'}{\partial t^2} -\nabla^2\rho' = 0`
Thus, the velocity potential, pressure, and density all obey the wave equation. Moreover, we only need to solve one such equation to determine all other three. In particular, we have
:
` \begin{align}`\
` \mathbf{v} & = -\nabla \phi \\`\
` p' & = \rho_0 \frac{\partial \phi}{\partial t}\\`
\\rho\' & = \\frac{\\rho_0}{c\^2}\\frac{\\partial\\phi}{\\partial t}
` \end{align}`
### For a moving medium {#for_a_moving_medium}
Again, we can derive the small-disturbance limit for sound waves in a moving medium. Again, starting with
:
` \begin{align}`\
` \frac{\partial \rho'}{\partial t} +\rho_0\nabla\cdot\mathbf{v}+\mathbf{u}\cdot\nabla\rho' + \nabla\cdot \rho'\mathbf{v} & = 0 \\`\
` (\rho_0+\rho')\frac{\partial \mathbf{v}}{\partial t} + (\rho_0+\rho')(\mathbf{u}\cdot\nabla)\mathbf{v} + (\rho_0+\rho')(\mathbf{v}\cdot\nabla)\mathbf{v} + \nabla p' & = 0`\
` \end{align}`
We can linearize these into
:
` \begin{align}`\
` \frac{\partial \rho'}{\partial t} +\rho_0\nabla\cdot\mathbf{v}+\mathbf{u}\cdot\nabla\rho' & = 0 \\`\
` \frac{\partial \mathbf{v}}{\partial t} + (\mathbf{u}\cdot\nabla)\mathbf{v} + \frac{1}{\rho_0}\nabla p' & = 0`\
` \end{align}`
#### For Irrotational Fluids in a Moving Medium {#for_irrotational_fluids_in_a_moving_medium}
Given that we saw that
:
` \begin{align}`\
` \frac{\partial \rho'}{\partial t} +\rho_0\nabla\cdot\mathbf{v}+\mathbf{u}\cdot\nabla\rho' & = 0 \\`\
` \frac{\partial \mathbf{v}}{\partial t} + (\mathbf{u}\cdot\nabla)\mathbf{v} + \frac{1}{\rho_0}\nabla p' & = 0`\
` \end{align}`
If we make the previous assumptions of the fluid being ideal and the velocity being irrotational, then we have
:
` \begin{align}`\
` p' & = \left(\frac{\partial p}{\partial \rho_{0}}\right)_{s}\rho' = c^{2}\rho' \\`\
` \mathbf{v} & = -\nabla\phi`\
` \end{align}`
Under these assumptions, our linearized sound equations become
:
` \begin{align}`\
` \frac{1}{c^2}\frac{\partial p'}{\partial t} -\rho_0\nabla^2\phi+\frac{1}{c^2}\mathbf{u}\cdot\nabla p' & = 0 \\`\
` -\frac{\partial}{\partial t}(\nabla\phi) - (\mathbf{u}\cdot\nabla)[\nabla\phi] + \frac{1}{\rho_0}\nabla p' & = 0`\
` \end{align}`
Importantly, since $\mathbf{u}$ is a constant, we have $(\mathbf{u}\cdot\nabla)[\nabla\phi] = \nabla[(\mathbf{u}\cdot\nabla)\phi]$, and then the second equation tells us that
:
` \frac{1}{\rho_0} \nabla p' = \nabla\left[\frac{\partial\phi}{\partial t} + (\mathbf{u}\cdot\nabla)\phi\right]`
Or just that
:
` p' = \rho_{0}\left[\frac{\partial\phi}{\partial t} + (\mathbf{u}\cdot\nabla)\phi\right]`
Now, when we use this relation with the fact that $\frac{1}{c^2}\frac{\partial p'}{\partial t} -\rho_0\nabla^2\phi+\frac{1}{c^2}\mathbf{u}\cdot\nabla p' = 0$, alongside cancelling and rearranging terms, we arrive at
:
` \frac{1}{c^2}\frac{\partial^2 \phi}{\partial t^2} - \nabla^2\phi + \frac{1}{c^2}\frac{\partial}{\partial t}[(\mathbf{u}\cdot\nabla)\phi] + \frac{1}{c^2}\frac{\partial}{\partial t}(\mathbf{u}\cdot\nabla\phi) + \frac{1}{c^2}\mathbf{u}\cdot\nabla[(\mathbf{u}\cdot\nabla)\phi] = 0`
We can write this in a familiar form as
$$\left[\frac{1}{c^2}\left(\frac{\partial}{\partial t} + \mathbf{u}\cdot\nabla\right)^{2} - \nabla^{2}\right]\phi = 0$$
This differential equation must be solved with the appropriate boundary conditions. Note that setting $\mathbf{u}=0$ returns us the wave equation
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The meaning of the word ***American*** in the English language varies according to the historical, geographical, and political context in which it is used. *American* is derived from *America*, a term originally denoting all of the Americas (also called the Western Hemisphere), ultimately derived from the name of the Florentine explorer and cartographer Amerigo Vespucci (1451--1512). In some expressions, it retains this Pan-American sense, but its usage has evolved over time and, for various historical reasons, the word came to denote people or things specifically from the United States of America. In contemporary English, *American* generally refers to persons or things related to the United States of America; among native English speakers this usage is almost universal, with any other use of the term requiring specification. However, some have argued that \"American\" should be widened to also include people or things from anywhere in the American continents.
The word can be used as either an adjective or a noun (viz. a demonym). In adjectival use, it means \"of or relating to the United States\"; for example, \"Elvis Presley was an American singer\" or \"the man prefers American English\". In its noun form, the word generally means a resident or citizen of the U.S., but is also used for someone whose ethnic identity is simply \"American\". The noun is rarely used in English to refer to people not connected to the United States when intending a geographical meaning.`{{Not verified in body|date=July 2023}}`{=mediawiki} When used with a grammatical qualifier, the adjective *American* can mean \"of or relating to the Americas\", as in Latin American or Indigenous American. Less frequently, the adjective can take this meaning without a qualifier, as in \"American Spanish dialects and pronunciation differ by country\" or the names of the Organization of American States and the American Registry for Internet Numbers (ARIN). A third use of the term pertains specifically to the indigenous peoples of the Americas, for instance, \"In the 16th century, many Americans died from imported diseases during the European conquest\", though this usage is rare, as \"indigenous\", \"First Nations\" or \"Amerindian\" are considered less confusing and generally more appropriate.
Compound constructions which indicate a minority ethnic group, such as \"African Americans\" likewise refer exclusively to people in or from the United States of America, as does the prefix \"Americo-\". For instance, the Americo-Liberians and their language Merico derive their name from the fact that they are descended from African-American settlers, i.e. Blacks who were formerly enslaved in the United States of America.
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## Other languages {#other_languages}
French, German, Italian, Japanese, Hebrew, Arabic, and Russian speakers may use cognates of *American* to refer to inhabitants of the Americas or to U.S. nationals. They generally have other terms specific to U.S. nationals, such as the German *US-Amerikaner*, French *étatsunien*, Japanese `{{nihongo||米国人|beikokujin}}`{=mediawiki}, and Italian *statunitense*. These specific terms may be less common than the term *American*.
In French, *états-unien*, *étas-unien* or *étasunien*, from *États-Unis d\'Amérique* (\"United States of America\"), is a rarely used word that distinguishes U.S. things and persons from the adjective *américain*, which denotes persons and things from the United States, but may also refer to \"the Americas\".
Likewise, German\'s use of *U.S.-amerikanisch* and *U.S.-Amerikaner* observe this cultural distinction, solely denoting U.S. things and people. In normal parlance, the adjective \"American\" and its direct cognates are usually used if the context renders the nationality of the person clear. This differentiation is prevalent in German-speaking countries, as indicated by the style manual of the *\[\[Neue Zürcher Zeitung\]\]* (one of the leading German-language newspapers in Switzerland) which dismisses the term *U.S.-amerikanisch* as both \'unnecessary\' and \'artificial\' and recommends replacing it with *amerikanisch*. The respective guidelines of the foreign ministries of Austria, Germany and Switzerland all prescribe *Amerikaner* and *amerikanisch* in reference to the United States for official usage, making no mention of *U.S.-Amerikaner* or *U.S.-amerikanisch*.
Portuguese has *americano*, denoting both a person or thing from the Americas and a U.S. national. For referring specifically to a U.S. national and things, some words used are *estadunidense* (also spelled *estado-unidense*, \"United States person\"), from *Estados Unidos da América*, and *ianque* (\"Yankee\")---both usages exist in Brazil (although \"americano\" is more frequent), but are uncommon in Portugal---but the term most often used, and the only one in Portugal, is *norte-americano*, even though it could, as with its Spanish equivalent, apply to Canadians and Mexicans as well.
In Spanish, *americano* denotes geographic and cultural origin in the New World, as well as (infrequently) a U.S. citizen; the more common term is *estadounidense* (\"United States person\"), which derives from *Estados Unidos de América* (\"United States of America\"). The Spanish term *norteamericano* (\"North American\") is frequently used to refer things and persons from the United States, but this term can also denote people and things from Canada and Mexico. Among Spanish-speakers, North America generally does not include Central America or the Caribbean.
Conversely, in Czech, there is no possibility for disambiguation. *Američan* (m.) and *američanka* (f.) can refer to persons from the United States or from the continents of the Americas, and there is no specific word capable of distinguishing the two meanings. For this reason, the latter meaning is very rarely used, and word *američan(ka)* is used almost exclusively to refer to persons from the United States. The usage is exactly parallel to the English word.
In other languages, however, there is no possibility for confusion. For example, the Chinese word for \"U.S. national\" is `{{Transliteration|zh|měiguórén}}`{=mediawiki} (`{{lang-zh|t=美國人|s=美国人}}`{=mediawiki}) is derived from a word for the United States, `{{Transliteration|zh|měiguó}}`{=mediawiki}, where `{{Transliteration|zh|měi}}`{=mediawiki} is an abbreviation for *Yàměilìjiā* (\"America\") and `{{Transliteration|zh|guó}}`{=mediawiki} is \"country\". The name for the American continents is `{{Transliteration|zh|měizhōu}}`{=mediawiki}, from `{{Transliteration|zh|měi}}`{=mediawiki} plus `{{Transliteration|zh|zhōu}}`{=mediawiki} (\"continent\"). Thus, a `{{Transliteration|zh|měi'''zhōu'''rén}}`{=mediawiki} is an American in the continent sense, and a `{{Transliteration|zh|měi'''guó'''rén}}`{=mediawiki} is an American in the U.S. sense.
Korean and Vietnamese also use unambiguous terms, with Korean having `{{Transliteration|ko|Migug}}`{=mediawiki} (*미국(인)*) for the country versus `{{Transliteration|ko|Amerika}}`{=mediawiki} (*아메리카*) for the continents, and Vietnamese having *Hoa Kỳ* for the country versus *Châu Mỹ* for the continents. Japanese has such terms as well (`{{Transliteration|ja|beikoku(jin)}}`{=mediawiki} \[*米国(人)* versus `{{Transliteration|ja|beishū(jin)}}`{=mediawiki} \[*米洲人*\]), but they are found more in newspaper headlines than in speech, where `{{Transliteration|ja|amerikajin}}`{=mediawiki} predominates.
In Swahili, *Marekani* means specifically the United States, and *Mmarekani* is a U.S. national, whereas the international form *Amerika* refers to the continents, and *Mwamerika* would be an inhabitant thereof. Likewise, the Esperanto word *Ameriko* refers to the continents. For the country there is the term *Usono*. Thus, a citizen of the United States is an *usonano*, whereas an *amerikano* is an inhabitant of the Americas.
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## History
The name *America* was coined by Martin Waldseemüller from *Americus Vesputius*, the Latinized version of the name of Amerigo Vespucci (1454--1512), the Florentine explorer who mapped South America\'s east coast and the Caribbean Sea in the early 16th century. Later, Vespucci\'s published letters were the basis of Waldseemüller\'s 1507 map, which is the first usage of *America*. The adjective *American* subsequently denoted the New World.
In the 16th century, European usage of *American* denoted the native inhabitants of the New World. The earliest recorded use of this term in English is in Thomas Hacket\'s 1568 translation of André Thévet\'s book *France Antarctique*; Thévet himself had referred to the natives as *Ameriques*. In the following century, the term was extended to European settlers and their descendants in the Americas. The earliest recorded use of \"English-American\" dates to 1648, in Thomas Gage\'s *The English-American his travail by sea and land: or, a new survey of the West India\'s*.
In English, *American* was used especially for people in British America. Samuel Johnson, the leading English lexicographer, wrote in 1775, before the United States declared independence: \"That the Americans are able to bear taxation is indubitable.\" The Declaration of Independence of July 1776 refers to \"\[the\] unanimous Declaration of the thirteen united States of America\" adopted by the \"Representatives of the united States of America\" on July 4, 1776. The official name of the country was reaffirmed on November 15, 1777, when the Second Continental Congress adopted the Articles of Confederation, the first of which says, \"The Stile of this Confederacy shall be \'The United States of America\'\". The Articles further state: `{{Blockquote|In Witness whereof we have hereunto set our hands in Congress. Done at Philadelphia in the State of Pennsylvania the ninth day of July in the Year of our Lord One Thousand Seven Hundred and Seventy-Eight, and in the Third Year of the independence of America.}}`{=mediawiki}
Thomas Jefferson, newly elected president in May 1801 wrote, \"I am sure the measures I mean to pursue are such as would in their nature be approved by every American who can emerge from preconceived prejudices; as for those who cannot, we must take care of them as of the sick in our hospitals. The medicine of time and fact may cure some of them.\"
In *The Federalist Papers* (1787--88), Alexander Hamilton and James Madison used the adjective *American* with two different meanings: one political and one geographic; \"the American republic\" in Federalist No. 51 and in Federalist No. 70, and, in Federalist No. 24, Hamilton used *American* to denote the lands beyond the U.S.\'s political borders.
Early official U.S. documents show inconsistent usage; the 1778 Treaty of Alliance with France used \"the United States of North America\" in the first sentence, then \"the said united States\" afterwards; \"the United States of America\" and \"the United States of North America\" derive from \"the United Colonies of America\" and \"the United Colonies of North America\". The Treaty of Peace and Amity of September 5, 1795, between the United States and the Barbary States contains the usages \"the United States of North America\", \"citizens of the United States\", and \"American Citizens\".`{{synthesis inline|date=October 2013}}`{=mediawiki}
U.S. President George Washington, in his 1796 *Farewell Address*, declaimed that \"The name of American, which belongs to you in your national capacity, must always exalt the just pride of patriotism more than any appellation.\" Political scientist Virginia L. Arbery notes that, in his *Farewell Address*:
> \"\...Washington invites his fellow citizens to view themselves now as Americans who, out of their love for the truth of liberty, have replaced their maiden names (Virginians, South Carolinians, New Yorkers, etc.) with that of "American". Get rid of, he urges, "any appellation derived from local discriminations." By defining himself as an American rather than as a Virginian, Washington set the national standard for all citizens. \"Over and over, Washington said that America must be something set apart. As he put it to Patrick Henry, \'In a word, I want an *American* character, that the powers of Europe may be convinced we act for *ourselves* and not for *others*.\'\"
As the historian Garry Wills has noted: \"This was a theme dear to Washington. He wrote to Timothy Pickering that the nation \'must never forget that we are Americans; the remembrance of which will convince us we ought not to be French or English\'.\" Washington\'s countrymen subsequently embraced his exhortation with notable enthusiasm.
This semantic divergence among North American anglophones, however, remained largely unknown in the Spanish-American colonies. In 1801, the document titled *Letter to American Spaniards*---published in French (1799), in Spanish (1801), and in English (1808)---might have influenced Venezuela\'s Act of Independence and its 1811 constitution.
The Latter-day Saints\' Articles of Faith refer to the American continents as where they are to build Zion.
Common short forms and abbreviations are the *United States*, the *U.S.*, the *U.S.A.*, and *America*; colloquial versions include the *U.S. of A.* and *the States*. The term *Columbia* (from the Columbus surname) was a popular name for the U.S. and for the entire geographic Americas; its usage is present today in the District of Columbia\'s name. Moreover, the womanly personification of Columbia appears in some official documents, including editions of the U.S. dollar.
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## Usage at the United Nations {#usage_at_the_united_nations}
Use of the term *American* for U.S. nationals is common at the United Nations, and financial markets in the United States are referred to as \"American financial markets\".
American Samoa, an unincorporated territory of the United States, is a recognized territorial name at the United Nations.
## Cultural views {#cultural_views}
### Canada
Modern Canadians typically refer to people from the United States as *Americans*, though they seldom refer to the United States as *America*; in English they use the terms *the United States*, *the U.S.*, or (informally) *the States* instead. Because of anti-American sentiment or simply national pride, Canadians never apply the term *American* to themselves. Not being an \"American\" is a part of Canadian identity, with many Canadians resenting being referred to as Americans or mistaken for U.S. citizens. This is often due to others\' inability, particularly overseas, to distinguish English-speaking Canadians from Americans, by their accent or other cultural attributes. Some Canadians have protested the use of *American* as a national demonym. People of American origin in Canada are categorized as \"Other North American origins\" by Statistics Canada for purposes of census counts.
### Spain and Hispanic America {#spain_and_hispanic_america}
The use of *American* as a national demonym for U.S. nationals is challenged, primarily by Hispanic Americans. Spanish speakers in Spain and Hispanic America use the term *estadounidense* to refer to people and things from the United States (from *Estados Unidos*), while *americano* refers to the continents as a whole (from *América*). The term *gringo* is also accepted in many parts of Hispanic America to refer to a person or something from the United States; however, this term may be ambiguous in certain parts. Up to and including the 1992 edition, the *Diccionario de la lengua española*, published by the Real Academia Española, did not include the United States definition in the entry for *americano*; this was added in the 2001 edition. The Real Academia Española advised against using *americanos* exclusively for U.S. nationals:
### Portugal and Brazil {#portugal_and_brazil}
Generally, *americano* denotes \"U.S. citizen\" in Portugal. The adjective currently used by the Portuguese press is *norte-americano*.
In Brazil, the term *americano* is used to address both that which pertains to the Americas and that which pertains to the U.S.; the particular meaning is deduced from context. Alternatively, the term *norte-americano* (\"North American\") is also used in more informal contexts, while *estadunidense* (of the U.S.) is the preferred form in academia. Use of the three terms is common in schools, government, and media. The term *América* is used exclusively for the whole continent, and the U.S. is called *Estados Unidos* (\"United States\") or *Estados Unidos da América* (\"United States of America\"), often abbreviated *EUA*.
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## In other contexts {#in_other_contexts}
\"American\" in the 1994 *Associated Press Stylebook* was defined as, \"An acceptable description for a resident of the United States. It also may be applied to any resident or citizen of nations in North or South America.\" Elsewhere, the *AP Stylebook* indicates that \"United States\" must \"be spelled out when used as a noun. Use U.S. (no space) only as an adjective.\"
The entry for \"America\" in *The New York Times Manual of Style and Usage* from 1999 reads: `{{blockquote|[the] terms "America", "American(s)" and "Americas" refer not only to the United States, but to all of North America and South America. They may be used in any of their senses, including references to just the United States, if the context is clear. The countries of the Western Hemisphere are collectively 'the Americas'.}}`{=mediawiki}
Media releases from the Pope and Holy See frequently use \"America\" to refer to the United States, and \"American\" to denote something or someone from the United States.
### International law {#international_law}
At least one international law uses *U.S. citizen* in defining a citizen of the United States rather than *American citizen*; for example, the English version of the North American Free Trade Agreement includes: `{{blockquote|Only air carriers that are "citizens of the United States" may operate aircraft in domestic air service (cabotage) and may provide international scheduled and non-scheduled air service as U.S. air carriers...
Under the Federal Aviation Act of 1958, a "citizen of the United States" means:
:(a) an individual who is a U.S. citizen;
:(b) a partnership in which each member is a U.S. citizen; or
:(c) a U.S. corporation of which the president and at least two-thirds of the board of directors and other managing officers are U.S. citizens, and at least 75 percent of the voting interest in the corporation is owned or controlled by U.S. citizens.<ref>{{cite web | url = http://www.sice.oas.org/trade/nafta/anx1usa.asp | work = North American Free Trade Agreement | title = Annex I: Reservations for Existing Measures and Liberalization Commitments (Chapters 11, 12, and 14) | date = October 7, 1992 | access-date = October 27, 2013 | archive-date = October 29, 2013 | archive-url = https://web.archive.org/web/20131029190838/http://www.sice.oas.org/trade/nafta/anx1usa.asp | url-status = live }}</ref>}}`{=mediawiki}
Many international treaties use the terms *American* and *American citizen*:
- 1796 -- The treaty between the United States and the Dey of the Regency of Algiers on March 7, 1796, protected \"American citizens\".
- 1806 -- The Louisiana Purchase Treaty between France and United States referred to \"American citizens\".
- 1825 -- The treaty between the United States and the Cheyenne tribe refers to \"American citizens\".
- 1848 -- The Treaty of Guadalupe Hidalgo between Mexico and the U.S. uses \"American Government\" to refer to the United States, and \"American tribunals\" to refer to U.S. courts.
- 1858 -- The Treaty of Amity and Commerce between the United States and Japan protected \"American citizens\" and also used \"American\" in other contexts.
- 1898 -- The Treaty of Paris ending the Spanish--American War, known in Spanish as the *Guerra Hispano--Estadounidense* (\"Spain--United States War\") uses \"American\" in reference to United States troops.
- 1966 -- The United States--Thailand Treaty of Amity protects \"Americans\" and \"American corporations\".
### U.S. commercial regulation {#u.s._commercial_regulation}
Products that are labeled, advertised, and marketed in the U.S. as \"Made in the USA\" must be, as set by the Federal Trade Commission (FTC), \"all or virtually all made in the U.S.\" The FTC, to prevent deception of customers and unfair competition, considers an unqualified claim of \"American Made\" to expressly claim exclusive manufacture in the U.S: \"The FTC Act gives the Commission the power to bring law enforcement actions against false or misleading claims that a product is of U.S. origin.\"
## Alternatives
There are a number of alternatives to the demonym *American* as a citizen of the United States that do not simultaneously mean any inhabitant of the Americas. One uncommon alternative is *Usonian*, which usually describes a certain style of residential architecture designed by Frank Lloyd Wright. Other alternatives have also surfaced, but most have fallen into disuse and obscurity. *Merriam-Webster\'s Dictionary of English Usage* says: `{{blockquote|The list contains (in approximate historical order from 1789 to 1939) such terms as Columbian, Columbard, Fredonian, Frede, Unisian, United Statesian, Colonican, Appalacian, Usian, Washingtonian, Usonian, Uessian, U-S-ian, Uesican, United Stater.<ref>{{cite book|title=Merriam-Webster's Dictionary of English Usage|url=https://archive.org/details/merriamwebstersd00merr|url-access=registration|page=[https://archive.org/details/merriamwebstersd00merr/page/88 88]|publisher=Merriam-Webster|year=1994|isbn=9780877791324}}</ref>}}`{=mediawiki} Nevertheless, no alternative to *American* is common
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\[[coins denarius Antoninus Pius Marcus Aurelius.jpg\|upright=1.35\|thumb\|Denarius, struck 140 AD with portrait of Antoninus Pius (obverse) and his adoptive son Marcus Aurelius (reverse). Inscription: ANTONINVS AVG PIVS P. P., TR. P., CO\[N](File:Roman)S. III / AVRELIVS CAES. AVG. PII F. CO\[N\]S.\]\] `{{Nerva–Antonine dynasty}}`{=mediawiki}
**Titus Aelius Hadrianus Antoninus Pius** (`{{IPAc-en|ˌ|æ|n|t|ə|ˈ|n|aɪ|n|ə|s|_|ˈ|p|aɪ|ə|s}}`{=mediawiki}; `{{IPA|la|antoˈniːnus ˈpiːjus|lang}}`{=mediawiki}; 19 September 86 -- 7 March 161) was Roman emperor from AD 138 to 161. He was the fourth of the Five Good Emperors from the Nerva--Antonine dynasty.
Born into a senatorial family, Antoninus held various offices during the reign of Emperor Hadrian. He married Hadrian\'s niece Faustina, and Hadrian adopted him as his son and successor shortly before his death. Antoninus acquired the cognomen Pius after his accession to the throne, either because he compelled the Senate to deify his adoptive father, or because he had saved senators sentenced to death by Hadrian in his later years. His reign is notable for the peaceful state of the Empire, with no major revolts or military incursions during this time. A successful military campaign in southern Scotland early in his reign resulted in the construction of the Antonine Wall.
Antoninus was an effective administrator, leaving his successors a large surplus in the treasury, expanding free access to drinking water throughout the Empire, encouraging legal conformity, and facilitating the enfranchisement of freed slaves. He died of illness in AD 161 and was succeeded by his adopted sons Marcus Aurelius and Lucius Verus as co-emperors.
## Early life {#early_life}
### Childhood and family {#childhood_and_family}
Antoninus Pius was born Titus Aurelius Fulvus Boionius Antoninus in 86, near Lanuvium (modern-day Lanuvio) in Italy to Titus Aurelius Fulvus, consul in 89, and wife Arria Fadilla. The Aurelii Fulvi were an Aurelian family settled in Nemausus (modern Nîmes). Titus Aurelius Fulvus was the son of a senator of the same name, who, as legate of Legio III Gallica, had supported Vespasian in his bid to the Imperial office and been rewarded with a suffect consulship, plus an ordinary one under Domitian in 85. The Aurelii Fulvi were therefore a relatively new senatorial family from Gallia Narbonensis whose rise to prominence was supported by the Flavians. The link between Antoninus\'s family and their home province explains the increasing importance of the post of proconsul of Gallia Narbonensis during the late second century.
Antoninus\'s father had no other children and died shortly after his 89 ordinary consulship. Antoninus was raised by his maternal grandfather Gnaeus Arrius Antoninus, reputed by contemporaries to be a man of integrity and culture and a friend of Pliny the Younger. The Arrii Antonini were an older senatorial family from Italy, very influential during Nerva\'s reign. Arria Fadilla, Antoninus\'s mother, married afterwards Publius Julius Lupus, suffect consul in 98; from that marriage came two daughters, Arria Lupula and Julia Fadilla.
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## Early life {#early_life}
### Marriage and children {#marriage_and_children}
Some time between 110 and 115, Antoninus married Annia Galeria Faustina the Elder. They are believed to have enjoyed a happy marriage. Faustina was the daughter of consul Marcus Annius Verus (II) and Rupilia Faustina (often thought to be a step-sister to the Empress Vibia Sabina or more likely a granddaughter of the emperor Vitellius.) Faustina was a beautiful woman, and despite rumours about her character, it is clear that Antoninus cared for her deeply.
Faustina bore Antoninus four children, two sons and two daughters. They were:
- Marcus Aurelius Fulvus Antoninus (died before 138); his sepulchral inscription has been found at the Mausoleum of Hadrian in Rome.
- Marcus Galerius Aurelius Antoninus (died before 138); his sepulchral inscription has been found at the Mausoleum of Hadrian in Rome. His name appears on a Greek Imperial coin.
- Aurelia Fadilla (died in 135); she married Lucius Plautius Lamia Silvanus, consul 145. She appeared to have no children with her husband; and her sepulchral inscription has been found in Italy.
- Annia Galeria Faustina Minor or Faustina the Younger (between 125 and 130--175), a future Roman Empress, married her maternal cousin Marcus Aurelius in 146.
When Faustina died in 141, Antoninus was greatly distressed. In honour of her memory, he asked the Senate to deify her as a goddess, and authorised the construction of a temple to be built in the Roman Forum in her name, with priestesses serving in her temple. He had various coins with her portrait struck in her honor. These coins were scripted \"DIVA FAUSTINA\" and were elaborately decorated. He further founded a charity, calling it *Puellae Faustinianae* or *Girls of Faustina*, which assisted destitute girls of good family. Finally, Antoninus created a new *alimenta*, a Roman welfare programme, as part of *Cura Annonae*.
The emperor never remarried. Instead, he lived with Galeria Lysistrate, Faustina\'s freedwoman. Concubinage was a form of female companionship sometimes chosen by powerful men in Ancient Rome, especially widowers like Vespasian, and Marcus Aurelius. Their union could not produce any legitimate offspring who could threaten any heirs, such as those of Antoninus. Also, as one could not have a wife and an official concubine (or two concubines) at the same time, Antoninus avoided being pressed into a marriage with a noblewoman from another family. (Later, Marcus Aurelius would also reject the advances of his former fiancée Ceionia Fabia, Lucius Verus\'s sister, on the grounds of protecting his children from a stepmother, and took a concubine instead.)
### Favour with Hadrian {#favour_with_hadrian}
Having filled the offices of quaestor and praetor with more than usual success, he obtained the consulship in 120 having as his colleague Lucius Catilius Severus. He was next appointed by the Emperor Hadrian as one of the four proconsuls to administer Italia, his district including Etruria, where he had estates. He then greatly increased his reputation by his conduct as proconsul of Asia, probably during 134--135.
He acquired much favor with Hadrian, who adopted him as his son and successor on 25 February 138, after the death of his first adopted son Lucius Aelius, on the condition that Antoninus would in turn adopt Marcus Annius Verus, the son of his wife\'s brother, and Lucius, son of Lucius Aelius, who afterwards became the emperors Marcus Aurelius and Lucius Verus. He also adopted (briefly) the name Imperator Titus Aelius Caesar Antoninus, in preparation for his rule. There seems to have been some opposition to Antoninus\'s appointment on the part of other potential claimants, among them his former consular colleague Lucius Catilius Severus, then prefect of the city. Nevertheless, Antoninus assumed power without opposition.
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## Emperor
On his accession, Antoninus\'s name and style became *Imperator Caesar Titus Aelius Hadrianus Antoninus Augustus*. One of his first acts as emperor was to persuade the Senate to grant divine honours to Hadrian, which they had at first refused; his efforts to persuade the Senate to grant these honours is the most likely reason given for his title of *Pius* (dutiful in affection; compare *pietas*). Two other reasons for this title are that he would support his aged father-in-law with his hand at Senate meetings and that he had saved those men that Hadrian, during his period of ill health, had condemned to death.
Immediately after Hadrian\'s death, Antoninus approached Marcus and requested that his marriage arrangements be amended: Marcus\'s betrothal to Ceionia Fabia would be annulled, and he would be betrothed to Faustina, Antoninus\'s daughter instead. Faustina\'s betrothal to Ceionia\'s brother Lucius Commodus, Marcus\'s future co-emperor, would also have to be annulled. Marcus consented to Antoninus\'s proposal.
Antoninus built temples, theaters, and mausoleums, promoted the arts and sciences, and bestowed honours and financial rewards upon the teachers of rhetoric and philosophy. Antoninus made few initial changes when he became emperor, leaving the arrangements instituted by Hadrian as undisturbed as possible. Epigraphical and prosopographical research has revealed that Antoninus\'s imperial ruling team centered around a group of closely knit senatorial families, most of them members of the priestly congregation for the cult of Hadrian, the *sodales Hadrianales*. According to the German historian H.-G. Pflaum, prosopographical research of Antoninus\'s ruling team allows us to grasp the deeply conservative character of the ruling senatorial caste.
He owned palatial villas near Lanuvium and Villa Magna (Latium) and his ancestral estate at Lorium (Etruria).
### Lack of warfare {#lack_of_warfare}
There are no records of his involvement in military acts during his tenure, with J. J. Wilkes noting that he likely never saw or commanded a Roman army and was never within five hundred miles of a legion throughout his twenty-three-year reign.
His reign was the most peaceful in the entire history of the Principate, even though there were several military disturbances in the Empire in his time. Such disturbances happened in Mauretania, where a senator was named as governor of Mauretania Tingitana in place of the usual equestrian procurator and cavalry reinforcements from Pannonia were brought in, towns such as Sala and Tipasa being fortified. Similar disturbances took place in Judea, and amongst the Brigantes in Britannia; however, these were considered less serious than prior (and later) revolts among both. It was however in Britain that Antoninus decided to follow a new, more aggressive path, with the appointment of a new governor in 139, Quintus Lollius Urbicus, a native of Numidia and previously governor of Germania Inferior as well as a new man.
Under instructions from the emperor, Lollius undertook an invasion of southern Scotland, winning some significant victories and constructing the Antonine Wall from the Firth of Forth to the Firth of Clyde. However, the wall was soon gradually decommissioned during the mid-150s and eventually abandoned late during the reign (early 160s) for reasons that are still unclear. Antonine\'s Wall is mentioned in just one literary source, Antoninus\'s biography in the *Historia Augusta*. Pausanias makes a brief and confused mention of a war in Britain. In one inscription honouring Antoninus, erected by Legio II Augusta, which participated in the building of the Wall, a relief showing four naked prisoners, one of them beheaded, seems to stand for some actual warfare.
Although Antonine\'s Wall was, in principle, much shorter (37 miles in length as opposed to 73) and, at first sight, more defensible than Hadrian\'s Wall, the additional area that it enclosed within the Empire was barren, with land use for grazing already in decay. This meant that supply lines to the wall were strained enough such that the costs of maintaining the additional territory outweighed the benefits of doing so. Also, in the absence of urban development and the ensuing Romanization process, the rear of the wall could not be lastingly pacified.
It has been speculated that the invasion of Lowland Scotland and the building of the wall had to do mostly with internal politics, that is, offering Antoninus an opportunity to gain some modicum of necessary military prestige at the start of his reign. An Imperial salutation followed the campaign in Britannia---that is, Antoninus formally took for the second (and last) time the title of Imperator in 142. The fact that around the same time coins were struck announcing a victory in Britain points to Antoninus\'s need to publicise his achievements. The orator Fronto was later to say that, although Antoninus bestowed the direction of the British campaign to others, he should be regarded as the helmsman who directed the voyage, whose glory, therefore, belonged to him.
That this quest for some military achievement responded to an actual need is proved by the fact that, although generally peaceful, Antoninus\'s reign was not free from attempts at usurpation: *Historia Augusta* mentions two, made by the senators Cornelius Priscianus (\"for disturbing the peace of Spain\"; Priscianus had also been Lollius Urbicus\'s successor as governor of Britain) and Atilius Rufius Titianus (possibly a troublemaker already exiled under Hadrian). Both attempts are confirmed by the Fasti Ostienses and by the erasing of Priscianus\' name from an inscription. In both cases, Antoninus was not in formal charge of the ensuing repression: Priscianus committed suicide and Titianus was found guilty by the Senate, with Antoninus abstaining from sequestering their families\' properties.
There were also some troubles in Dacia Inferior, which required the granting of additional powers to the procurator governor and the dispatch of additional soldiers to the province. On the northern Black Sea coast, the Greek city of Olbia was held against the Scythians. Also during his reign the governor of Upper Germany, probably Gaius Popillius Carus Pedo, built new fortifications in the Agri Decumates, advancing the Limes Germanicus fifteen miles forward in his province and neighboring Raetia. In the East, Roman suzerainty over Armenia was retained by the choice in AD 140 of Arsacid scion Sohaemus as client king.
Nevertheless, Antoninus was virtually unique among emperors in that he dealt with these crises without leaving Italy once during his reign, but instead dealt with provincial matters of war and peace through their governors or through imperial letters to the cities such as Ephesus (of which some were publicly displayed). His contemporaries and later generations highly praised this style of government.
Antoninus was the last Roman Emperor recognised by the Indian Kingdoms, especially the Kushan Empire. Raoul McLaughlin quotes Aurelius Victor as saying, \"The Indians, the Bactrians, and the Hyrcanians all sent ambassadors to Antoninus. They had all heard about the spirit of justice held by this great emperor, justice that was heightened by his handsome and grave countenance, and his slim and vigorous figure.\" Due to the outbreak of the Antonine epidemic and wars against northern Germanic tribes, the reign of Marcus Aurelius was forced to alter the focus of foreign policies, and matters relating to the Far East were increasingly abandoned in favour of those directly concerning the Empire\'s survival.
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## Emperor
### Economy and administration {#economy_and_administration}
Antoninus was regarded as a skilled administrator and builder. Despite an extensive building directive---the free access of the people of Rome to drinking water was expanded with the construction of aqueducts, not only in Rome but throughout the Empire, as well as bridges and roads---the emperor still managed to leave behind a sizable public treasury of around 2.7 billion sesterces. Rome would not witness another Emperor leaving his successor with a surplus for a long time, but the treasury was depleted almost immediately after Antoninus\'s reign due to the Antonine Plague brought back by soldiers after the Parthian victory.
The Emperor also famously suspended the collection of taxes from multiple cities affected by natural disasters, such as when fires struck Rome and Narbona, and earthquakes affected Rhodes and the Province of Asia. He offered hefty financial grants for rebuilding and recovery of various Greek cities after two serious earthquakes: the first, c. 140, which mainly affected Rhodes and other islands; the second, in 152, which hit Cyzicus (where the huge and newly built Temple to Hadrian was destroyed), Ephesus, and Smyrna. Antoninus\'s financial help earned him praise from Greek writers such as Aelius Aristides and Pausanias. These cities received the usual honorific accolades from Antoninus, such as when he commanded that all governors of Asia should enter the province when taking office through Ephesus. Ephesus was especially favoured by Antoninus, who confirmed and upheld its distinction of having two temples for the imperial cult (neocorate), therefore having first place in the list of imperial honor titles, surpassing both Smyrna and Pergamon.
In his dealings with Greek-speaking cities, Antoninus followed the policy adopted by Hadrian of ingratiating himself with local elites, especially with local intellectuals: philosophers, teachers of literature, rhetoricians, and physicians were explicitly exempted from any duties involving private spending for civic purposes, a privilege granted by Hadrian that Antoninus confirmed by means of an edict preserved in the Digest (27.1.6.8). Antoninus also created a chair for the teaching of rhetoric in Athens.
Antoninus was known as an avid observer of rites of religion and formal celebrations, both Roman and foreign. He is known for having increasingly formalized the official cult offered to the Great Mother, which from his reign onwards included a bull sacrifice, a taurobolium, formerly only a private ritual, now being also performed for the sake of the Emperor\'s welfare. Antoninus also offered patronage to the worship of Mithras, to whom he erected a temple in Ostia. In 148, he presided over the celebrations of the 900th anniversary of the founding of Rome.
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## Emperor
### Legal reforms {#legal_reforms}
Antoninus tried to portray himself as a magistrate of the *res publica*, no matter how extended and ill-defined his competencies were. He is credited with splitting the imperial treasury, the fiscus. This splitting had to do with the division of imperial properties into two parts. Firstly, the fiscus itself, or *patrimonium*, meaning the properties of the \"Crown\", the hereditary properties of each succeeding person that sat on the throne, transmitted to his successors in office, regardless of their previous membership in the imperial family. Secondly, the *res privata*, the \"private\" properties tied to the personal maintenance of the emperor and his family, something like a Privy Purse. An anecdote in the *Historia Augusta* biography, where Antoninus replies to Faustina (who complained about his stinginess) that \"we have gained an empire \[and\] lost even what we had before,\" possibly relates to Antoninus\'s actual concerns at the creation of the *res privata*. While still a private citizen, Antoninus had increased his personal fortune significantly using various legacies, the consequence of his caring scrupulously for his relatives. Also, Antoninus left behind him a reputation for stinginess and was probably determined not to leave his personal property to be \"swallowed up by the demands of the imperial throne\".
The *res privata* lands could be sold and/or given away, while the *patrimonium* properties were regarded as public. It was a way of pretending that the Imperial function---and most properties attached to it---was a public one, formally subject to the authority of the Senate and the Roman people. That the distinction played no part in subsequent political history---that the *personal* power of the princeps absorbed his role as office-holder---proves that the autocratic logic of the imperial order had already subsumed the old republican institutions.
Of the public transactions of this period, there is only the scantiest of information. However, to judge by what is extant, those twenty-two years were not remarkably eventful compared to those before and after the reign. However, Antoninus did take a great interest in the revision and practice of the law throughout the empire. One of his chief concerns was to having local communities conform their legal procedures to existing Roman norms: in a case concerning the repression of banditry by local police officers (\"irenarchs\", Greek for \"peacekeepers\") in Asia Minor, Antoninus ordered that these officers should not treat suspects as already condemned, and also keep a detailed copy of their interrogations, to be used in the possibility of an appeal to the Roman governor. Also, although Antoninus was not an innovator, he would not always follow the absolute letter of the law. Rather, he was driven by concerns over humanity and equality and introduced into Roman law many important new principles based upon this notion.
In this, the emperor was assisted by five chief lawyers: Lucius Fulvius Aburnius Valens, an author of legal treatises; Lucius Ulpius Marcellus, a prolific writer; and three others. Of these three, the most prominent was Lucius Volusius Maecianus, a former military officer turned by Antoninus into a civil procurator, and who, given his subsequent career (discovered on the basis of epigraphical and prosopographic research), was the emperor\'s most important legal adviser. Maecianus would eventually be chosen to occupy various prefectures (see below) as well as to conduct the legal studies of Marcus Aurelius. He also authored an extensive work on *Fidei commissa* (Testamentary Trusts). As a hallmark of the increased connection between jurists and the imperial government, Antoninus\'s reign also saw the appearance of the *Institutes* of Gaius, an elementary legal textbook for beginners. Antoninus passed measures to facilitate the enfranchisement of slaves. Mostly, he favoured the principle of *favor libertatis*, giving the putative freedman the benefit of the doubt when the claim to freedom was not clear-cut. Also, he punished the killing of a slave by their master without previous trial and determined that slaves could be forcibly sold to another master by a proconsul in cases of consistent mistreatment. Antoninus upheld the enforcement of contracts for selling of female slaves forbidding their further employment in prostitution. In criminal law, Antoninus introduced the important principle of the presumption of innocence---namely, that accused persons are not to be treated as guilty before trial, as in the case of the irenarchs (see above). Antoninus also asserted the principle that the trial was to be held and the punishment inflicted in the place where the crime had been committed. He mitigated the use of torture in examining slaves by certain limitations. Thus, he prohibited the application of torture to children under fourteen years, though this rule had exceptions. However, it must be stressed that Antoninus *extended*, using a rescript, the use of torture as a means of obtaining evidence to pecuniary cases, when it had been applied up until then only in criminal cases. Also, already at the time torture of free men of low status (*humiliores*) had become legal, as proved by the fact that Antoninus exempted town councillors expressly from it, and also free men of high rank (*honestiores*) in general.
One highlight during his reign occurred in 148, with the 900th anniversary of the foundation of Rome being celebrated by hosting magnificent games in the city. It lasted many days, and a host of exotic animals were killed, including elephants, giraffes, tigers, rhinoceroses, crocodiles and hippopotamuses. While this increased Antoninus\'s popularity, the frugal emperor had to debase the Roman currency. He decreased the silver purity of the denarius from 89% to 83.5, the actual silver weight dropping from 2.88 grams to 2.68 grams.
Antoninus is a likely candidate for the Antoninus named multiple times in the Talmud as a friend of Rabbi Judah Ha-Nasi. In the Talmudic tractate *Avodah Zarah* 10a--b, Rabbi Judah---exceptionally wealthy and highly revered in Rome---shared a close friendship with a man named Antoninus (possibly Antoninus Pius), who frequently sought his counsel on spiritual (in this context, Jewish), philosophical, and governance matters.
### Diplomatic mission to China {#diplomatic_mission_to_china}
The first group of people claiming to be an ambassadorial mission of Romans to China was recorded in 166 AD by the *Hou Hanshu*. Harper (2017) states that the embassy was likely to be a group of merchants, as many Roman merchants traveled to India and some might have gone beyond, while there are no records of official ambassadors of Rome travelling as far east. The group came to Emperor Huan of Han China and claimed to be an embassy from \"Andun\" (`{{Lang-zh|安敦 ''āndūn''}}`{=mediawiki}; for *Anton*-inus), \"king of Daqin\" (Rome). As Antoninus Pius died in 161, leaving the empire to his adoptive son Marcus Aurelius (Antoninus), and the envoy arrived in 166, confusion remains about who sent the mission, given that both emperors were named \"Antoninus\". The Roman mission came from the south (therefore probably by sea), entering China by the frontier province of Jiaozhi at Rinan or Tonkin (present-day northern Vietnam). It brought presents of rhinoceros horns, ivory, and tortoise shell, probably acquired in South Asia. The text states explicitly that it was the first time there had been direct contact between the two countries.
Furthermore, a piece of Republican-era Roman glassware has been found at a Western Han tomb in Guangzhou along the South China Sea, dated to the early 1st century BC. Roman golden medallions made during the reign of Antoninus Pius and perhaps even Marcus Aurelius have been found at Óc Eo in southern Vietnam, then part of the Kingdom of Funan near the Chinese province of Jiaozhi. This may have been the port city of Kattigara, described by Ptolemy (c. 150) as being visited by a Greek sailor named Alexander and lying beyond the Golden Chersonese (i.e., Malay Peninsula). Roman coins from the reigns of Tiberius to Aurelian have been discovered in Xi\'an, China (site of the Han capital Chang\'an), although the significantly greater amount of Roman coins unearthed in India suggest the Roman maritime trade for purchasing Chinese silk was centered there, not in China or even the overland Silk Road running through ancient Iran.
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## Death and legacy {#death_and_legacy}
In 156, Antoninus Pius turned 70. He found it difficult to keep himself upright without stays. He started nibbling on dry bread to give him the strength to stay awake through his morning receptions.
Marcus Aurelius had already been created consul with Antoninus in 140, receiving the title of Caesar, i.e., heir apparent. As Antoninus aged, Marcus took on more administrative duties. Marcus\'s administrative duties increased again after the death, in 156 or 157, of one of Antoninus\'s most trusted advisers, Marcus Gavius Maximus.
For twenty years, Gavius Maximus had been praetorian prefect, an office that was as much secretarial as military. Gavius Maximus had been awarded with the consular insignia and the honours due a senator. He had a reputation as a most strict disciplinarian (*vir severissimus*, according to *Historia Augusta*) and some fellow equestrian procurators held lasting grudges against him. A procurator named Gaius Censorius Niger died while Gavius Maximus was alive. In his will, Censorius Niger vilified Maximus, creating serious embarrassment for one of the heirs, the orator Fronto.
Gavius Maximus\'s death initiated a change in the ruling team. It has been speculated that it was the legal adviser Lucius Volusius Maecianus who assumed the role of grey eminence. Maecianus was briefly Praefect of Egypt, and subsequently Praefectus annonae in Rome. If it was Maecianus who rose to prominence, he may have risen precisely in order to prepare the incoming---and unprecedented---joint succession. In 160, Marcus and Lucius were designated joint consuls for the following year. Perhaps Antoninus was already ill; in any case, he died before the year was out, probably on 7 March.
Two days before his death, the biographer reports, Antoninus was at his ancestral estate at Lorium, in Etruria, about 12 mi from Rome. He ate Alpine cheese at dinner quite greedily. In the night he vomited; he had a fever the next day. The day after that, he summoned the imperial council, and passed the state and his daughter to Marcus. The emperor gave the keynote to his life in the last word that he uttered: when the tribune of the night-watch came to ask the password, he responded, \"aequanimitas\" (equanimity). He then turned over, as if going to sleep, and died. His death closed out the longest reign since Augustus (surpassing Tiberius by a couple of months). His record for the second-longest reign would be unbeaten for 168 years, until 329 when it was surpassed by Constantine the Great.
Antoninus Pius\' funeral ceremonies were, in the words of the biographer, \"elaborate\". If his funeral followed the pattern of past funerals, his body would have been incinerated on a pyre at the Campus Martius, while his spirit would rise to the gods\' home in the heavens. However, it seems that this was not the case: according to his *Historia Augusta* biography (which seems to reproduce an earlier, detailed report) Antoninus\'s body (and not his ashes) was buried in Hadrian\'s mausoleum. After a seven-day interval (*justitium*), Marcus and Lucius nominated their father for deification. In contrast to their behaviour during Antoninus\'s campaign to deify Hadrian, the senate did not oppose the emperors\' wishes. A *flamen*, or cultic priest, was appointed to minister the cult of the deified Antoninus, now *Divus Antoninus*.
A column was dedicated to Antoninus on the Campus Martius, and the temple he had built in the Forum in 141 to his deified wife Faustina was rededicated to the deified Faustina and the deified Antoninus. It survives as the church of San Lorenzo in Miranda.
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## Death and legacy {#death_and_legacy}
### Historiography
The only intact account of his life handed down to us is that of the *Augustan History*, an unreliable and mostly fabricated work. Nevertheless, it still contains information that is considered reasonably sound; for instance, it is the only source that mentions the erection of the Antonine Wall in Britain.
Antoninus in many ways was the ideal of the landed gentleman praised not only by ancient Romans, but also by later scholars of classical history, such as Edward Gibbon or the author of the article on Antoninus Pius in the *Encyclopædia Britannica* Eleventh Edition.
Some historians have a less positive view of his reign. According to the historian J. B. Bury,
German historian Ernst Kornemann has had it in his *Römische Geschichte* \[2 vols., ed. by H. Bengtson, Stuttgart 1954\] that the reign of Antoninus comprised \"a succession of grossly wasted opportunities\", given the upheavals that were to come. There is more to this argument, given that the Parthians in the East were themselves soon to make no small amount of mischief after Antoninus\'s death. Kornemann\'s brief is that Antoninus might have waged preventive wars to head off these outsiders. Michael Grant agrees that it is possible that had Antoninus acted decisively sooner (it appears that, on his death bed, he was preparing a large-scale action against the Parthians), the Parthians might have been unable to choose their own time, but current evidence is not conclusive. Grant opines that Antoninus and his officers did act in a resolute manner dealing with frontier disturbances of his time, although conditions for long-lasting peace were not created. On the whole, according to Grant, Marcus Aurelius\'s eulogistic picture of Antoninus seems deserved, and Antoninus appears to have been a conservative and nationalistic (although he respected and followed Hadrian\'s example of Philhellenism moderately) emperor who was not tainted by the blood of either citizen or foe, combined and maintained Numa Pompilius\'s good fortune, pacific dutifulness and religious scrupulousness, and whose laws removed anomalies and softened harshnesses.
Krzysztof Ulanowski argues that the claims of military inability are exaggerated, considering that although the sources praise Antoninus\'s love for peace and his efforts \"rather to defend, than enlarge the provinces\", he could hardly be considered a pacifist, as shown by the conquest of the Lowlands, the building of the Antonine Wall and the expansion of Germania Superior. Ulanowski also praises Antoninus for being successful in deterrence by diplomatic means.
### Descendants
Although only one of his four children survived to adulthood, Antoninus came to be ancestor to four generations of prominent Romans, including the Emperor Commodus. Hans-Georg Pflaum has identified five direct descendants of Antoninus and Faustina who were consuls in the first half of the third century.
1. Marcus Aurelius Fulvus Antoninus (died before 138), died young without issue
2. Marcus Galerius Aurelius Antoninus (died before 138), died young without issue
3. Aurelia Fadilla (died in 135), who married Lucius Plautius Lamia Silvanus, suffect consul in 145; no children known for certain.
4. Annia Galeria Faustina the Younger (21 September between 125 and 130--175), had several children; those who had children were:
1. Annia Aurelia Galeria Lucilla (7 March 150--182?), whose children included:
1. Tiberius Claudius Pompeianus
2. Annia Galeria Aurelia Faustina (151--?), whose children included:
1. Tiberius Claudius Severus Proculus
1. Empress Annia Faustina, Elagabalus\'s third wife
3. Annia Aurelia Fadilla (159 -- after 211)
4
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thumb\|upright=1.36\|WMAP image of the tiny anisotropies in the cosmic microwave background radiation **Anisotropy** (`{{IPAc-en|ˌ|ae|n|aɪ|ˈ|s|ɒ|t|r|ə|p|i|,_|ˌ|æ|n|ɪ|-}}`{=mediawiki}) is the structural property of non-uniformity in different directions, as opposed to isotropy. An anisotropic object or pattern has properties that differ according to direction of measurement. For example, many materials exhibit very different physical or mechanical properties when measured along different axes, e.g. absorbance, refractive index, conductivity, and tensile strength.
An example of anisotropy is light coming through a polarizer. Another is wood, which is easier to split along its grain than across it because of the directional non-uniformity of the grain (the grain is the same in one direction, not all directions).
## Fields of interest {#fields_of_interest}
### Computer graphics {#computer_graphics}
In the field of computer graphics, an anisotropic surface changes in appearance as it rotates about its geometric normal, as is the case with velvet.
Anisotropic filtering (AF) is a method of enhancing the image quality of textures on surfaces that are far away and viewed at a shallow angle. Older techniques, such as bilinear and trilinear filtering, do not take into account the angle a surface is viewed from, which can result in aliasing or blurring of textures. By reducing detail in one direction more than another, these effects can be reduced easily.
### Chemistry
A chemical anisotropic filter, as used to filter particles, is a filter with increasingly smaller interstitial spaces in the direction of filtration so that the proximal regions filter out larger particles and distal regions increasingly remove smaller particles, resulting in greater flow-through and more efficient filtration.
In fluorescence spectroscopy, the fluorescence anisotropy, calculated from the polarization properties of fluorescence from samples excited with plane-polarized light, is used, e.g., to determine the shape of a macromolecule. Anisotropy measurements reveal the average angular displacement of the fluorophore that occurs between absorption and subsequent emission of a photon.
In NMR spectroscopy, the orientation of nuclei with respect to the applied magnetic field determines their chemical shift. In this context, anisotropic systems refer to the electron distribution of molecules with abnormally high electron density, like the pi system of benzene. This abnormal electron density affects the applied magnetic field and causes the observed chemical shift to change.
### Real-world imagery {#real_world_imagery}
Images of a gravity-bound or man-made environment are particularly anisotropic in the orientation domain, with more image structure located at orientations parallel with or orthogonal to the direction of gravity (vertical and horizontal).
### Physics
Physicists from University of California, Berkeley reported about their detection of the cosmic anisotropy in cosmic microwave background radiation in 1977. Their experiment demonstrated the Doppler shift caused by the movement of the earth with respect to the early Universe matter, the source of the radiation. Cosmic anisotropy has also been seen in the alignment of galaxies\' rotation axes and polarization angles of quasars.`{{fact|date=March 2025}}`{=mediawiki}
Physicists use the term anisotropy to describe direction-dependent properties of materials. Magnetic anisotropy, for example, may occur in a plasma, so that its magnetic field is oriented in a preferred direction. Plasmas may also show \"filamentation\" (such as that seen in lightning or a plasma globe) that is directional.`{{fact|date=March 2025}}`{=mediawiki}
An *anisotropic liquid* has the fluidity of a normal liquid, but has an average structural order relative to each other along the molecular axis, unlike water or chloroform, which contain no structural ordering of the molecules. Liquid crystals are examples of anisotropic liquids.`{{fact|date=March 2025}}`{=mediawiki}
Some materials conduct heat in a way that is isotropic, that is independent of spatial orientation around the heat source. Heat conduction is more commonly anisotropic, which implies that detailed geometric modeling of typically diverse materials being thermally managed is required. The materials used to transfer and reject heat from the heat source in electronics are often anisotropic.
Many crystals are anisotropic to light (\"optical anisotropy\"), and exhibit properties such as birefringence. Crystal optics describes light propagation in these media. An \"axis of anisotropy\" is defined as the axis along which isotropy is broken (or an axis of symmetry, such as normal to crystalline layers). Some materials can have multiple such optical axes.`{{fact|date=March 2025}}`{=mediawiki}
### Geophysics and geology {#geophysics_and_geology}
Seismic anisotropy is the variation of seismic wavespeed with direction. Seismic anisotropy is an indicator of long range order in a material, where features smaller than the seismic wavelength (e.g., crystals, cracks, pores, layers, or inclusions) have a dominant alignment. This alignment leads to a directional variation of elasticity wavespeed. Measuring the effects of anisotropy in seismic data can provide important information about processes and mineralogy in the Earth; significant seismic anisotropy has been detected in the Earth\'s crust, mantle, and inner core.
Geological formations with distinct layers of sedimentary material can exhibit electrical anisotropy; electrical conductivity in one direction (e.g. parallel to a layer), is different from that in another (e.g. perpendicular to a layer). This property is used in the gas and oil exploration industry to identify hydrocarbon-bearing sands in sequences of sand and shale. Sand-bearing hydrocarbon assets have high resistivity (low conductivity), whereas shales have lower resistivity. Formation evaluation instruments measure this conductivity or resistivity, and the results are used to help find oil and gas in wells. The mechanical anisotropy measured for some of the sedimentary rocks like coal and shale can change with corresponding changes in their surface properties like sorption when gases are produced from the coal and shale reservoirs.
The hydraulic conductivity of aquifers is often anisotropic for the same reason. When calculating groundwater flow to drains or to wells, the difference between horizontal and vertical permeability must be taken into account; otherwise the results may be subject to error.
Most common rock-forming minerals are anisotropic, including quartz and feldspar. Anisotropy in minerals is most reliably seen in their optical properties. An example of an isotropic mineral is garnet.
Igneous rock like granite also shows the anisotropy due to the orientation of the minerals during the solidification process.
### Medical acoustics {#medical_acoustics}
Anisotropy is also a well-known property in medical ultrasound imaging describing a different resulting echogenicity of soft tissues, such as tendons, when the angle of the transducer is changed. Tendon fibers appear hyperechoic (bright) when the transducer is perpendicular to the tendon, but can appear hypoechoic (darker) when the transducer is angled obliquely. This can be a source of interpretation error for inexperienced practitioners.
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## Fields of interest {#fields_of_interest}
### Materials science and engineering {#materials_science_and_engineering}
Anisotropy, in materials science, is a material\'s directional dependence of a physical property. This is a critical consideration for materials selection in engineering applications. A material with physical properties that are symmetric about an axis that is normal to a plane of isotropy is called a transversely isotropic material. Tensor descriptions of material properties can be used to determine the directional dependence of that property. For a monocrystalline material, anisotropy is associated with the crystal symmetry in the sense that more symmetric crystal types have fewer independent coefficients in the tensor description of a given property. When a material is polycrystalline, the directional dependence on properties is often related to the processing techniques it has undergone. A material with randomly oriented grains will be isotropic, whereas materials with texture will be often be anisotropic. Textured materials are often the result of processing techniques like cold rolling, wire drawing, and heat treatment.
Mechanical properties of materials such as Young\'s modulus, ductility, yield strength, and high-temperature creep rate, are often dependent on the direction of measurement. Fourth-rank tensor properties, like the elastic constants, are anisotropic, even for materials with cubic symmetry. The Young\'s modulus relates stress and strain when an isotropic material is elastically deformed; to describe elasticity in an anisotropic material, stiffness (or compliance) tensors are used instead.
In metals, anisotropic elasticity behavior is present in all single crystals with three independent coefficients for cubic crystals, for example. For face-centered cubic materials such as nickel and copper, the stiffness is highest along the \<111\> direction, normal to the close-packed planes, and smallest parallel to \<100\>. Tungsten is so nearly isotropic at room temperature that it can be considered to have only two stiffness coefficients; aluminium is another metal that is nearly isotropic.
For an isotropic material, $G = E/[2(1 + \nu)],$ where $G$ is the shear modulus, $E$ is the Young\'s modulus, and $\nu$ is the material\'s Poisson\'s ratio. Therefore, for cubic materials, we can think of anisotropy, $a_r$, as the ratio between the empirically determined shear modulus for the cubic material and its (isotropic) equivalent: $a_r = \frac{G}{E/[2(1 + \nu)]} = \frac{2(1+\nu)G}{E} \equiv \frac{2 C_{44}}{C_{11} - C_{12}}.$
The latter expression is known as the Zener ratio, $a_r$, where $C_{ij}$ refers to elastic constants in Voigt (vector-matrix) notation. For an isotropic material, the ratio is one.
Limitation of the Zener ratio to cubic materials is waived in the Tensorial anisotropy index A^T^ that takes into consideration all the 27 components of the fully anisotropic stiffness tensor. It is composed of two major parts $A^I$and $A^A$, the former referring to components existing in cubic tensor and the latter in anisotropic tensor so that $A^T = A^I+A^A .$ This first component includes the modified Zener ratio and additionally accounts for directional differences in the material, which exist in orthotropic material, for instance. The second component of this index $A^A$ covers the influence of stiffness coefficients that are nonzero only for non-cubic materials and remains zero otherwise.
Fiber-reinforced or layered composite materials exhibit anisotropic mechanical properties, due to orientation of the reinforcement material. In many fiber-reinforced composites like carbon fiber or glass fiber based composites, the weave of the material (e.g. unidirectional or plain weave) can determine the extent of the anisotropy of the bulk material. The tunability of orientation of the fibers allows for application-based designs of composite materials, depending on the direction of stresses applied onto the material.
Amorphous materials such as glass and polymers are typically isotropic. Due to the highly randomized orientation of macromolecules in polymeric materials, polymers are in general described as isotropic. However, mechanically gradient polymers can be engineered to have directionally dependent properties through processing techniques or introduction of anisotropy-inducing elements. Researchers have built composite materials with aligned fibers and voids to generate anisotropic hydrogels, in order to mimic hierarchically ordered biological soft matter. 3D printing, especially Fused Deposition Modeling, can introduce anisotropy into printed parts. This is because FDM is designed to extrude and print layers of thermoplastic materials. This creates materials that are strong when tensile stress is applied in parallel to the layers and weak when the material is perpendicular to the layers.
### Microfabrication
Anisotropic etching techniques (such as deep reactive-ion etching) are used in microfabrication processes to create well defined microscopic features with a high aspect ratio. These features are commonly used in MEMS (microelectromechanical systems) and microfluidic devices, where the anisotropy of the features is needed to impart desired optical, electrical, or physical properties to the device. Anisotropic etching can also refer to certain chemical etchants used to etch a certain material preferentially over certain crystallographic planes (e.g., KOH etching of silicon \[100\] produces pyramid-like structures)
### Neuroscience
Diffusion tensor imaging is an MRI technique that involves measuring the fractional anisotropy of the random motion (Brownian motion) of water molecules in the brain. Water molecules located in fiber tracts are more likely to move anisotropically, since they are restricted in their movement (they move more in the dimension parallel to the fiber tract rather than in the two dimensions orthogonal to it), whereas water molecules dispersed in the rest of the brain have less restricted movement and therefore display more isotropy. This difference in fractional anisotropy is exploited to create a map of the fiber tracts in the brains of the individual.
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## Fields of interest {#fields_of_interest}
### Remote sensing and radiative transfer modeling {#remote_sensing_and_radiative_transfer_modeling}
Radiance fields (see Bidirectional reflectance distribution function (BRDF)) from a reflective surface are often not isotropic in nature. This makes calculations of the total energy being reflected from any scene a difficult quantity to calculate. In remote sensing applications, anisotropy functions can be derived for specific scenes, immensely simplifying the calculation of the net reflectance or (thereby) the net irradiance of a scene. For example, let the BRDF be $\gamma(\Omega_i, \Omega_v)$ where \'i\' denotes incident direction and \'v\' denotes viewing direction (as if from a satellite or other instrument). And let P be the Planar Albedo, which represents the total reflectance from the scene. $P(\Omega_i) = \int_{\Omega_v} \gamma(\Omega_i, \Omega_v)\hat{n} \cdot d\hat\Omega_v$ $A(\Omega_i, \Omega_v) = \frac{\gamma(\Omega_i, \Omega_v)}{P(\Omega_i)}$
It is of interest because, with knowledge of the anisotropy function as defined, a measurement of the BRDF from a single viewing direction (say, $\Omega_v$) yields a measure of the total scene reflectance (planar albedo) for that specific incident geometry (say, $\Omega_i$)
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thumb\|upright=1.35\|Visual representation of alpha decay `{{Nuclear physics}}`{=mediawiki} **Alpha decay** or **α-decay** is a type of radioactive decay in which an atomic nucleus emits an alpha particle (helium nucleus). The parent nucleus transforms or \"decays\" into a daughter product, with a mass number that is reduced by four and an atomic number that is reduced by two. An alpha particle is identical to the nucleus of a helium-4 atom, which consists of two protons and two neutrons. It has a charge of `{{val|+2|ul=e}}`{=mediawiki} and a mass of `{{val|4|ul=Da}}`{=mediawiki}, and is represented as ${}^{4}_{2}\alpha$. For example, uranium-238 undergoes alpha decay to form thorium-234.
While alpha particles have a charge `{{val|+2|u=e}}`{=mediawiki}, this is not usually shown because a nuclear equation describes a nuclear reaction without considering the electrons -- a convention that does not imply that the nuclei necessarily occur in neutral atoms.
Alpha decay typically occurs in the heaviest nuclides. Theoretically, it can occur only in nuclei somewhat heavier than nickel (element 28), where the overall binding energy per nucleon is no longer a maximum and the nuclides are therefore unstable toward spontaneous fission-type processes. In practice, this mode of decay has only been observed in nuclides considerably heavier than nickel, with the lightest known alpha emitter being the second lightest isotope of antimony, ^104^Sb. Exceptionally, however, beryllium-8 decays to two alpha particles.
Alpha decay is by far the most common form of cluster decay, where the parent atom ejects a defined daughter collection of nucleons, leaving another defined product behind. It is the most common form because of the combined extremely high nuclear binding energy and relatively small mass of the alpha particle. Like other cluster decays, alpha decay is fundamentally a quantum tunneling process. Unlike beta decay, it is governed by the interplay between both the strong nuclear force and the electromagnetic force.
Alpha particles have a typical kinetic energy of 5 MeV (or ≈ 0.13% of their total energy, 110 TJ/kg) and have a speed of about 15,000,000 m/s, or 5% of the speed of light. There is surprisingly small variation around this energy, due to the strong dependence of the half-life of this process on the energy produced. Because of their relatively large mass, the electric charge of `{{val|+2|u=e}}`{=mediawiki} and relatively low velocity, alpha particles are very likely to interact with other atoms and lose their energy, and their forward motion can be stopped by a few centimeters of air.
Approximately 99% of the helium produced on Earth is the result of the alpha decay of underground deposits of minerals containing uranium or thorium. The helium is brought to the surface as a by-product of natural gas production.
## History
Alpha particles were first described in the investigations of radioactivity by Ernest Rutherford in 1899, and by 1907 they were identified as He^2+^ ions. By 1928, George Gamow had solved the theory of alpha decay via tunneling. The alpha particle is trapped inside the nucleus by an attractive nuclear potential well and a repulsive electromagnetic potential barrier. Classically, it is forbidden to escape, but according to the (then) newly discovered principles of quantum mechanics, it has a tiny (but non-zero) probability of \"tunneling\" through the barrier and appearing on the other side to escape the nucleus. Gamow solved a model potential for the nucleus and derived, from first principles, a relationship between the half-life of the decay, and the energy of the emission, which had been previously discovered empirically and was known as the Geiger--Nuttall law.
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## Mechanism
The nuclear force holding an atomic nucleus together is very strong, in general much stronger than the repulsive electromagnetic forces between the protons. However, the nuclear force is also short-range, dropping quickly in strength beyond about 3 femtometers, while the electromagnetic force has an unlimited range. The strength of the attractive nuclear force keeping a nucleus together is thus proportional to the number of the nucleons, but the total disruptive electromagnetic force of proton-proton repulsion trying to break the nucleus apart is roughly proportional to the square of its atomic number. A nucleus with 210 or more nucleons is so large that the strong nuclear force holding it together can just barely counterbalance the electromagnetic repulsion between the protons it contains. Alpha decay occurs in such nuclei as a means of increasing stability by reducing size.
One curiosity is why alpha particles, helium nuclei, should be preferentially emitted as opposed to other particles like a single proton or neutron or other atomic nuclei. Part of the reason is the high binding energy of the alpha particle, which means that its mass is less than the sum of the masses of two free protons and two free neutrons. This increases the disintegration energy. Computing the total disintegration energy given by the equation $E_{di} = (m_\text{i} - m_\text{f} - m_\text{p})c^2,$ where `{{math|''m''<sub>i</sub>}}`{=mediawiki} is the initial mass of the nucleus, `{{math|''m''<sub>f</sub>}}`{=mediawiki} is the mass of the nucleus after particle emission, and `{{math|''m''<sub>p</sub>}}`{=mediawiki} is the mass of the emitted (alpha-)particle, one finds that in certain cases it is positive and so alpha particle emission is possible, whereas other decay modes would require energy to be added. For example, performing the calculation for uranium-232 shows that alpha particle emission releases 5.4 MeV of energy, while a single proton emission would *require* 6.1 MeV. Most of the disintegration energy becomes the kinetic energy of the alpha particle, although to fulfill conservation of momentum, part of the energy goes to the recoil of the nucleus itself (see atomic recoil). However, since the mass numbers of most alpha-emitting radioisotopes exceed 210, far greater than the mass number of the alpha particle (4), the fraction of the energy going to the recoil of the nucleus is generally quite small, less than 2%. Nevertheless, the recoil energy (on the scale of keV) is still much larger than the strength of chemical bonds (on the scale of eV), so the daughter nuclide will break away from the chemical environment the parent was in. The energies and ratios of the alpha particles can be used to identify the radioactive parent via alpha spectrometry.
These disintegration energies, however, are substantially smaller than the repulsive potential barrier created by the interplay between the strong nuclear and the electromagnetic force, which prevents the alpha particle from escaping. The energy needed to bring an alpha particle from infinity to a point near the nucleus just outside the range of the nuclear force\'s influence is generally in the range of about 25 MeV. An alpha particle within the nucleus can be thought of as being inside a potential barrier whose walls are 25 MeV above the potential at infinity. However, decay alpha particles only have energies of around 4 to 9 MeV above the potential at infinity, far less than the energy needed to overcome the barrier and escape.
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## Mechanism
### Quantum tunneling {#quantum_tunneling}
Quantum mechanics, however, allows the alpha particle to escape via quantum tunneling. The quantum tunneling theory of alpha decay, independently developed by George Gamow and by Ronald Wilfred Gurney and Edward Condon in 1928, was hailed as a very striking confirmation of quantum theory. Essentially, the alpha particle escapes from the nucleus not by acquiring enough energy to pass over the wall confining it, but by tunneling through the wall. Gurney and Condon made the following observation in their paper on it:
> It has hitherto been necessary to postulate some special arbitrary \'instability\' of the nucleus, but in the following note, it is pointed out that disintegration is a natural consequence of the laws of quantum mechanics without any special hypothesis\... Much has been written of the explosive violence with which the α-particle is hurled from its place in the nucleus. But from the process pictured above, one would rather say that the α-particle almost slips away unnoticed.
The theory supposes that the alpha particle can be considered an independent particle within a nucleus, that is in constant motion but held within the nucleus by strong interaction. At each collision with the repulsive potential barrier of the electromagnetic force, there is a small non-zero probability that it will tunnel its way out. An alpha particle with a speed of 1.5×10^7^ m/s within a nuclear diameter of approximately 10^−14^ m will collide with the barrier more than 10^21^ times per second. However, if the probability of escape at each collision is very small, the half-life of the radioisotope will be very long, since it is the time required for the total probability of escape to reach 50%. As an extreme example, the half-life of the isotope bismuth-209 is `{{val|2.01|e=19|u=years}}`{=mediawiki}.
The isotopes in beta-decay stable isobars that are also stable with regards to double beta decay with mass number *A* = 5, *A* = 8, 143 ≤ *A* ≤ 155, 160 ≤ *A* ≤ 162, and *A* ≥ 165 are theorized to undergo alpha decay. All other mass numbers (isobars) have exactly one theoretically stable nuclide. Those with mass 5 decay to helium-4 and a proton or a neutron, and those with mass 8 decay to two helium-4 nuclei; their half-lives (helium-5, lithium-5, and beryllium-8) are very short, unlike the half-lives for all other such nuclides with *A* ≤ 209, which are very long. (Such nuclides with *A* ≤ 209 are primordial nuclides except ^146^Sm.)
Working out the details of the theory leads to an equation relating the half-life of a radioisotope to the decay energy of its alpha particles, a theoretical derivation of the empirical Geiger--Nuttall law.
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## Uses
Americium-241, an alpha emitter, is used in smoke detectors. The alpha particles ionize air in an open ion chamber and a small current flows through the ionized air. Smoke particles from the fire that enter the chamber reduce the current, triggering the smoke detector\'s alarm.
Radium-223 is also an alpha emitter. It is used in the treatment of skeletal metastases (cancers in the bones).
Alpha decay can provide a safe power source for radioisotope thermoelectric generators used for space probes and were used for artificial heart pacemakers. Alpha decay is much more easily shielded against than other forms of radioactive decay.
Static eliminators typically use polonium-210, an alpha emitter, to ionize the air, allowing the \"static cling\" to dissipate more rapidly.
## Toxicity
Highly charged and heavy, alpha particles lose their several MeV of energy within a small volume of material, along with a very short mean free path. This increases the chance of double-strand breaks to the DNA in cases of internal contamination, when ingested, inhaled, injected or introduced through the skin. Otherwise, touching an alpha source is typically not harmful, as alpha particles are effectively shielded by a few centimeters of air, a piece of paper, or the thin layer of dead skin cells that make up the epidermis; however, many alpha sources are also accompanied by beta-emitting radio daughters, and both are often accompanied by gamma photon emission.
Relative biological effectiveness (RBE) quantifies the ability of radiation to cause certain biological effects, notably either cancer or cell-death, for equivalent radiation exposure. Alpha radiation has a high linear energy transfer (LET) coefficient, which is about one ionization of a molecule/atom for every angstrom of travel by the alpha particle. The RBE has been set at the value of 20 for alpha radiation by various government regulations. The RBE is set at 10 for neutron irradiation, and at 1 for beta radiation and ionizing photons.
However, the recoil of the parent nucleus (alpha recoil) gives it a significant amount of energy, which also causes ionization damage (see ionizing radiation). This energy is roughly the weight of the alpha (`{{val|4|ul=Da}}`{=mediawiki}) divided by the weight of the parent (typically about 200 Da) times the total energy of the alpha. By some estimates, this might account for most of the internal radiation damage, as the recoil nucleus is part of an atom that is much larger than an alpha particle, and causes a very dense trail of ionization; the atom is typically a heavy metal, which preferentially collect on the chromosomes. In some studies, this has resulted in an RBE approaching 1,000 instead of the value used in governmental regulations.
The largest natural contributor to public radiation dose is radon, a naturally occurring, radioactive gas found in soil and rock. If the gas is inhaled, some of the radon particles may attach to the inner lining of the lung. These particles continue to decay, emitting alpha particles, which can damage cells in the lung tissue. The death of Marie Curie at age 66 from aplastic anemia was probably caused by prolonged exposure to high doses of ionizing radiation, but it is not clear if this was due to alpha radiation or X-rays. Curie worked extensively with radium, which decays into radon, along with other radioactive materials that emit beta and gamma rays. However, Curie also worked with unshielded X-ray tubes during World War I, and analysis of her skeleton during a reburial showed a relatively low level of radioisotope burden.
The Russian defector Alexander Litvinenko\'s 2006 murder by radiation poisoning is thought to have been carried out with polonium-210, an alpha emitter
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\[\[<File:World-population-in-extreme-poverty-absolute.svg%7Cthumb%7Cupright=1.6%7CNumber> of people living in extreme poverty from 1820 to 2015.
\]\] thumb\|upright=1.6\|Total population living in extreme poverty, by world region 1990 to 2015. `{{legend|#97cb72|Latin America and Caribbean}}`{=mediawiki} `{{legend|#eb6d6a|East Asia and Pacific Islands}}`{=mediawiki} `{{legend|#facfaf|South Asia}}`{=mediawiki} `{{legend|#6ab3b8|Middle East and North Africa}}`{=mediawiki} `{{legend|#ffe178|Europe and Central Asia}}`{=mediawiki} `{{legend|#6f8fc2|Sub-Saharan Africa}}`{=mediawiki} `{{legend|#b890ba|Other high income countries}}`{=mediawiki} thumb\|upright=1.6\|The number of people living on less than \$1.90, \$3.20, \$5.50, and \$10 globally from 1981 to 2015. `{{legend|#70b678|More than $10 a day}}`{=mediawiki} `{{legend|#badaac|$5.50 to $10 a day}}`{=mediawiki} `{{legend|#fddf75|$3.20 to $5.50 a day}}`{=mediawiki} `{{legend|#da6668|$1.90 to $3.20 a day}}`{=mediawiki} `{{legend|#6f8fc2|Less than $1.90 a day}}`{=mediawiki}
**Extreme poverty** is the most severe type of poverty, defined by the United Nations (UN) as \"a condition characterized by severe deprivation of basic human needs, including food, safe drinking water, sanitation facilities, health, shelter, education and information. It depends not only on income but also on access to services\". Historically, other definitions have been proposed within the United Nations.
Extreme poverty mainly refers to an income below the international poverty line of \$1.90 per day in 2018 (\$`{{format price|{{Inflation|US|1.90|2011|r=2}}}}`{=mediawiki} in `{{Inflation-year|US}}`{=mediawiki} dollars),`{{Inflation-fn|US}}`{=mediawiki} set by the World Bank. This is the equivalent of \$1.00 a day in 1996 US prices, hence the widely used expression \"living on less than a dollar a day\". The vast majority of those in extreme poverty reside in South Asia and Sub-Saharan Africa. As of 2018, it is estimated that the country with the most people living in extreme poverty is Nigeria, at 86 million.
In the past, the vast majority of the world population lived in conditions of extreme poverty. The percentage of the global population living in absolute poverty fell from over 80% in 1800 to around 10% by 2015. According to UN estimates, `{{as of|alt=in 2015|2015}}`{=mediawiki} roughly 734 million people or 10% remained under those conditions. The number had previously been measured as 1.9 billion in 1990, and 1.2 billion in 2008. Despite the significant number of individuals still below the international poverty line, these figures represent significant progress for the international community, as they reflect a decrease of more than one billion people over 15 years.
In public opinion surveys around the globe, people surveyed tend to think that extreme poverty has not decreased.
The reduction of extreme poverty and hunger was the first Millennium Development Goal (MDG1), as set by the United Nations in 2000. Specifically, the target was to reduce the extreme poverty rate by half by 2015, a goal that was met five years ahead of schedule. In the Sustainable Development Goals, which succeeded the MDGs, the goal is to end extreme poverty in all its forms everywhere. With this declaration the international community, including the UN and the World Bank have adopted the target of ending extreme poverty by 2030.
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## Definition
### Previous definitions {#previous_definitions}
In July 1993, Leandro Despouy, the then UN Special Rapporteur on extreme poverty and human rights made use of a definition he adapted from a 1987 report to the French Economic and Social Council by Fr. Joseph Wresinski, founder of the International Movement ATD Fourth World, distinguishing \"lack of basic security\" (poverty) and \"chronic poverty\" (extreme poverty), linking the eradication of extreme poverty by allowing people currently experiencing it a real opportunity to exercise all their human rights:
This definition was mentioned previously, in June 1989, in the preliminary report on the realization of economic, social and cultural rights by the UN Special Rapporteur Danilo Türk. It is still in use today, among others, in the current UN Guiding Principles on Extreme Poverty and Human Rights adopted by the UN Human Rights Council in September 2012.
### Consumption-based definition {#consumption_based_definition}
Extreme poverty is defined by the international community as living below \$1.90 a day, as measured in 2011 international prices (equivalent to \$2.12 in 2018). This number, also known as the international poverty line, is periodically updated to account for inflation and differences in the cost of living; it was originally defined at \$1.00 a day in 1996. The updates are made according to new price data to portray the costs of basic food, health services, clothing, and shelter around the world as accurately as possible. The latest revision was made in 2015 when the World Bank increased the line to international-\$1.90.
Because many of the world\'s poorest people do not have a monetary income, the poverty measurement is based on the monetary value of a person\'s *consumption*. Otherwise the poverty measurement would be missing the home production of subsistence farmers that consume largely their own production.
### Alternative definitions {#alternative_definitions}
thumb\|upright=1.6\|Share of population living in multidimensional poverty in 2014 The \$1.90/day extreme poverty line remains the most widely used metric as it highlights the reality of those in the most severe conditions. Although widely used by most international organizations, it has come under scrutiny due to a variety of factors. For example, it does not account for how far below the line people are, referred to as the depth of poverty. For this purpose, the same institutions publish data on the poverty gap.
The international poverty line is designed to stay constant over time, to allow comparisons between different years. It is therefore a measure of absolute poverty and is not measuring relative poverty. It is also not designed to capture how people view their own financial situation (known as the socially subjective poverty line). Moreover, the calculation of the poverty line relies on information about consumer prices to calculate purchasing power parity, which are very hard to measure and are necessarily debatable. As with all other metrics, there may also be missing data from the poorest and most fragile countries.
Several alternative instruments for measuring extreme poverty have been suggested which incorporate other factors such as malnutrition and lack of access to a basic education. The Multidimensional Poverty Index (MPI), based on the Alkire-Foster Method, is published by the Oxford Poverty & Human Development Initiative (OPHI): it measures deprivation in basic needs and can be broken down to reflect both the incidence and the intensity of poverty. For example, under conventional measures, in both Ethiopia and Uzbekistan about 40% of the population is considered extremely poor, but based on the MPI, 90% of Ethiopians but only 2% of Uzbeks are in multidimensional poverty.
The MPI is useful for development officials to determine the most likely causes of poverty within a region, using the M0 measure of the method (which is calculated by multiplying the fraction of people in poverty by the fraction of dimensions they are deprived in). For example, in the Gaza Strip of Palestine, using the M0 measure of the Alkire-Foster method reveals that poverty in the region is primarily caused by a lack of access to electricity, lack of access to drinking water, and widespread overcrowding. In contrast, data from the Chhukha District of Bhutan reveals that income is a much larger contributor to poverty as opposed to other dimensions within the region. However, the MPI only presents data from 105 countries, so it cannot be used for global measurements.
## Share of the population living in extreme poverty {#share_of_the_population_living_in_extreme_poverty}
Region 1990 1995 2000 2005 2010 2015 2017
---------------------------- ----------- ----------- ----------- ----------- ----------- ------------ ------------
Developed countries 4.06 4.99 4.7 5.48 5.28 7.91 7.45
Latin America & Caribbean 66.61 64.75 65.77 54.04 35.3 22.95 23.73
Middle East & North Africa 14.8 16.49 9.95 9.6 6.86 15.74 24.16
South Asia 557.05 550.44 564.92 533.28 425.32 230.51 173.1
East Asia & Pacific 977.29 766.14 632.26 347.99 212.12 42.08 29.15
Europe & Central Asia 11.51 32 34.28 22.04 11.27 7.35 6.37
Sub-Saharan Africa 280.95 352.76 388.27 393.57 412.49 417.6 432.5
**Total** **1,910** **1,790** **1,700** **1,370** **1,110** **744.14** **696.45**
: Number of people pushed below the \$1.90 (\$2011 PPP) poverty line (in millions) \|+
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## Current trends {#current_trends}
### Getting to zero {#getting_to_zero}
upright=2.0\|right\|thumb\|Various projections for the prospect of ending extreme poverty by 2030. The *y*-axis represents the percentage of people living in extreme poverty worldwide.
Using the World Bank definition of \$1.90/day, `{{as of|2021|lc=y}}`{=mediawiki}, roughly 710 million people remained in extreme poverty (or roughly 1 in 10 people worldwide). Nearly half of them live in India and China, with more than 85% living in just 20 countries. Since the mid-1990s, there has been a steady decline in both the worldwide poverty rate and the total number of extreme poor. In 1990, the percentage of the global population living in extreme poverty was 43%, but in 2011, that percentage had dropped down to 21%. This halving of the extreme poverty rate falls in line with the first Millennium Development Goal (MDG1) proposed by former UN Secretary-General Kofi Annan, who called on the international community at the turn of the century to reduce the percentage of people in extreme poverty by half by 2015.
This reduction in extreme poverty took place most notably in China, Indonesia, India, Pakistan and Vietnam. These five countries accounted for the alleviation of 715 million people out of extreme poverty between 1990 and 2010 -- more than the global net total of roughly 700 million. This statistical oddity can be explained by the fact that the number of people living in extreme poverty in Sub-Saharan Africa rose from 290 million to 414 million over the same period. However, there have been many positive signs for extensive, global poverty reduction as well. Since 1999, the total number of extreme poor has declined by an average of 50 million per year. Moreover, in 2005, for the first time in recorded history, poverty rates began to fall in every region of the world, including Africa.
As aforementioned, the number of people living in extreme poverty has reduced from 1.9 billion to 766 million over the span of the last decades. If we remain on our current trajectory, many economists predict we could reach global zero by 2030--2035, thus ending extreme poverty. Global zero entails a world in which fewer than 3% of the global population lives in extreme poverty (projected under most optimistic scenarios to be fewer than 200 million people). This zero figure is set at 3% in recognition of the fact that some amount of frictional (temporary) poverty will continue to exist, whether it is caused by political conflict or unexpected economic fluctuations, at least for the foreseeable future. However, the Brookings Institution notes that any projection about poverty more than a few years into the future runs the risk of being highly uncertain. This is because changes in consumption and distribution throughout the developing world over the next two decades could result in monumental shifts in global poverty, for better or worse.
Others are more pessimistic about this possibility, predicting a range of 193 million to 660 million people still living in extreme poverty by 2035. Additionally, some believe the rate of poverty reduction will slow down in the developing world, especially in Africa, and as such it will take closer to five decades to reach global zero. Despite these reservations, several prominent international and national organizations, including the UN, the World Bank and the United States Federal Government (via USAID), have set a target of reaching global zero by the end of 2030.
More recent analyses in 2022 on real wages have questioned whether extreme poverty was a \"natural\" condition of humanity and decreased with the rise of capitalism.
upright=1.4\|thumb\|Reduction in global poverty by year in percentage points
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## Current trends {#current_trends}
### Exacerbating factors {#exacerbating_factors}
There are a variety of factors that may reinforce or instigate the existence of extreme poverty, such as weak institutions, cycles of violence and a low level of growth. Recent World Bank research shows that some countries can get caught in a \"fragility trap\", in which self-reinforcing factors prevent the poorest nations from emerging from low-level equilibrium in the long run. Moreover, most of the reduction in extreme poverty over the past twenty years has taken place in countries that have not experienced a civil conflict or have had governing institutions with a strong capacity to actually govern. Thus, to end extreme poverty, it is also important to focus on the interrelated problems of fragility and conflict.
USAID defines fragility as a government\'s lack of both legitimacy (the perception the government is adequate at doing its job) and effectiveness (how good the government is at maintaining law and order, in an equitable manner). As fragile nations are unable to equitably and effectively perform the functions of a state, these countries are much more prone to violent unrest and mass inequality. Additionally, in countries with high levels of inequality (a common problem in countries with inadequate governing institutions), much higher growth rates are needed to reduce the rate of poverty when compared with other nations. Additionally, if China and India are removed from the equation, up to 70% of the world\'s poor live in fragile states by some definitions of fragility. Some analysts project that extreme poverty will be increasingly concentrated in fragile, low-income states like Haiti, Yemen and the Central African Republic. However, some academics, such as Andy Sumner, say that extreme poverty will be increasingly concentrated in middle-income countries, creating a paradox where the world\'s poor do not actually live in the poorest countries.
To help low-income earners, fragile states make the transition towards peace and prosperity, the New Deal for Engagement in Fragile States, endorsed by roughly forty countries and multilateral institutions, was created in 2011. This represents an important step towards redressing the problem of fragility as it was originally articulated by self-identified fragile states who called on the international community to not only \"do things differently\", but to also \"do different things\".
Civil conflict also remains a prime cause for the perpetuation of poverty throughout the developing world. Armed conflict can have severe effects on economic growth for many reasons such as the destruction of assets, destruction of livelihoods, creation of unwanted mass migration, and diversion of public resources towards war. Significantly, a country that experienced major violence during 1981--2005 had extreme poverty rates 21 percentage points higher than a country with no violence. On average, each civil conflict will cost a country roughly 30 years of GDP growth. Therefore, a renewed commitment from the international community to address the deteriorating situation in highly fragile states is necessary to both prevent the mass loss of life, but to also prevent the vicious cycle of extreme poverty.
Population trends and dynamics (e.g. population growth) can also have a large impact on prospects for poverty reduction. According to the United Nations, \"in addition to improving general health and well-being, analysis shows that meeting the reproductive health and contraceptive needs of all women in the developing world more than pays for itself\").
In 2013, a prominent finding in a report by the World Bank was that extreme poverty is most prevalent in low-income countries. In these countries, the World Bank found that progress in poverty reduction is the slowest, the poor live under the worst conditions, and the most affected persons are children age 12 and under.
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## International initiatives {#international_initiatives}
### Millennium Summit and Millennium Development Goals {#millennium_summit_and_millennium_development_goals}
In September 2000, world leaders gathered at the Millennium Summit held in New York, launching the United Nations Millennium Project suggested by then UN Secretary-General Kofi Annan. Prior to the launch of the conference, the office of Secretary-General Annan released a report entitled \"We The Peoples: The Role of the United Nations in the 21st Century\". In this document, now widely known as the Millennium Report, Kofi Annan called on the international community to reduce the proportion of people in extreme poverty by half by 2015, a target that would affect over 1 billion people. Citing the close correlation between economic growth and the reduction of poverty in poor countries, Annan urged international leaders to indiscriminately target the problem of extreme poverty across every region. In charge of managing the project was Jeffrey Sachs, a noted development economist, who in 2005 released a plan for action called \"Investing in Development: A Practical Plan to Achieve the Millennium Development Goals\". Thomas Pogge criticized the 2000 Millennium Declaration for being less ambitious than a previous declaration from the World Food Summit due to using 1990 as the benchmark rather than 1996.
Overall, there has been significant progress towards reducing extreme poverty, with the MDG1 target of reducing extreme poverty rates by half being met five years early, representing 700 million people being lifted out of extreme poverty from 1990 to 2010, with 1.2 billion people still remaining under those conditions. The notable exception to this trend was in Sub-Saharan Africa, the only region where the number of people living in extreme poverty rose from 290 million in 1990 to 414 million in 2010, comprising more than a third of those living in extreme poverty worldwide.
#### 2005 World Summit {#world_summit}
The 2005 World Summit, held in September which was organized to measure international progress towards fulfilling the Millennium Development Goals (MDGs). Notably, the conference brought together more than 170 Heads of State. While world leaders at the summit were encouraged by the reduction of poverty in some nations, they were concerned by the uneven decline of poverty within and among different regions of the globe. However, at the end of the summit, the conference attendees reaffirmed the UN\'s commitment to achieve the MDGs by 2015 and urged all supranational, national and non-governmental organizations to follow suit.
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## International initiatives {#international_initiatives}
### Sustainable Development Goals {#sustainable_development_goals}
As the expiration of the Millennium Development Goals approached in 2015, the UN convened a panel to advise on a Post-2015 Development Agenda, which led to a new set of 17 goals for 2030 titled the Sustainable Development Goals (SDGs). The first goal (SDG 1) is to \"End poverty in all its forms everywhere.\"
The HLP report, entitled A New Global Partnership: Eradicate Poverty and Transform Economies Through Sustainable Development, was published in May 2013. In the report, the HLP wrote that:
> Ending extreme poverty is just the beginning, not the end. It is vital, but our vision must be broader: to start countries on the path of sustainable development -- building on the foundations established by the 2012 UN Conference on Sustainable Development in Rio de Janeiro, and meeting a challenge that no country, developed or developing, has met so far. We recommend to the Secretary-General that deliberations on a new development agenda must be guided by the vision of eradicating extreme poverty once and for all, in the context of sustainable development.
Therefore, the report determined that a central goal of the Post-Millennium Development agenda is to eradicate extreme poverty by 2030. However, the report also emphasized that the MDGs were not enough on their own, as they did not \"focus on the devastating effects of conflict and violence on development \... the importance to development of good governance and institution \... nor the need for inclusive growth\...\" Consequently, there now exists synergy between the policy position papers put forward by the United States (through USAID), the World Bank and the UN itself in terms of viewing fragility and a lack of good governance as exacerbating extreme poverty. However, in a departure from the views of other organizations, the commission also proposed that the UN focus not only on extreme poverty (a line drawn at \$1.25), but also on a higher target, such as \$2. The report notes this change could be made to reflect the fact that escaping extreme poverty is only a first step.
In addition to the UN, a host of other supranational and national actors such as the European Union and the African Union have published their own positions or recommendations on what should be incorporated in the Post-2015 agenda. The European Commission\'s communication, published in A decent Life for all: from vision to collective action, affirmed the UN\'s commitment to \"eradicate extreme poverty in our lifetime and put the world on a sustainable path to ensure a decent life for all by 2030\". A unique vision of the report was the commission\'s environmental focus (in addition to a plethora of other goals such as combating hunger and gender inequality). Specifically, the Commission argued, \"long-term poverty reduction \... requires inclusive and sustainable growth. Growth should create decent jobs, take place with resource efficiency and within planetary boundaries, and should support efforts to mitigate climate change.\" The African Union\'s report, entitled Common African Position (CAP) on the Post-2015 Development Agenda, likewise encouraged the international community to focus on eradicating the twin problems of poverty and exclusion in our lifetime. Moreover, the CAP pledged that \"no person -- regardless of ethnicity, gender, geography, disability, race or other status -- is denied universal human rights and basic economic opportunities\".
### Least developed country conferences {#least_developed_country_conferences}
The UN least developed country (LDC) conferences were a series of summits organized by the UN to promote the substantial and even development of the world\'s least developed countries.
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## Organizations working to end extreme poverty {#organizations_working_to_end_extreme_poverty}
### International organizations {#international_organizations}
#### World Bank {#world_bank}
In 2013, the Board of Governors of the World Bank Group (WBG) set two overriding goals for the WBG to commit itself to in the future. First, to end extreme poverty by 2030, an objective that echoes the sentiments of the UN and the Obama administration. Additionally, the WBG set an interim target of reducing extreme poverty to below 9% by 2020. Second, to focus on growth among the bottom 40% of people, as opposed to standard GDP growth. This commitment ensures that the growth of the developing world lifts people out of poverty, rather than exacerbating inequality.
As the World Bank\'s primary focus is on delivering economic growth to enable equitable prosperity, its developments programs are primarily commercial-based in nature, as opposed to the UN. Since the World Bank recognizes better jobs will result in higher income, and thus less poverty, the WBG seeks to support employment training initiatives, small business development programs and strong labor protection laws. However, since much of the growth in the developing world has been inequitable, the World Bank has also begun teaming with client states to map out trends in inequality and to propose public policy changes that can level the playing field.
Moreover, the World Bank engages in a variety of nutritional, transfer payments and transport-based initiatives. Children who experience under-nutrition from conception to two years of age have a much higher risk of physical and mental disability. Thus, they are often trapped in poverty and are unable to make a full contribution to the social and economic development of their communities as adults. The WBG estimates that as much as 3% of GDP can be lost as a result of under-nutrition among the poorest nations. To combat undernutrition, the WBG has partnered with UNICEF and the WHO to ensure all small children are fully fed. The WBG also offers conditional cash transfers to poor households who meet certain requirements such as maintaining children\'s healthcare or ensuring school attendance. Finally, the WBG understands investment in public transportation and better roads is key to breaking rural isolation, improving access to healthcare and providing better job opportunities for the World\'s poor.
#### United Nations {#united_nations}
The UN Office for the Coordination of Humanitarian Affairs (OCHA) works to synchronize the disparate international, national and non-governmental efforts to contest poverty. OCHA seeks to prevent \"confusion\" in relief operations and to ensure that the humanitarian response to disaster situations has greater accountability and predictability. To do so, OCHA has begun deploying Humanitarian Coordinators and Country Teams to provide a solid architecture for the international community to work through.
The United Nation\'s Children\'s Fund (UNICEF) was created by the UN to provide food, clothing and healthcare to European children facing famine and disease in the immediate aftermath of World War II. After the UN General Assembly extended UNICEF\'s mandate indefinitely in 1953, it actively worked to help children in extreme poverty in more than 190 countries and territories to overcome the obstacles that poverty, violence, disease and discrimination place in a child\'s path. Its current focus areas are 1) Child survival & development 2) Basic education & gender equality 3) Children and HIV/AIDS and 4) Child protection.
The UN Refugee Agency (UNHCR) is mandated to lead and coordinate international action to protect refugees worldwide. Its primary purpose is to safeguard the rights of refugees by ensuring anyone can exercise the right to seek asylum in another state, with the option to return home voluntarily, integrate locally or resettle in a third country. The UNHCR operates in over 125 countries, helping approximately 33.9 million persons.
The World Food Programme (WFP) is the largest agency dedicated to fighting hunger worldwide. On average, the WFP brings food assistance to more than 90 million people in 75 countries. The WFP not only strives to prevent hunger in the present, but also in the future by developing stronger communities which will make food even more secure on their own. The WFP has a range of expertise from Food Security Analysis, Nutrition, Food Procurement and Logistics.
The World Health Organization (WHO) is responsible for providing leadership on global health matters, shaping the health research agenda, articulating evidence-based policy decisions and combating diseases that are induced from poverty, such as HIV/AIDS, malaria and tuberculosis. Moreover, the WHO deals with pressing issues ranging from managing water safety, to dealing with maternal and newborn health.
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## Organizations working to end extreme poverty {#organizations_working_to_end_extreme_poverty}
### Governmental agencies {#governmental_agencies}
#### USAID
The US Agency for International Development (USAID) is the lead US government agency dedicated to ending extreme poverty. Currently the largest bilateral donor in the world, the United States channels the majority of its development assistance through USAID and the US Department of State. In President Obama\'s 2013 State of the Union address, he declared, \"So the United States will join with our allies to eradicate such extreme poverty in the next two decades \... which is within our reach.\" In response to Obama\'s call to action, USAID has made ending extreme poverty central to its mission statement. Under its New Model of Development, USAID seeks to eradicate extreme poverty through the use of innovation in science and technology, by putting a greater emphasis on evidence based decision-making, and through leveraging the ingenuity of the private sector and global citizens.
A major initiative of the Obama administration is Power Africa, which aims to bring energy to 20 million people in Sub-Saharan Africa. By reaching out to its international partners, whether commercial or public, the US has leveraged over \$14 billion in outside commitments after investing only US\$7 billion of its own. To ensure that Power Africa reaches the region\'s poorest, the initiative engages in a transaction based approach to create systematic change. This includes expanding access to electricity to more than 20,000 additional households which already live without power.
In terms of specific programming, USAID works in a variety of fields from preventing hunger, reducing HIV/AIDS, providing general health assistance and democracy assistance, as well as dealing with gender issues. To deal with food security, which affects roughly 842 million people (who go to bed hungry each night), USAID coordinates the Feed the Future Initiative (FtF). FtF aims to reduce poverty and under-nutrition each by 20% over five years. Because of the President\'s Emergency Plan for AIDS Relief (PEPFAR) and a variety of congruent actors, the incidence of AIDS and HIV, which used to ravage Africa, reduced in scope and intensity. Through PEPFAR, the United States has ensured over five million people have received life-saving antiviral drugs, a significant proportion of the eight million people receiving treatment in relatively poor nations.
In terms of general health assistance, USAID has worked to reduce maternal mortality by 30%, under-five child mortality by 35%, and has accomplished a host of other goals. USAID also supports the gamut of democratic initiatives, from promoting human rights and accountable, fair governance, to supporting free and fair elections and the rule of law. In pursuit of these goals, USAID has increased global political participation by training more than 9,800 domestic election observers and providing civic education to more than 6.5 million people. Since 2012, the Agency has begun integrating critical gender perspectives across all aspects of its programming to ensure all USAID initiatives work to eliminate gender disparities. To do so, USAID seeks to increase the capability of women and girls to realize their rights and determine their own life outcomes. Moreover, USAID supports additional programs to improve women\'s access to capital and markets, builds theirs skills in agriculture, and supports women\'s desire to own businesses.
#### Others
Other major government development agencies with annual aid programmes of more than \$10 billion include: GIZ (Germany), FCDO (United Kingdom), JICA (Japan), European Union and AFD (France).
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## Organizations working to end extreme poverty {#organizations_working_to_end_extreme_poverty}
### Non-Governmental Organizations {#non_governmental_organizations}
A multitude of non-governmental organizations operate in the field of extreme poverty, actively working to alleviate the poorest of the poor of their deprivation. To name but a few notable organizations: Save the Children, the Overseas Development Institute, Concern Worldwide, ONE, Trickle Up and Oxfam have all done a considerable amount of work in extreme poverty.
Save the Children is the leading international organization dedicated to helping the world\'s indigent children. In 2013, Save the Children reached over 143 million children through their work, including over 52 million children directly. Save the Children also recently released their own report titled \"Getting to Zero\", in which they argued the international community could feasibly do more than lift the world\'s poor above \$1.25/day.
The Overseas Development Institute (ODI) is a UK based think tank on international development and humanitarian issues. ODI is dedicated to alleviating the suffering of the world\'s poor by providing high-quality research and practical policy advice to the World\'s development officials. ODI also recently released a paper entitled, \"The Chronic Poverty Report 2014--2015: The road to zero extreme poverty\", in which its authors assert that though the international communities\' goal of ending extreme poverty by 2030 is laudable, much more targeted resources will be necessary to reach said target. The report states that \"To eradicate extreme poverty, massive global investment is required in social assistance, education and pro-poorest economic growth\".
Concern Worldwide is an international humanitarian organization whose mission is to end extreme poverty by influencing decision makers at all levels of government (from local to international). Concern has also produced a report on extreme poverty in which they explain their own conception of extreme poverty from a NGO\'s standpoint. In this paper, named \"How Concern Understands Extreme Poverty\", the report\'s creators write that extreme poverty entails more than just living under \$1.25/day, it also includes having a small number of assets and being vulnerable to severe negative shocks (whether natural or man made).
ONE, the organization co-founded by Bono, is a non-profit organization funded almost entirely by foundations, individual philanthropists and corporations. ONE\'s goals include raising public awareness and working with political leaders to fight preventable diseases, increase government accountability and increase investment in nutrition. Finally, Trickle Up is a micro-enterprise development program targeted at those living on under \$1.25/day, which provides the indigent with resources to build a sustainable livelihood through both direct financing and considerable training efforts.
Oxfam is a non-governmental organization that works prominently in Africa; their mission is to improve local community organizations and it works to reduce impediments to the development of the country. Oxfam helps families suffering from poverty receive food and healthcare to survive. There are many children in Africa experiencing growth stunting, and this is one example of an issue that Oxfam targets and aims to resolve.
Cash transfers appear to be an effective intervention for reducing extreme poverty, while at the same time improving health and education outcomes
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The **geography of Antarctica** is dominated by its south polar location and, thus, by ice. The Antarctic continent, located in the Earth\'s southern hemisphere, is centered asymmetrically around the South Pole and largely south of the Antarctic Circle. It is washed by the Southern (or Antarctic) Ocean or, depending on definition, the southern Pacific, Atlantic, and Indian Oceans. It has an area of more than 14200000 sqkm. Antarctica is the largest ice desert in the world.
Some 98% of Antarctica is covered by the Antarctic ice sheet, the world\'s largest ice sheet and also its largest reservoir of fresh water. Averaging at least 1.6 km thick, the ice is so massive that it has depressed the continental bedrock in some areas more than 2.5 km below sea level; subglacial lakes of liquid water also occur (e.g. Lake Vostok). Ice shelves and rises populate the ice sheet on the periphery. The present Antarctic ice sheet accounts for 90 percent of Earth\'s total ice volume and 70 percent of its fresh water. It houses enough water to raise global sea level by 200 ft.
In September 2018, researchers at the National Geospatial-Intelligence Agency released a high resolution terrain map (detail down to the size of a car, and less in some areas) of Antarctica, named the \"Reference Elevation Model of Antarctica\" (REMA).
## Regions
Physically, Antarctica is divided in two by the Transantarctic Mountains, close to the neck between the Ross Sea and the Weddell Sea. Western Antarctica and Eastern Antarctica correspond roughly to the western and eastern hemispheres relative to the Greenwich meridian.
West Antarctica is covered by the West Antarctic Ice Sheet. There has been some concern about this ice sheet, as there is a small chance it will collapse due to rising temperatures in the region. If it does, global ocean levels will rise by a few metres in a short period of time.
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## Volcanoes
Volcanic activity occurring beneath glacial ice sheets is known as glaciovolcanism. An article published in 2017 claims that researchers from the University of Edinburgh discovered 91 new volcanoes below the Antarctic ice sheet, adding to the 47 volcanoes that were already known. As of 2017, 138 possible volcanoes have been identified in West Antarctica. There is limited knowledge about West Antarctic Volcanoes due to the presence of the West Antarctic Ice Sheet, which heavily covers the West Antarctic Rift System --- a likely hub for volcanic activity. Researchers find it difficult to properly identify volcanic activity due to the comprehensive ice covering.
East Antarctica is significantly larger than West Antarctica, and similarly remains widely unexplored in terms of its volcanic potential. While there are some indications that there is volcanic activity under the East Antarctic Ice Sheet, there is not a significant amount of present information on the subject.
Mount Erebus, as the southernmost historically active volcanic site on the planet, is one of the most notable sites in the study of Antarctic volcanism.
Deception Island is another active Antarctic volcano. It is one of the most protected areas in the Antarctic, given its situation between the South Shetland Islands and the Antarctic Peninsula. As the most active volcano in the Antarctic Peninsula, it has been studied closely since its initial discovery in 1820.
There are four volcanoes on the mainland of Antarctica that are considered to be active on the basis of observed fumarolic activity or \"recent\" tephra deposits:
1. Mount Melbourne (2,730 m) (74°21\'S., 164°42\'E.), a stratovolcano;
2. Mount Berlin (3,500 m) (76°03\'S., 135°52\'W.), a stratovolcano;
3. Mount Kauffman (2,365 m) (75°37\'S., 132°25\'W.), a stratovolcano; and
4. Mount Hampton (3,325 m) (76°29\'S., 125°48\'W.), a volcanic caldera.
Mount Rittmann (2,600 m) (73.45°S 165.5° E), a volcanic caldera, is dormant.
Several volcanoes on offshore islands have records of historic activity. Mount Erebus (3,795 m), a stratovolcano on Ross Island with 10 known eruptions and 1 suspected eruption. On the opposite side of the continent, Deception Island (62°57\'S., 60°38\'W.), a volcanic caldera with 10 known and 4 suspected eruptions, has been the most active. Buckle Island in the Balleny Islands (66°50\'S., 163°12\'E.), Penguin Island (62°06\'S., 57°54\'W.), Paulet Island (63°35\'S., 55°47\'W.), and Lindenberg Island (64°55\'S., 59°40\'W.) are also considered to be active. In 2017, the researchers of Edinburgh University discovered 91 underwater volcanoes under West Antarctica.
### Marie Byrd Land {#marie_byrd_land}
Marie Byrd Land makes up a large portion of West Antarctica, consisting of the Area below the Antarctic Peninsula. The Marie Byrd Land is a large formation of volcanic rock, characterized by 18 exposed and subglacial volcanoes. 16 of the 18 volcanoes are entirely covered by the antarctic ice sheet. There have been no eruptions recorded from any of the volcanoes in this area, however scientists believe that some of the volcanoes may be potentially active.
### Activity
Scientists and researchers debate whether or not the 138 identified possible volcanoes are active or dormant. It is very hard to definitively say, given that many of these volcanic structures are buried underneath several kilometers of ice. However, ash layers within the West Antarctic Ice Sheet, as well as deformations in the ice surface indicate that the West Antarctic Rift System could be active and contain erupting volcanoes. Additionally, seismic activity in the region hints at magma movement beneath the crust, a sign of volcanic activity. Despite this, however, there is not yet definitive evidence of presently active volcanoes.
Subglacial volcanism is often characterized by ice melt and subglacial water. Though there are other sources of subglacial water, such as geothermal heat, it almost always is a condition of volcanism. Scientists remain uncertain about the presence of liquid water underneath the West Antarctic Ice Sheet, with some claiming to have found evidence indicating its existence.
### Conditions of formation {#conditions_of_formation}
In West Antarctica\'s Marie Byrd Land, volcanoes are typically composed of alkaline and basaltic lava. Sometimes, the volcanoes are entirely basaltic in composition. Due to the geographic similarity of the Marie Byrd Land, it is believed that the volcanoes in the West Antarctic Rift System are also composed of basalt.
Above-ice basaltic volcanoes, also known as subaerial basaltic volcanoes, generally form in tall, broad cone shapes. Since they are formed from repeated piling of liquid magma sourced from the center, they spread widely and grow upwards relatively slowly. However, West Antarctic Volcanoes form underneath ice sheets, and are thus categorized as subglacial volcanoes. Subglacial volcanoes that are monogenetic are far more narrow, steeper, flat topped structures. Polygenetic subglacial volcanoes have a wider variety of shapes and sizes due to being made up of many different eruptions. Often, they look more cone shaped, like stratovolcanoes.
### Hazards
#### Hazardous ash {#hazardous_ash}
Little has been studied about the implications of volcanic ash from eruptions within the Antarctic Circle. It is likely that an eruption at lower latitudes would cause global health and aviation hazards due to ash disbursement. The clockwise air circulation around the low pressure system at the South Pole forces air upwards, hypothetically sending ash upwards towards the Stratospheric jet streams, and thus quickly dispersing it throughout the globe.
#### Melting ice {#melting_ice}
Recently, in 2017, a study found evidence of subglacial volcanic activity within the West Antarctic Ice Sheet. This activity poses a threat to the stability of the Ice Sheet, as volcanic activity leads to increased melting. This could possibly plunge the West Antarctic Ice Sheet into a positive feedback loop of rising temperatures and increased melting.
## Canyons
There are three vast canyons that run for hundreds of kilometers, cutting through tall mountains. None of the canyons are visible at the snow-covered surface of the continent since they are buried under hundreds of meters of ice. The largest of the canyons is called Foundation Trough and is over 350 km long and 35 km wide. The Patuxent Trough is more than 300 km long and over 15 km wide, while the Offset Rift Basin is 150 km long and 30 km wide. These three troughs all lie under and cross the so-called \"ice divide\" -- the high ice ridge that runs all the way from the South Pole out towards the coast of West Antarctica.
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