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April 19
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1901–present
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1901–present
1903 – The Kishinev pogrom in Kishinev (Bessarabia) begins, forcing tens of thousands of Jews to later seek refuge in Palestine and the Western world.
1925 – Colo-Colo, the most successful and popular soccer football team in the South American nation of Chile, was founded at the El Llano Stadium in San Miguel, Santiago, by footballer David Arellano and some of his teammates who had also left the Deportes Magallanes club.Sebastián Salinas, Por empuje y coraje. Los Albos en la época amateur 1925-1933 ("By drive and courage: The Albos in the amateur era 1925-1933")(Centro de Estudios del Deporte, 2004)|p.44
1927 – Mae West is sentenced to ten days in jail for obscenity for her play Sex.
1936 – The Jaffa riots commence, initiating the 1936–1939 Arab revolt in Palestine."9 Jews, 2 Arabs Dead, 54 Hurt In Jaffa Riots: Moslems Slain by British Police, Foes Knifed in Batlle (sic) Following Killing of a Jew by Bandits," New York Herald Tribune, 20 April 1936, p. 1.
1942 – World War II: In German-occupied Poland, the Majdan-Tatarski ghetto is established, situated between the Lublin Ghetto and a Majdanek subcamp.
1943 – World War II: In German-occupied Poland, the Warsaw Ghetto Uprising begins, after German troops enter the Warsaw Ghetto to round up the remaining Jews.
1943 – Albert Hofmann deliberately doses himself with LSD for the first time, three days after having discovered its effects on April 16, an event commonly known and celebrated as Bicycle Day.
1956 – Actress Grace Kelly marries Prince Rainier of Monaco.
1960 – Students in South Korea hold a nationwide pro-democracy protest against president Syngman Rhee, eventually forcing him to resign.
1971 – Sierra Leone becomes a republic, and Siaka Stevens the president.
1971 – Launch of Salyut 1, the first space station.
1971 – Charles Manson is sentenced to death (later commuted to life imprisonment) for conspiracy in the Tate–LaBianca murders.
1973 – The Portuguese Socialist Party is founded in the German town of Bad Münstereifel.
1975 – India's first satellite Aryabhata launched in orbit from Kapustin Yar, Russia.
1975 – South Vietnamese forces withdraw from the town of Xuan Loc in the last major battle of the Vietnam War.
1976 – A violent F5 tornado strikes around Brownwood, Texas, injuring 11 people. Two people were thrown at least by the tornado and survived uninjured.
1984 – Advance Australia Fair is proclaimed as Australia's national anthem, and green and gold as the national colours.
1985 – Two hundred ATF and FBI agents lay siege to the compound of the white supremacist survivalist group The Covenant, the Sword, and the Arm of the Lord in Arkansas; the CSA surrenders two days later.
1987 – The Simpsons first appear as a series of shorts on The Tracey Ullman Show, first starting with "Good Night".
1989 – A gun turret explodes on the , killing 47 sailors.
1993 – The 51-day FBI siege of the Branch Davidian building in Waco, Texas, USA, ends when a fire breaks out. Seventy-six Davidians, including 18 children under age 10, died in the fire.
1995 – Oklahoma City bombing: The Alfred P. Murrah Federal Building in Oklahoma City, USA, is bombed, killing 168 people including 19 children under the age of six.
1999 – The German Bundestag returns to Berlin.
2000 – Air Philippines Flight 541 crashes in Samal, Davao del Norte, killing all 131 people on board.
2001 – Space Shuttle Endeavour is launched on STS-100 carrying the Canadarm2 to the International Space Station.
2005 – Cardinal Joseph Ratzinger is elected to the papacy and becomes Pope Benedict XVI.
2011 – Fidel Castro resigns as First Secretary of the Communist Party of Cuba after holding the title since July 1961.
2013 – Boston Marathon bombing suspect Tamerlan Tsarnaev is killed in a shootout with police. His brother Dzhokhar is later captured hiding in a boat inside a backyard in the suburb of Watertown.
2020 – A killing spree in Nova Scotia, Canada, leaves 22 people and the perpetrator dead, making it the deadliest rampage in the country's history.
2021 – The Ingenuity helicopter becomes the first aircraft to achieve flight on another planet.
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April 19
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Births
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Births
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April 19
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Pre-1600
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Pre-1600
1452 – Frederick IV, King of Naples (d. 1504)
1593 – Sir John Hobart, 2nd Baronet, English politician (d. 1647)
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April 19
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1601–1900
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1601–1900
1603 – Michel Le Tellier, French politician, French Minister of Defence (d. 1685)
1613 – Christoph Bach, German musician (d. 1661)
1633 – Willem Drost, Dutch painter (d. 1659)
1655 – George St Lo(e), Royal Navy officer and administrator (d. 1718)
1658 – Johann Wilhelm, Elector Palatine, German husband of Archduchess Maria Anna Josepha of Austria (d. 1716)
1665 – Jacques Lelong, French author (d. 1721)
1686 – Vasily Tatishchev, Russian ethnographer and politician (d. 1750)
1715 – James Nares, English organist and composer (d. 1783)
1721 – Roger Sherman, American lawyer and politician (d. 1793)
1734 – Karl von Ordóñez, Austrian violinist and composer (d. 1786)
1757 – Edward Pellew, 1st Viscount Exmouth, English admiral and politician (d. 1833)
1758 – William Carnegie, 7th Earl of Northesk, Scottish admiral (d. 1831)
1785 – Alexandre Pierre François Boëly, French pianist and composer (d. 1858)
1787 – Deaf Smith, American soldier (d. 1837)
1793 – Ferdinand I of Austria (d. 1875)
1806 – Sarah Bagley, American labor organizer (d. 1889)
1814 – Louis Amédée Achard, French journalist and author (d. 1875)
1831 – Mary Louise Booth, American writer, editor and translator (d. 1889)
1832 – José Echegaray, Spanish poet and playwright, Nobel Prize laureate (d. 1916)
1835 – Julius Krohn, Finnish poet and journalist (d. 1888)
1861 – Amalie Andersen, Norwegian actress (d. 1924)
1863 – Hemmo Kallio, Finnish actor (d. 1940)
1872 – Alice Salomon, German social reformer (d. 1948)
1873 – Sydney Barnes, English cricketer (d. 1967)
1874 – Ernst Rüdin, Swiss psychiatrist, geneticist, and eugenicist (d. 1952)
1877 – Ole Evinrude, Norwegian-American engineer, invented the outboard motor (d. 1934)
1879 – Arthur Robertson, Scottish runner (d. 1957)
1882 – Getúlio Vargas, Brazilian lawyer and politician, 14th President of Brazil (d. 1954)
1883 – Henry Jameson, American soccer player (d. 1938)
1883 – Richard von Mises, Austrian-American mathematician and physicist (d. 1953)
1885 – Karl Tarvas, Estonian architect (d. 1975)
1889 – Otto Georg Thierack, German jurist and politician (d. 1946)
1891 – Françoise Rosay, French actress (d. 1974)
1892 – Germaine Tailleferre, French composer and educator (d. 1983)
1894 – Elizabeth Dilling, American author and activist (d. 1966)
1897 – Peter de Noronha, Indian businessman and philanthropist (d. 1970)
1897 – Jiroemon Kimura, Japanese super-centenarian, oldest verified man ever (d. 2013)
1898 – Constance Talmadge, American actress and producer (d. 1973)
1899 – George O'Brien, American actor (d. 1985)
1899 – Cemal Tollu, Turkish lieutenant and painter (d. 1968)
1900 – Iracema de Alencar, Brazilian film actress (d. 1978)
1900 – Richard Hughes, English author, poet, and playwright (d. 1976)
1900 – Roland Michener, Canadian lawyer and politician, 20th Governor General of Canada (d. 1991)
1900 – Rhea Silberta, American Yiddish songwriter and singing teacher (d. 1959)
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April 19
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1901–present
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1901–present
1902 – Veniamin Kaverin, Russian author and screenwriter (d. 1989)
1903 – Eliot Ness, American law enforcement agent (d. 1957)
1908 – Irena Eichlerówna, Polish actress (d. 1990)
1912 – Glenn T. Seaborg, American chemist and academic, Nobel Prize laureate (d. 1999)
1913 – Ken Carpenter, American discus thrower and coach (d. 1984)
1917 – Sven Hassel, Danish-German soldier and author (d. 2012)
1919 – Sol Kaplan, American pianist and composer (d. 1990)
1920 – Marvin Mandel, American lawyer and politician, 56th Governor of Maryland (d. 2015)
1920 – Julien Ries, Belgian cardinal (d. 2013)
1920 – Ragnar Ulstein, Norwegian journalist and war historian (d. 2019)
1921 – Anna Lee Aldred, American jockey (d. 2006)
1921 – Leon Henkin, American logician (d. 2006)
1921 – Roberto Tucci, Italian Jesuit leader, cardinal, and theologian (d. 2015)
1922 – Erich Hartmann, German colonel and pilot (d. 1993)
1925 – John Kraaijkamp, Sr., Dutch actor (d. 2011)
1925 – Hugh O'Brian, American actor (d. 2016)
1927 – Cora Sue Collins, American child actress (d.2025)
1926 – Rawya Ateya, Egyptian captain and politician (d. 1997)
1928 – John Horlock, English engineer and academic (d. 2015)
1928 – Azlan Shah of Perak, Yang di-Pertuan Agong of Malaysia (d. 2014)
1931 – Walter Stewart, Canadian journalist and author (d. 2004)
1932 – Fernando Botero, Colombian painter and sculptor (d. 2023)
1933 – Jayne Mansfield, American model and actress (d. 1967)
1934 – Dickie Goodman, American singer-songwriter and producer (d. 1989)
1935 – Dudley Moore, English actor, comedian, and pianist (d. 2002)
1935 – Justin Francis Rigali, American cardinal
1936 – Wilfried Martens, Belgian politician, 60th Prime Minister of Belgium (d. 2013)
1936 – Jack Pardee, American football player and coach (d. 2013)
1937 – Antonio Carluccio, Italian-English chef and author (d. 2017)
1937 – Elinor Donahue, American actress
1937 – Joseph Estrada, Filipino politician, 13th President of the Philippines
1938 – Stanley Fish, American theorist, author, and scholar
1939 – Clay Shaw, American accountant, judge, and politician (d. 2013)
1941 – Michel Roux, French-English chef and author (d. 2020)
1941 – Bobby Russell, American singer-songwriter (d. 1992)
1942 – Alan Price, English keyboard player, singer, and composer
1943 – Margo MacDonald, Scottish journalist and politician (d. 2014)
1944 – James Heckman, American economist and academic, Nobel Prize laureate
1944 – Bernie Worrell, American keyboard player and songwriter (d. 2016)
1946 – Tim Curry, English actor and singer
1951 – Jóannes Eidesgaard, Faroese educator and politician, Prime Minister of the Faroe Islands
1952 – Simon Cowell, English conservationist and author (d. 2024)
1954 – Trevor Francis, English footballer and manager (d. 2023)
1956 – Anne Glover, Scottish biologist and academic
1957 – Mukesh Ambani, Indian businessman, chairman of Reliance Industries
1960 – Ara Gevorgyan, Armenian pianist, composer, and producer
1960 – Gustavo Petro, Colombian politician, 34th and current President of Colombia
1960 – Frank Viola, American baseball player and coach
1964 – Kim Weaver, American astrophysicist, astronomer, and academic
1965 – Suge Knight, American record executive
1966 – Véronique Gens, French soprano and actress
1968 – Ashley Judd, American actress
1968 – Mswati III, King (Ngwenyama) of Eswatini (Swaziland)
1970 – Kelly Holmes, English athlete and double Olympic champion
1972 – Rivaldo Vitor Borba Ferreira, Brazilian footballer
1978 – James Franco, American actor, director, producer, and screenwriter
1978 – Amanda Sage, American-Austrian painter and educator
1979 – Kate Hudson, American actress
1981 – Hayden Christensen, Canadian actor
1981 – Lise Klaveness, Norwegian footballer and lawyer, president of the Norwegian Football Federation
1981 – Troy Polamalu, American football player
1982 – Samuel C. Morrison, Jr., Liberian-American journalist, producer, and screenwriter
1982 – Ali Wong, American comedian and actress
1983 – Joe Mauer, American baseball player
1986 – Candace Parker, American basketball player
1987 – Joe Hart, English footballer
1987 – Maria Sharapova, Russian tennis player
1989 – Simu Liu, Canadian actor
1990 – Jackie Bradley Jr., American baseball player
1990 – Kim Chiu, Filipino actress, singer, and dancer
1991 – Kelly Olynyk, Canadian basketball player
2001 – Dalton Knecht, American basketball player
2002 – Loren Gray, American singer and internet personality
2003 – Jackson Merrill, American baseball player
2016 – The Rizzler, American internet personality
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April 19
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Deaths
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Deaths
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April 19
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Pre-1600
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Pre-1600
843 – Judith of Bavaria, Frankish empress
1012 – Ælfheah of Canterbury, English archbishop and saint (b. 954)
1013 – Hisham II, Umayyad caliph of Córdoba (b. 966)
1044 – Gothelo I, duke of Lorraine
1054 – Leo IX, pope of the Catholic Church (b. 1002)
1321 – Gerasimus I, patriarch of Constantinople
1390 – Robert II, king of Scotland (b. 1316)
1405 – Thomas West, 1st Baron West, English nobleman (b. 1335)
1431 – Adolph III, count of Waldeck (b. 1362)
1560 – Philip Melanchthon, German theologian and reformer (b. 1497)
1567 – Michael Stifel, German monk and mathematician (b. 1487)
1578 – Uesugi Kenshin, Japanese samurai and warlord (b. 1530)
1588 – Paolo Veronese, Italian painter (b. 1528)
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April 19
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1601–1900
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1601–1900
1608 – Thomas Sackville, 1st Earl of Dorset, English poet, playwright, and politician, Lord High Treasurer (b. 1536)
1618 – Thomas Bastard, English priest and author (b. 1566)
1619 – Jagat Gosain, Mughal empress (b. 1573)
1629 – Sigismondo d'India, Italian composer (b. 1582)
1686 – Antonio de Solís y Ribadeneyra, Spanish historian and playwright (b. 1610)
1689 – Christina, queen of Sweden (b. 1626)
1733 – Elizabeth Hamilton, countess of Orkney (b. 1657)
1739 – Nicholas Saunderson, English mathematician and academic (b. 1682)
1768 – Canaletto, Italian painter and etcher (b. 1697)
1776 – Jacob Emden, German rabbi and author (b. 1697)
1791 – Richard Price, Welsh-English preacher and philosopher (b. 1723)
1813 – Benjamin Rush, American physician and educator (b. 1745)
1824 – Lord Byron, English-Scottish poet and playwright (b. 1788)
1831 – Johann Gottlieb Friedrich von Bohnenberger, German astronomer and mathematician (b. 1765)
1833 – James Gambier, 1st Baron Gambier, Bahamian-English admiral and politician, 36th Commodore Governor of Newfoundland (b. 1756)
1840 – Jean-Jacques Lartigue, Canadian bishop (b. 1777)
1854 – Robert Jameson, Scottish mineralogist and academic (b. 1774)
1881 – Benjamin Disraeli, English journalist and politician, Prime Minister of the United Kingdom (b. 1804)
1882 – Charles Darwin, English biologist and theorist (b. 1809)
1893 – Martin Körber, Estonian-German pastor, composer, and conductor (b. 1817)
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April 19
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1901–present
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1901–present
1901 – Alfred Horatio Belo, American publisher, founded The Dallas Morning News (b. 1839)
1903 – Oliver Mowat, Canadian politician, third Premier of Ontario, eighth Lieutenant Governor of Ontario (b. 1820)
1906 – Pierre Curie, French physicist and academic, Nobel Prize laureate (b. 1859)
1906 – Spencer Gore, English tennis player and cricketer (b. 1850)
1909 – Signe Rink, Greenland-born Danish writer and ethnologist (b. 1836)
1914 – Charles Sanders Peirce, American mathematician and philosopher (b. 1839)
1915 – Thomas Playford II, English-Australian politician, 17th Premier of South Australia (b. 1837)
1916 – Ephraim Shay, American engineer, designed the Shay locomotive (b. 1839)
1926 – Alexander Alexandrovich Chuprov, Russian-Swiss statistician and theorist (b. 1874)
1930 – Georges-Casimir Dessaulles, Canadian businessman and politician (b. 1827)
1937 – Martin Conway, 1st Baron Conway of Allington, English cartographer and politician (b. 1856)
1937 – William Morton Wheeler, American entomologist and zoologist (b. 1865)
1940 – Jack McNeela, Irish Republican Army, died on hunger strike
1941 – Johanna Müller-Hermann, Austrian composer (b. 1878)
1949 – Ulrich Salchow, Danish-Swedish figure skater (b. 1877)
1950 – Ernst Robert Curtius, French-German philologist and scholar (b. 1886)
1952 – Steve Conway, British singer (b. 1921)
1955 – Jim Corbett, British-Indian colonel, hunter, and author (b. 1875)
1960 – Beardsley Ruml, American economist and statistician (b. 1894)
1961 – Max Hainle, German swimmer (b. 1882)
1966 – Väinö Tanner, Finnish politician of Social Democratic Party of Finland; the Prime Minister of Finland (b. 1881)
1967 – Konrad Adenauer, German politician, 1st Chancellor of Germany (b. 1876)
1971 – Luigi Piotti, Italian race car driver (b. 1913)
1975 – Percy Lavon Julian, American chemist and academic (b. 1899)
1988 – Kwon Ki-ok, Korean pilot (b. 1901)
1989 – Daphne du Maurier, English novelist and playwright (b. 1907)
1991 – Stanley Hawes, English-Australian director and producer (b. 1905)
1992 – Frankie Howerd, English actor and screenwriter (b. 1917)
1993 – David Koresh, American cult leader (b. 1959)
1993 – George S. Mickelson, American captain, lawyer, and politician, 28th Governor of South Dakota (b. 1941)
1998 – Octavio Paz, Mexican poet, philosopher, and academic Nobel Prize laureate (b. 1914)
1999 – Hermine Braunsteiner, Austrian-German SS officer (b. 1919)
2000 – Louis Applebaum, Canadian composer and conductor (b. 1918)
2002 – Reginald Rose, American writer (b. 1920)
2004 – Norris McWhirter, English author and activist co-founded the Guinness World Records (b. 1925)
2004 – John Maynard Smith, English biologist and geneticist (b. 1920)
2004 – Jenny Pike, Canadian WWII servicewoman and photographer (b. 1922)
2006 – Albert Scott Crossfield, American engineer, pilot, and astronaut (b. 1921)
2007 – Jean-Pierre Cassel, French actor (b. 1932)
2009 – J. G. Ballard, English novelist, short story writer, and essayist (b. 1930)
2011 – Elisabeth Sladen, English actress (b. 1946)
2012 – Levon Helm, American musician and actor (b. 1940)
2013 – François Jacob, French biologist and academic, Nobel Prize laureate (b. 1920)
2013 – Al Neuharth, American journalist, author, and publisher, founded USA Today (b. 1924)
2015 – Raymond Carr, English historian and academic (b. 1919)
2015 – Roy Mason, English miner and politician, Secretary of State for Defence (b. 1924)
2016 – Patricio Aylwin, Chilean politician (b. 1918)
2017 – Lu Chao-Hsuan, Taiwanese guitarist, performer and educator. (b. 1929)
2020 – Ian Whitcomb, English singer-songwriter (b. 1941)
2021 – Walter Mondale, American politician, 42nd Vice President of the United States (b. 1928)
2021 – Jim Steinman, American composer, lyricist (b. 1947)
2022 – Kane Tanaka, Japanese supercentenarian (b. 1903)
2023 – Moonbin, South Korean singer and actor (b. 1998)
2023 – Ron Hamilton, American musician (b. 1950)
2024 – Daniel Dennett, American philosopher and author (b. 1942)
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April 19
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Holidays and observances
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Holidays and observances
Christian feast day:
Ælfheah of Canterbury (Anglican, Catholic)
Conrad of Ascoli
Emma of Lesum
Expeditus
George of Antioch
Olaus and Laurentius Petri (Lutheran)
Pope Leo IX
Ursmar
April 19 (Eastern Orthodox liturgics)
Bicycle Day, a psychedelic holiday
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April 19
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References
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References
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April 19
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External links
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External links
BBC: On This Day
Historical Events on April 19
Category:Days of April
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April 19
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Table of Content
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short description, Events, Pre-1600, 1601–1900, 1901–present, Births, Pre-1600, 1601–1900, 1901–present, Deaths, Pre-1600, 1601–1900, 1901–present, Holidays and observances, References, External links
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Amstrad CPC
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short description
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The Amstrad CPC (short for "Colour Personal Computer") is a series of 8-bit home computers produced by Amstrad between 1984 and 1990. It was designed to compete in the mid-1980s home computer market dominated by the Commodore 64 and the ZX Spectrum; it successfully established itself primarily in the United Kingdom, France, Spain, and the German-speaking parts of Europe, and also Canada.
The series spawned a total of six distinct models: The CPC 464, CPC 664, and CPC 6128 were highly successful competitors in the European home computer market. The later 464 plus and 6128 plus, intended to prolong the system's lifecycle with hardware updates, were considerably less successful, as was the attempt to repackage the plus hardware into a game console as the GX4000.
The CPC models' hardware is based on the Zilog Z80A CPU, complemented with either 64 or 128 KB of RAM. Their computer-in-a-keyboard design prominently features an integrated storage device, either a compact cassette deck or 3-inch floppy disk drive. The main units were only sold bundled with either a colour, green-screen or monochrome monitor that doubles as the main unit's power supply.CPC464 User Manual, p. 11, Amstrad Consumer Electronics Plc. Additionally, a wide range of first and third-party hardware extensions such as external disk drives, printers, and memory extensions, was available.
The CPC series was pitched against other home computers primarily used to play video games and enjoyed a strong supply of game software. The comparatively low price for a complete computer system with dedicated monitor, its high-resolution monochrome text and graphic capabilities and the possibility to run CP/M software also rendered the system attractive for business users, which was reflected by a wide selection of application software.
During its lifetime, the CPC series sold approximately three million units.
thumb|300px|right|The Schneider CPC 6128 was a Schneider-branded version of the Amstrad CPC 6128, and very similar in appearance.
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Amstrad CPC
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Models
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Models
The philosophy behind the CPC series was twofold, firstly the concept was of an "all-in-one", where the computer, keyboard and its data storage device were combined in a single unit and sold with its own dedicated display monitor. Most home computers at that time such as ZX Spectrum series, Commodore 64, and BBC Micro relied on the use of the domestic television set and a separately connected tape recorder or disk drive. In itself, the all-in-one concept was not new, having been seen before on business-oriented machines and the Commodore PET.
Secondly, Amstrad founder Alan Sugar wanted the machine to resemble a "real computer, similar to what someone would see being used to check them in at the airport for their holidays", and for the machine to not look like "a pregnant calculator" – in reference presumably to the ZX81 and ZX Spectrum with their low cost, membrane-type keyboards.
thumb|Children playing Paperboy on the CPC 464 in 1988
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Amstrad CPC
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CPC 464
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CPC 464
The CPC 464 was one of the most successful computers in Europe and sold more than two million units.
The CPC 464 featured 64 KB RAM and an internal cassette deck. It was introduced in June 1984 in the UK. Initial suggested retail prices for the CPC 464 were £249.00/DM899.00 with a green screen and £359.00/DM1398.00 with a colour monitor. Following the introduction of the CPC 6128 in late 1985, suggested retail prices for the CPC 464 were cut by £50.00/DM100.00.
In 1990, the 464plus replaced the CPC 464 in the model line-up, and production of the CPC 464 was discontinued.
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Amstrad CPC
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CPC 664
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CPC 664
thumb|A CPC 664 main unit (German Schneider-brand variant)
The CPC 664 features 64 KB RAM and an internal 3-inch floppy disk drive. It was introduced on 25 April 1985 in the UK. Initial suggested retail prices for the CPC 664 were £339.00/DM1198.00 with a green screen and £449.00/DM1998.00 with a colour monitor.
After the successful release of the CPC 464, consumers were constantly asking for two improvements: more memory and an internal disk drive. For Amstrad, the latter was easier to realise. At the deliberately low-key introduction of the CPC 664, the machine was positioned not only as the lowest-cost disk system but even the lowest-cost CP/M 2.2 machine. In the Amstrad CPC product range the CPC 664 complemented the CPC 464 which was neither discontinued nor reduced in price.The CPC664, Amstrad Computer User May 1985, P. 42-46.
Compared to the CPC 464, the CPC 664's main unit has been significantly redesigned, not only to accommodate the floppy disk drive but also with a redesigned keyboard area. Touted as "ergonomic" by Amstrad's promotional material, the keyboard is noticeably tilted to the front with MSX-style cursor keys above the numeric keypad. Compared to the CPC 464's multicoloured keyboard, the CPC 664's keys are kept in a much quieter grey and pale blue colour scheme.
The back of the CPC 664 main unit features the same connectors as the CPC 464, with the exception of an additional 12V power lead. Unlike the CPC 464's cassette tape drive that could be powered off the main unit's 5V voltage, the CPC 664's floppy disk drive requires an additional 12V voltage. This voltage had to be separately supplied by an updated version of the bundled green screen/colour monitor (GT-65 and CTM-644 respectively).
The CPC 664 was only produced for approximately six months. In late 1985, when the CPC 6128 was introduced in Europe, Amstrad decided not to keep three models in the line-up, and production of the CPC 664 was discontinued.
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Amstrad CPC
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CPC 6128
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CPC 6128
thumb|CPC 6128 main circuit board.
The CPC 6128 features 128 KB RAM and an internal 3-inch floppy disk drive. Aside from various hardware and firmware improvements, one of the CPC 6128's most prominent features is the compatibility with the CP/M+ operating system that rendered it attractive for business uses.
The CPC 6128 was released on 13 June 1985 and initially only sold in the US. Imported and distributed by Indescomp, Inc. of Chicago, it was the first Amstrad product to be sold in the United States, a market that at the time was traditionally hostile towards European computer manufacturers.Amstrad Computer User, "User News...", August 1985, p. 7. Two months later, on 15 August 1985, it arrived in Europe and replaced the CPC 664 in the CPC model line-up. Initial suggested retail prices for the CPC 6128 were US$699.00/£299.00/DM1598.00 with a green screen and US$799.00/£399.00/DM2098.00 with a colour monitor.
In 1990, the 6128plus replaced the CPC 6128 in the model line-up, and production of the CPC 6128 was discontinued.
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Amstrad CPC
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The ''plus range''
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The plus range
In 1990, confronted with a changing home computer market, Amstrad decided to refresh the CPC model range by introducing a new range variantly labelled plus or PLUS, 1990, or CPC+ range. The main goals were numerous enhancements to the existing CPC hardware platform, to restyle the casework to provide a contemporary appearance, and to add native support of cartridge media. The new model palette includes three variants, the 464plus and 6128plus computers and the GX4000 video game console. The "CPC" abbreviation was dropped from the model names.
The redesign significantly enhanced the CPC hardware, mainly to rectify its previous shortcomings as a gaming platform. The redesigned video hardware allows for 16 hardware sprites and soft scrolling, with a colour palette extended from a maximum of 16 colours (plus separately definable border) at one time from a choice of 27, increased to a maximum of 31 (16 for background and 15 for hardware sprites) out of 4096. The enhanced sound hardware offers automatic DMA transfer, allowing more complex sound effects with a significantly reduced processor overhead. Other hardware enhancements include the support of analogue joysticks, 8-bit printers, and ROM cartridges up to 4 Mbits.
The new range of models was intended to be completely backwards compatible with the original CPC models. Its enhanced features are only available after a deliberately obscure unlocking mechanism has been triggered, thus preventing existing CPC software from accidentally invoking them.
Despite the significant hardware enhancements, many viewed it as outdated, being based on an 8-bit CPU, and it failed to attract both customers and software producers who were moving towards systems such as the Amiga and Mega Drive which was launched a few short months after the plus range. The plus range was a commercial failure,Retro Gamer issue 83, From the Archives: Radical Software and production was discontinued shortly after its introduction in 1990.
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Amstrad CPC
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464 plus, 6128 plus
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464 plus, 6128 plus
thumb|A 6128 plus main unit (with Spanish keyboard layout)
The 464 plus and 6128 plus models were intended as "more sophisticated and stylish" replacements of the CPC 464 and CPC 6128. Based on the redesigned plus hardware platform, they share the same base characteristics as their predecessors: The 464 plus is equipped with 64 KB RAM and a cassette tape drive, the 6128 plus features 128 KB RAM and a 3" floppy disk drive. Both models share a common case layout with a keyboard taken over from the CPC 6128 model, and the respective mass storage drive inserted in a case breakout.
In order to simplify the EMC screening process, the edge connectors of the previous models have been replaced with micro-ribbon connectors as previously used on the German Schneider CPC 6128. As a result, a wide range of extensions for the original CPC range are connector-incompatible with the 464 plus and 6128 plus. In addition, the 6128plus does not have a tape socket for an external tape drive.
The plus range is not equipped with an on-board ROM, and thus the 464 plus and the 6128 plus do not contain a firmware. Instead, Amstrad provided the firmware for both models via the ROM extension facility, contained on the included Burnin' Rubber and Locomotive BASIC cartridge. This resulted in reduced hardware localization cost (only some select key caps and case labels had to be localized) with the added benefit of a rudimentary copy protection mechanism (without a firmware present, the machine itself could not copy a game cartridge's content). As the enhanced V4 firmware's structural differences causes problems with some CPC software directly calling firmware functions by their memory addresses, Amstrad separately sold a cartridge containing the original CPC 6128's V3 firmware.
Both the 464 plus and the 6128 plus were introduced to the public in September 1990. Initial suggested retail prices were / with a monochrome monitor and / with a colour monitor for the 464 plus, and / with a monochrome monitor and / with a colour monitor for the 6128plus.Paris in the Spring, Amstrad Action Issue 60, September 1990, P. 34-36
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Amstrad CPC
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GX4000
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GX4000
thumb|The Amstrad GX4000
Developed as part of the plus range, the GX4000 was Amstrad's short-lived attempt to enter the video game consoles market. Sharing the plus range's enhanced hardware characteristics, it represents the bare minimum variant of the range without a keyboard or support for mass storage devices. It came bundled with 2 paddle controllers and the racing game Burnin' Rubber.
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Amstrad CPC
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Special models and clones
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Special models and clones
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Amstrad CPC
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CPC 472
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CPC 472
thumb|CPC 472
During the August holidays of 1985, Spain briefly introduced an import tax of 15 000 pesetas () on computers containing 64 KB or less of RAM (Royal Decree 1215/1985 and 1558/1985), and a new law (Royal Decree 1250/1985) mandated that all computers sold in Spain must have a Spanish keyboard. To circumvent this, Amstrad's Spanish distributor Indescomp (later to become Amstrad Spain) created and distributed the CPC 472, a modified version of the CPC 464. Its main differences are a small additional daughter board containing a CPC 664 ROM chip and an 8 KB memory chip, and a keyboard with a ñ key (although some of them were temporarily manufactured without the ñ key). The sole purpose of the 8 KB memory chip (which is not electrically connected to the machine, so consequently rendered unusable) is to increase the machine's total memory specs to 72 KB in order to circumvent the import tax. Some months later, Spain joined the European Communities by the Treaty of Accession 1985 and the import tax was suppressed, so Amstrad added the ñ key for the 464 and production of the CPC 472 was discontinued.
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Amstrad CPC
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KC compact
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KC compact
thumb|right|The Kleincomputer KC compact
The ("" - which means "small computer" - being a rather literal German translation of the English "microcomputer") is a clone of the Amstrad CPC built by East Germany's , part of , in October 1989. Although the machine included various substitutes and emulations of an Amstrad CPC's hardware, the machine is largely compatible with Amstrad CPC software. It is equipped with 64 KB of memory and a CPC 6128's firmware customized to the modified hardware, including a copy of Locomotive BASIC 1.1 modified in the startup banner only. The expansion port is a K 1520 bus slot. The KC compact is the last 8-bit computer introduced in East Germany. Due to the German reunification happening at the time of the release, only a very small number of systems were sold. The KC compact can be emulated by free software JKCEMU.
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Amstrad CPC
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Aleste 520EX
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Aleste 520EX
In 1993, Omsk, Russia based company Patisonic released the Aleste 520EX, a computer highly compatible with the Amstrad CPC 6128. It could also be switched into an MSX mode. An expansion board named Magic Sound allowed to play Scream Tracker files.
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Amstrad CPC
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Reception
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Reception
Your Computer concluded that the CPC 464 had "Superior graphics and sound, an excellent Basic coupled with a flexible operating system" and that Amstrad's target sales of 200,000 by the end of 1984 were realistic.
A BYTE columnist in January 1985 called the CPC 464 "the closest yet to filling" his criteria for a useful home computer, including good keyboard, 80-column text, inexpensive disk drive, and support for a mainstream operating system like CP/M.
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Amstrad CPC
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Hardware
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Hardware
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Amstrad CPC
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Processor
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Processor
The entire CPC series is based on the Zilog Z80; a processor, clocked at 4 MHz.Technical Specification, CPC464 Service Manual, p. 2., Amstrad Consumer Electronics Plc. In order to avoid the CPU and the video logic simultaneously accessing the shared main memory and causing video corruption ("snowing"), CPU memory access is constrained to occur on microsecond boundaries. This effectively pads every machine cycle to four clock cycles, causing a minor loss of processing power and resulting in what Amstrad estimated to be an "effective clock rate" of "approximately 3.3 MHz".CPC464/664/6128 Firmware (Soft 968), Section 1
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Amstrad CPC
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Memory
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Memory
Amstrad CPCs are equipped with either 64 (CPC 464, CPC 664, 464plus, GX4000) or 128 (CPC 6128, 6128plus) KB of RAM.Technical Specification, CPC6128 Service Manual, p. 31., Amstrad Consumer Electronics Plc. This base memory can be extended by up to 512 KB using memory expansions sold by third-party manufacturers, and by up to 4096 KB using experimental methods developed by hardware enthusiasts. Because the Z80 processor is only able to directly address 64 KB of memory, additional memory from the 128 KB models and memory expansions is made available using bank switching.
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Amstrad CPC
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Video
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Video
thumb|Mode 1 image on a GT65 green monitor
Underlying a CPC's video output is the unusual pairing of a CRTC (Motorola 6845 or compatible) with a custom-designed gate array to generate a pixel display output. CPC 6128s later in production as well as the models from the plus range integrate both the CRTC and the gate array's functions with the system's ASIC.
Three built-in display resolutions are available: 160×200 pixels with 16 colours ("Mode 0", 20 text columns), 320×200 pixels with 4 colours ("Mode 1", 40 text columns), and 640×200 pixels with 2 colours ("Mode 2", 80 text columns). Increased screen size can be achieved by reprogramming the CRTC.
The original CPC video hardware supports a colour palette of 27 colours, generated from RGB colour space with each colour component assigned as either off, half on, or on (3 level RGB palette). The plus range extended the palette to 4096 colours, also generated from RGB with 4 bits each for red, green and blue (12-bit RGB).
thumb|Amstrad MP1 external television adapter
With the exception of the GX4000, all CPC models lack an RF television or composite video output and instead shipped with a 6-pin RGB DIN connector, also used by Acorn computers, to connect the supplied Amstrad monitor. This connector delivers a 1v p-p analogue RGB with a 50 Hz composite sync signal that, if wired correctly, can drive a 50 Hz SCART television. External adapters for RF television were available as a first-party hardware accessory.
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Amstrad CPC
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Audio
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Audio
The CPC uses the General Instrument AY-3-8912 sound chip, providing three channels, each configurable to generate square waves, white noise or both. A small array of hardware volume envelopes are available.
Output is provided in mono by a small (4 cm) built-in loudspeaker with volume control, driven by an internal amplifier. Stereo output is provided through a headphones jack.
It is possible to play back digital sound samples at a resolution of approximately 5-bit by sending a stream of values to the sound chip. This technique is very processor-intensive and hard to combine with any other processing. Examples are the title screens or other non-playable scenes of games like Chase H.Q., Meltdown, and RoboCop. The later Plus models incorporated a DMA engine in order to offload this processing.
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Amstrad CPC
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Floppy disk drive
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Floppy disk drive
thumb|Built-in disk drive of the CPC 6128
thumb|A CPC 6128 loading Turbo Esprit from its internal floppy drive
right|thumbnail|3-inch floppy disks used on CPC machines
Amstrad uses Matsushita's 3" floppy disk drive [ref: CPCWiki], which was compatible with Hitachi's existing 3" floppy disk format. The chosen drive (built-in for later models) is a single-sided 40-track unit that requires the user to remove and flip the disk to access the other side. Each side has its own independent write-protect switch. The sides are termed "A" and "B", with each one commonly formatted to 180 KB (in AMSDOS format, comprising 2 KB directory and 178 KB storage) for a total of 360 KB per disk.
The interface with the drives is an NEC 765 FDC, used for the same purpose in the IBM PC/XT, PC/AT and PS/2 machines. Its features are not fully used in order to cut costs, namely DMA transfers and support for single density disks; they were formatted as double density using modified frequency modulation.
Discs were shipped in a paper sleeve or a hard plastic case resembling a compact disc "jewel" case. The casing is thicker and more rigid than that of 3.5 inch diskettes, and designed to be mailed without any additional packaging. A sliding metal cover to protect the media surface is internal to the casing and latched, unlike the simple external sliding cover of Sony's version. They were significantly more expensive than both 5.25 inch and 3.5 inch alternatives. This, combined with their low nominal capacities and their essentially proprietary nature, led to the format being discontinued shortly after the CPC itself was discontinued.
Apart from Amstrad's other 3-inch machines (the PCW and the ZX Spectrum +3), the few other computer systems to use them included the Sega SF-7000 and CP/M systems such as the Tatung Einstein and Osborne machines. They also found use on embedded systems.
The Shugart-standard interface means that Amstrad CPC machines are able to use standard 3", 3½" or 5¼" drives as their second drive. Programs such as ROMDOS and ParaDOS extend the standard AMSDOS system to provide support for double-sided, 80-track formats, enabling up to 800 KB to be stored on a single disk.
The 3-inch disks themselves are usually known as "discs" on the CPC, following the spelling on the machine's plastic casing and conventional British English spelling.
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Amstrad CPC
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Expansion
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Expansion
thumb|Back of the case of a CPC 464, with the mini-jack, joystick and printer ports.
The hardware and firmware was designed to be able to access software provided on external ROMs. Each ROM has to be a 16 KB block and is switched in and out of the memory space shared with the video RAM. The Amstrad firmware is deliberately designed so that new software could be easily accessed from these ROMs. Popular applications were marketed on ROM, particularly word processing and programming utility software (examples are Protext and Brunword of the former, and the MAXAM assembler of the latter type).
Such extra ROM chips do not plug directly into the CPC itself, but into extra plug-in "rom boxes" which contain sockets for the ROM chips and a minimal amount of decoding circuitry for the main machine to be able to switch between them. These boxes were either marketed commercially or could be built by competent hobbyists and they attached to the main expansion port at the back of the machine. Software on ROM loads much faster than from disc or tape and the machine's boot-up sequence was designed to evaluate ROMs it found and optionally hand over control of the machine to them. This allows significant customisation of the functionality of the machine, something that enthusiasts exploited for various purposes. However, the typical users would probably not be aware of this added ROM functionality unless they read the CPC press, as it is not described in the user manual and was hardly ever mentioned in marketing literature. It is, however, documented in the official Amstrad firmware manual.
The machines also feature a 9-pin Atari joystick port that will either directly take one joystick, or two joysticks by use of a splitter cable.
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Amstrad CPC
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Peripherals
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Peripherals
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Amstrad CPC
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RS232 serial adapters
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RS232 serial adapters
Amstrad issued two RS-232-C D25 serial interfaces, attached to the expansion connector on the rear of the machine, with a through-connector for the CPC 464 disk drive or other peripherals.
The original interface came with a Book of Spells for facilitating data transfer between other systems using a proprietary protocol in the device's own ROM, as well as terminal software to connect to British Telecom's Prestel service. A separate version of the ROM was created for the U.S. market due to the use of the commands "|SUCK" and "|BLOW", which were considered unacceptable there.
Software and hardware limitations in this interface led to its replacement with an Amstrad-branded version of a compatible alternative by Pace. Serial interfaces were also available from third-party vendors such as KDS Electronics and Cirkit.
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Amstrad CPC
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Software
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Software
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Amstrad CPC
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BASIC and operating system
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BASIC and operating system
thumb|right|Locomotive BASIC on the Amstrad CPC 464
Like most home computers at the time, the CPC has its OS and a BASIC interpreter built in as ROM. It uses Locomotive BASIC - an improved version of Locomotive Software's Z80 BASIC for the BBC Micro co-processor board. It is particularly notable for providing easy access to the machine's video and audio resources in contrast to the POKE commands required on generic Microsoft implementations. Other unusual features include timed event handling with the AFTER and EVERY commands, and text-based windowing.
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Amstrad CPC
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CP/M
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CP/M
Digital Research's CP/M operating system was supplied with the 664 and 6128 disk-based systems, and the DDI-1 disk expansion unit for the 464. 64k machines shipped with CP/M 2.2 alone, while the 128k machines also include CP/M 3.1. The compact CP/M 2.2 implementation is largely stored on the boot sectors of a 3" disk in what was called "System format"; typing |CPM from Locomotive BASIC would load code from these sectors, making it a popular choice for custom game loading routines. The CP/M 3.1 implementation is largely in a separate file which is in turn loaded from the boot sector.
Much public domain CP/M software was made available for the CPC, from word-processors such as VDE to complete bulletin board systems such as ROS.
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Amstrad CPC
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Other languages
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Other languages
Although it was possible to obtain compilers for Locomotive BASIC, C and Pascal, the majority of the CPC's software was written in native Z80 assembly language. Popular assemblers were Hisoft's Devpac, Arnor's Maxam, and (in France) DAMS. Disk-based CPC (not Plus) systems shipped with an interpreter for the educational language LOGO, booted from CP/M 2.2 but largely CPC-specific with much code resident in the AMSDOS ROM; 6128 machines also include a CP/M 3.1, non-ROM version. A C compiler was also written and made available for the European market through Tandy Europe, by Micro Business products.
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Amstrad CPC
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''Roland''
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Roland
In an attempt to give the CPC a recognisable mascot, a number of games by Amstrad's in-house software publisher Amsoft have been tagged with the Roland name. However, as the games had not been designed around the Roland character and only had the branding added later, the character design varies immensely, from a spiky-haired blonde teenager (Roland Goes Digging) to a white cube with legs (Roland Goes Square Bashing) or a mutant flea (Roland in the Caves). The only two games with similar gameplay and main character design are Roland in Time and its sequel Roland in Space. The Roland character was named after Roland Perry, one of the lead designers of the original CPC range.
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Amstrad CPC
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Schneider Computer Division
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Schneider Computer Division
thumb|right|Schneider Computer Division logo
thumb|Schneider CPC 6128 with visible micro ribbon connectors at the top (back) side
thumb|Schneider CPC Demo Tape Presentation Compact Cassette came with the CPC 464
In order to market its computers in Germany, Austria, and Switzerland where Amstrad did not have any distribution structures, Amstrad entered a partnership with Schneider Rundfunkwerke AG, a German company that - very much like Amstrad itself - was previously only known for value-priced audio products. In 1984, Schneider's Schneider Computer Division daughter company was created specifically for the task, and the complete Amstrad CPC line-up was branded and sold as Schneider CPC.
Although they are based on the same hardware, the Schneider CPC models differ from the Amstrad CPC models in several details. Most prominently, the Schneider CPC 464 and CPC 664 keyboards featured grey instead of coloured keys, but still in the original British keyboard layout. To achieve a German "QWERTZ" keyboard layout, Schneider marketed a small software program to reassign the keys as well as sticker labels for the keys.CPC Schneider International 6/85, P. 7 In order to conform with stricter German EMC regulations, the complete Schneider CPC line-up is equipped with an internal metal shielding. For the same reason, the Schneider CPC 6128 features micro ribbon type connectors instead of edge connectors. Both the greyscale keyboard and the micro ribbon connectors found their way up into the design of later Amstrad CPC models.
In 1988, after Schneider refused to market Amstrad's AT-compatible computer line, the cooperation ended. Schneider went on to sell the remaining stock of Schneider CPC models and used their now well-established market position to introduce its own PC designs. With the formation of its German daughter company Amstrad GmbH to distribute its product lines including the CPC 464 and CPC 6128, Amstrad attempted but ultimately failed to establish their own brand in the German-speaking parts of Europe.CeBIT '88, Schneider Magazin 5/88, P. 6-8
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Amstrad CPC
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Community
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Community
The Amstrad CPC enjoyed a strong and long lifetime, mainly due to the machines use for businesses as well as gaming. Dedicated programmers continued working on the CPC range, even producing graphical user interface (GUI) operating systems such as SymbOS. Internet sites devoted to the CPC have appeared from around the world featuring forums, news, hardware, software, programming and games. CPC Magazines appeared during the 1980s including publications in countries such as Britain, France, Spain, Germany, Denmark, Australia, and Greece. Titles included the official Amstrad Computer User publication, as well as independent titles like Amstrad Action, Amtix!, Computing with the Amstrad CPC, CPC Attack, Australia's The Amstrad User, France's Amstrad Cent Pour Cent and Amstar. Following the CPC's end of production, Amstrad gave permission for the CPC ROMs to be distributed freely as long as the copyright message is not changed and that it is acknowledged that Amstrad still holds copyright, giving emulator authors the possibility to ship the CPC firmware with their programs.
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Amstrad CPC
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Influence on other Amstrad machines
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Influence on other Amstrad machines
Amstrad followed their success with the CPC 464 by launching the Amstrad PCW word-processor range, another Z80-based machine with a 3" disk drive and software by Locomotive Software. The PCW was originally developed to be partly compatible with an improved version of the CPC (ANT, or Arnold Number Two - the CPC's development codename was Arnold). However, Amstrad decided to focus on the PCW, and the ANT project never came to market.
On 7 April 1986, Amstrad announced it had bought from Sinclair Research "...the worldwide rights to sell and manufacture all existing and future Sinclair computers and computer products, together with the Sinclair brand name and those intellectual property rights where they relate to computers and computer-related products." which included the ZX Spectrum, for £5 million. This included Sinclair's unsold stock of Sinclair QLs and Spectrums. Amstrad made more than £5 million on selling these surplus machines alone. Amstrad launched two new variants of the Spectrum: the ZX Spectrum +2, based on the ZX Spectrum 128, with a built-in tape drive (like the CPC 464) and, the following year, the ZX Spectrum +3, with a built-in floppy disk drive (similar to the CPC 664 and 6128), taking the 3" discs that Amstrad CPC machines used.
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Amstrad CPC
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Production Timeline
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Production Timeline
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Amstrad CPC
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See also
|
See also
Amstrad CPC character set
Amstrad CP/M Plus character set
List of Amstrad CPC emulators
List of Amstrad CPC games
GX4000
SymbOS (multitasking operating system)
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Amstrad CPC
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Notes and references
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Notes and references
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Amstrad CPC
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External links
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External links
CPC-Wiki (CPC specific Wiki containing further information)
CPC-Power
Unofficial Amstrad WWW Resource
New OS for the CPC
Category:Computer-related introductions in 1984
CPC
Category:Z80-based home computers
Category:Computers designed in the United Kingdom
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Amstrad CPC
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Table of Content
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short description, Models, CPC 464, CPC 664, CPC 6128, The ''plus range'', 464 plus, 6128 plus, GX4000, Special models and clones, CPC 472, KC compact, Aleste 520EX, Reception, Hardware, Processor, Memory, Video, Audio, Floppy disk drive, Expansion, Peripherals, RS232 serial adapters, Software, BASIC and operating system, CP/M, Other languages, ''Roland'', Schneider Computer Division, Community, Influence on other Amstrad machines, Production Timeline, See also, Notes and references, External links
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Abdulaziz al-Omari
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Short description
|
Abdulaziz al-Omari (, , also transliterated as Alomari or al-Umari; 28 May 1979 – 11 September 2001) was a Saudi imam and terrorist who was one of five hijackers of American Airlines Flight 11 as part of the September 11 attacks in 2001.
Prior to the attacks, al-Omari was an imam at his mosque in Saudi Arabia's al-Qassim province. He arrived in the United States in June 2001 on a tourist visa, obtained through the Visa Express program. On September 11, 2001, al-Omari boarded American Airlines Flight 11 and assisted in the hijacking of the plane, which was crashed into the North Tower of the World Trade Center, as part of the coordinated attacks.
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Abdulaziz al-Omari
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Early life and career
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Early life and career
Abdulaziz al-Omari (or Alomari) was born on 28 May 1979 in a poor Arab family. He was born in Aseer, Saudi Arabia and was a fellow countryman of brothers Wail al-Shehri and Waleed al-Shehri, fellow hijackers in the September 11 attacks. It is alleged he graduated with honors from high school. He attained a degree from Imam Muhammad ibn Saud Islamic University, got married, and had a daughter briefly before the attacks. He taught as an imam at his mosque in al-Qassim province, which was the "heartland" of Wahhabism, a strict form of Islam. At the mosque, which experts refer to as a "terrorist factory", he was possibly taught by the radical cleric Sulayman al Alwan.
According to Walid bin Attash, al-Omari was one of a group of future hijackers who provided security at Kandahar airport after their basic training at an al-Qaeda camp. During the 2000 Al Qaeda Summit in Kuala Lumpur, American authorities state that immigration records show that a person named Abdulaziz al-Omari was visiting the country, although they say they are not sure that this was the same person.
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Abdulaziz al-Omari
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September 11 attacks
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September 11 attacks
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Abdulaziz al-Omari
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Planning
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Planning
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Abdulaziz al-Omari
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Early 2001
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Early 2001
al-Omari eventually became involved in the planning for the September 11 attacks on the United States, an idea formulated by Osama bin Laden. The attacks involved hijacking commercial airplanes and crashing them into buildings; al-Omari would hijack American Airlines Flight 11, which would crash into the World Trade Center in New York City. At the time of the hijacking, al-Omari was 22. In the autumn of 2001, after the attacks, al Jazeera television broadcast a tape they claim was made by him. The speaker made a farewell suicide video. In it he read, "I am writing this with my full conscience and I am writing this in expectation of the end, which is near... God praise everybody who trained and helped me, namely the leader Sheikh Osama bin Laden."
A person with al-Omari's name visited the Philippines twice in February 2001. al-Omari and hijacker Salem al-Hazmi entered the United States through a Dubai flight on June 29, 2001, landing in New York City. al-Omari had used the controversial Visa Express program to gain entry. The two were probably picked up by Salem's brother, Nawaf al-Hazmi, on the 30th; this is assumed because of a recorded traffic accident by Nawaf on George Washington Bridge that day. al-Omari likely stayed with several other hijackers in Paterson, New Jersey (where he rented a mailbox), before moving to his own place in Vero Beach, Florida with his wife and three children. On his rental agreement form for that house, al-Omari gave two license-plates authorized to park in his space, one of which was registered to Mohamed Atta,FBI Affidavit: Page 11 ABC the attacks' mastermind.
al-Omari attended the FlightSafety academy in Vero Beach with fellow hijackers Mohand al-Shehri and Saeed al-Ghamdi. He also obtained a fake United States ID card from All Services Plus in Passaic County, New Jersey, which was in the business of selling fake documents; another was given to Khalid al-Mihdhar. The employee who gave them the IDs claimed he had no idea they were "anything more [than ordinary] customers". Atta bought tickets for Flight 11 for himself and al-Omari on August 28. On September 6, al-Omari and fellow hijacker Satam al-Suqami flew from Florida to Boston to stay at the Park Inn Hotel.
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Abdulaziz al-Omari
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September 10
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September 10
On September 10, 2001, Atta picked up al-Omari from the Park Inn Hotel, and the two drove to South Portland, Maine, in a rented Nissan Altima. Some sources state there is no evidence as to why they went to Portland, whereas ABC News says it was a last-minute decision by Atta to stagger the Flight 11 hijackers' entrances into Logan International Airport on the 11th. Multiple people have claimed to see Atta and other hijackers in Portland that summer, but the FBI has found no evidence of this. On the 10th, Atta and al-Omari purchased a room (233) at the town's Comfort Inn. They did not ask for a wake-up call. Their luggage included a folding knife, "a videocassette [about] a Boeing 757 flight simulator, pepper spray, Atta’s will, [and Atta's] handwritten instructions to his 18 fellow hijackers"; American Airlines Flight 11 was a Boeing 767.
They stayed in their hotel room for two hours, until 8 p.m., when al-Omari made a four-minute phone call from a nearby Pizza Hut's pay phone to a phone belonging to Marwan al-Shehhi, who would hijack United Airlines Flight 175. Five minutes later, at a restaurant named Pizzeria Uno, the two withdrew $80 from an ATM. They then drove back to the Pizza Hut, where a second pay phone call was placed at 8:50. They decided to go to Walmart, but got lost and went to a gas station to ask for directions. In a video recorded at the gas station, Atta has a piece of paper in his hand and shows it to al-Omari, and then they leave. At the Walmart, the two purchased a six-volt battery converter for an unknown reason. Staff of the Walmart said that weeks earlier, Atta had bought a box cutter there, but this is uncorroborated. The two then returned to the Comfort Inn, where they stayed for hours.
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Abdulaziz al-Omari
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Day of the attacks
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Day of the attacks
At 5:33 a.m. on September 11, al-Omari and Atta checked out of the hotel. al-Omari made another cash withdrawal at the Pizzeria Uno ATM, and then the two went to Portland International Jetport. At around 5:40, the two spoke with a ticket agent, who raised no suspicions about them. Both men boarded their flight, which landed in Logan International Airport at 6:45. Eight other hijackers were waiting at the airport. It is unknown why this connecting flight through Portland happened, especially because the two almost missed their flight at Logan. Their flight, American 11, was supposed to fly to Los Angeles.
Atta and al-Omari then boarded Flight 11 with fellow hijackers Satam al-Suqami, Wail al-Shehri, and Waleed al-Shehri. The other hijackers at the airport went on United Airlines Flight 175. al-Omari's passport, which would identify him as a hijacker to investigators later, was in the two men's aforementioned luggage; this luggage was accidentally left at Portland International Airport, failing to make it onto the connecting flight to Logan. The two men probably decided they did not need the luggage's folding knife and pepper spray in their attacks. Atta and al-Omari had seats next to each other in first class, row 8, on Flight 11. The flight left the Logan runway at 7:59. The hijackers took over the plane starting at 8:14, when multiple passengers were maced and stabbed. Atta then commanded the plane's controls, and at 8:37, the plane began a rapid descent. At 8:46, it was crashed into the World Trade Center's North Tower, and everyone onboard was killed. Floors 93 to 99 were impacted, and many inside died.
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Abdulaziz al-Omari
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Aftermath
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Aftermath
Controversy over the identity of al-Omari erupted shortly after the attacks. At first, the FBI had named Abdul Rahman al-Omari, a pilot for Saudi Arabian Airlines, as the pilot of Flight 11. It was quickly shown that this person was still alive, and the FBI issued an apology. It was also quickly determined that Mohamed Atta was the pilot among the hijackers. The FBI then named Abdulaziz al-Omari as a hijacker.
A man with the same name as those given by the FBI turned up alive in Saudi Arabia, saying that he had studied at the University of Denver and his passport was stolen there in 1995. The name, origin, birth date, and occupation were released by the FBI, but the picture was not of him. "I couldn't believe it when the FBI put me on their list", he said. "They gave my name and my date of birth, but I am not a suicide bomber. I am here. I am alive. I have no idea how to fly a plane. I had nothing to do with this."
The FBI gave a press conference on October 5, 2001, where they gave details regarding Atta and the real al-Omari's movements on September 10 and 11.
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Abdulaziz al-Omari
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See also
|
See also
PENTTBOM
Hijackers in the 11 September attacks
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Abdulaziz al-Omari
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References
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References
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Abdulaziz al-Omari
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External links
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External links
The Final 9/11 Commission Report
portal.telegraph.co.uk (Article which reports that the Saudi Arabian Airlines pilot named Omari was not involved with the terrorist attacks)
Category:1979 births
Category:2001 deaths
Category:American Airlines Flight 11 hijackers
Category:People from Al-Bahah Province
Category:Saudi Arabian al-Qaeda members
Category:Saudi Arabian mass murderers
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Abdulaziz al-Omari
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Table of Content
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Short description, Early life and career, September 11 attacks, Planning, Early 2001, September 10, Day of the attacks, Aftermath, See also, References, External links
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Aage Bohr
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Short description
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Aage Niels Bohr (; 19 June 1922 – 8 September 2009) was a Danish nuclear physicist who shared the Nobel Prize in Physics in 1975 with Ben Roy Mottelson and James Rainwater "for the discovery of the connection between collective motion and particle motion in atomic nuclei and the development of the theory of the structure of the atomic nucleus based on this connection". His father was Niels Bohr.
Starting from Rainwater's concept of an irregular-shaped liquid drop model of the nucleus, Bohr and Mottelson developed a detailed theory that was in close agreement with experiments.
Since his father, Niels Bohr, had won the prize in 1922, he and his father are one of the six pairs of fathers and sons who have both won the Nobel Prize and one of the four pairs who have both won the Nobel Prize in Physics.
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Aage Bohr
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Early life and education
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Early life and education
Bohr was born in Copenhagen on 19 June 1922, the fourth of six sons of the physicist Niels Bohr and his wife Margrethe Bohr (née Nørlund). His oldest brother, Christian, died in a boating accident in 1934, and his youngest, Harald, was severely disabled and placed away from the home in Copenhagen at the age of four. He would later die from childhood meningitis. Of the others, Hans became a physician; Erik, a chemical engineer; and Ernest, a lawyer and Olympic athlete who played field hockey for Denmark at the 1948 Summer Olympics in London. The family lived at the Institute of Theoretical Physics at the University of Copenhagen, now known as the Niels Bohr Institute, where he grew up surrounded by physicists who were working with his father, such as Hans Kramers, Oskar Klein, Yoshio Nishina, Wolfgang Pauli and Werner Heisenberg. In 1932, the family moved to the Carlsberg Æresbolig, a mansion donated by Carl Jacobsen, the heir to Carlsberg breweries, to be used as an honorary residence by the Dane who had made the most prominent contribution to science, literature, or the arts.
Bohr went to high school at Sortedam Gymnasium in Copenhagen. In 1940, shortly after the German occupation of Denmark in April, he entered the University of Copenhagen, where he studied physics. He assisted his father, helping draft correspondence and articles related to epistemology and physics. In September 1943, word reached his family that the Nazis considered them to be Jewish, because Bohr's grandmother, Ellen Adler Bohr, had been Jewish, and that they therefore were in danger of being arrested. The Danish resistance helped the family escape by sea to Sweden. Bohr arrived there in October 1943, and then flew to Britain on a de Havilland Mosquito operated by British Overseas Airways Corporation. The Mosquitoes were unarmed high-speed bomber aircraft that had been converted to carry small, valuable cargoes or important passengers. By flying at high speed and high altitude, they could cross German-occupied Norway, and yet avoid German fighters. Bohr, equipped with parachute, flying suit and oxygen mask, spent the three-hour flight lying on a mattress in the aircraft's bomb bay.
On arrival in London, Bohr rejoined his father, who had flown to Britain the week before. He officially became a junior researcher at the Department of Scientific and Industrial Research, but actually served as personal assistant and secretary to his father. The two worked on Tube Alloys, the British atomic bomb project. On 30 December 1943, they made the first of a number of visits to the United States, where his father was a consultant to the Manhattan Project. Due to his father's fame, they were given false names; Bohr became James Baker, and his father, Nicholas Baker. In 1945, the director of the Los Alamos Laboratory, J. Robert Oppenheimer, asked them to review the design of the modulated neutron initiator. They reported that it would work. That they had reached this conclusion put Enrico Fermi's concerns about the viability of the design to rest. The initiators performed flawlessly in the bombs used in the atomic bombings of Hiroshima and Nagasaki in August 1945.
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Aage Bohr
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Career
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Career
In August 1945, with the war ended, Bohr returned to Denmark, where he resumed his university education, graduating with a master's degree in 1946, with a thesis concerned with some aspects of atomic stopping power problems. In early 1948, Bohr became a member of the Institute for Advanced Study in Princeton, New Jersey. While paying a visit to Columbia University, he met Isidor Isaac Rabi, who sparked in him an interest in recent discoveries related to the hyperfine structure of deuterium. This led to Bohr becoming a visiting fellow at Columbia from January 1949 to August 1950. While in the United States, Bohr married Marietta Soffer on 11 March 1950. They had three children: Vilhelm, Tomas and Margrethe.
By the late 1940s it was known that the properties of atomic nuclei could not be explained by then-current models such as the liquid drop model developed by Niels Bohr amongst others. The shell model, developed in 1949 by Maria Goeppert Mayer and others, allowed some additional features to be explained, in particular the so-called magic numbers. However, there were also properties that could not be explained, including the non-spherical distribution of charge in certain nuclei. In a 1950 paper, James Rainwater of Columbia University suggested a variant of the drop model of the nucleus that could explain a non-spherical charge distribution. Rainwater's model postulated a nucleus like a balloon with balls inside that distort the surface as they move about. He discussed the idea with Bohr, who was visiting Columbia at the time, and had independently conceived the same idea, and had, about a month after Rainwater's submission, submitted for publication a paper that discussed the same problem, but along more general lines. Bohr imagined a rotating, irregular-shaped nucleus with a form of surface tension. Bohr developed the idea further, in 1951 publishing a paper that comprehensively treated the relationship between oscillations of the surface of the nucleus and the movement of the individual nucleons.
Upon his return to Copenhagen in 1950, Bohr began working with Ben Roy Mottelson to compare the theoretical work with experimental data. In three papers, that were published in 1952 and 1953, Bohr and Mottelson demonstrated close agreement between theory and experiment; for example, showing that the energy levels of certain nuclei could be described by a rotation spectrum. They were thereby able to reconcile the shell model with Rainwater's concept. This work stimulated many new theoretical and experimental studies. Bohr, Mottelson and Rainwater were jointly awarded the 1975 Nobel Prize in Physics "for the discovery of the connection between collective motion and particle motion in atomic nuclei and the development of the theory of the structure of the atomic nucleus based on this connection". Because his father had been awarded the prize in 1922, Bohr became one of only four pairs of fathers and sons to win the Nobel Prize in Physics. The others: William Henry Bragg (1915) and William Lawrence Bragg (1915); J. J. Thomson (1906) and George Paget Thomson (1937); and Manne Siegbahn (1924) and Kai M. Siegbahn (1981). Two pairs of fathers and sons have won Nobel Prizes in other fields: Hans von Euler-Chelpin (chemistry, 1929) and Ulf von Euler (medicine, 1970); and Arthur Kornberg (medicine, 1969) and Roger D. Kornberg (chemistry, 2006).
Only after doing his Nobel Prize-winning research did Bohr receive his doctorate from the University of Copenhagen, in 1954, writing his thesis on "Rotational States of Atomic Nuclei". Bohr became a professor at the University of Copenhagen in 1956, and, following his father's death in 1962, succeeded him as director of the Niels Bohr Institute, a position he held until 1970. He remained active there until he retired in 1992. He was also a member of the board of the Nordic Institute for Theoretical Physics from its inception in 1957, and was its director from 1975 to 1981. In addition to the Nobel Prize, he won the Dannie Heineman Prize for Mathematical Physics in 1960, the Atoms for Peace Award in 1969, H. C. Ørsted Medal in 1970, Rutherford Medal and Prize in 1972, John Price Wetherill Medal in 1974, and the Ole Rømer medal in 1976. Bohr and Mottelson continued to work together, publishing a two-volume monograph, Nuclear Structure. The first volume, Single-Particle Motion, appeared in 1969; the second, Nuclear Deformations, in 1975.
In 1972 Bohr was awarded an honorary degree, doctor philos. honoris causa, at the Norwegian Institute of Technology, later part of Norwegian University of Science and Technology. He was a member of the Norwegian Academy of Science and Letters from 1980. Bohr was also an elected member of the American Academy of Arts and Sciences, the American Philosophical Society, and the United States National Academy of Sciences.
In 1981, Bohr became a founding member of the World Cultural Council.
Bohr's wife Marietta died on 2 October 1978. In 1981, he married Bente Scharff Meyer (1926–2011). His son, Tomas Bohr, is a professor of physics at the Technical University of Denmark, working in the area of fluid dynamics. Aage Bohr died in Copenhagen on 9 September 2009. He was survived by his second wife and children.
Bohr's Nobel Prize medal was sold at auction in November 2011. It was subsequently sold at auction in April 2019 for $90,000.
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Aage Bohr
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Notes
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Notes
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Aage Bohr
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References
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References
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Aage Bohr
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External links
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External links
including the Nobel Lecture, 11 December 1975: "Rotational Motion in Nuclei"
Oral History interview transcript with Aage Bohr 23 & 30 January 1963, American Institute of Physics, Niels Bohr Library and Archives
Category:1922 births
Category:2009 deaths
Category:20th-century Danish physicists
Category:Atoms for Peace Award recipients
Aage
Category:Burials at Mariebjerg Cemetery
Category:Columbia University faculty
Category:Danish expatriates in the United States
Category:Danish Nobel laureates
Category:Danish nuclear physicists
Category:Danish people of Jewish descent
Category:Foreign associates of the National Academy of Sciences
Category:Founding members of the World Cultural Council
Category:Institute for Advanced Study visiting scholars
Category:Manhattan Project people
Category:Members of the American Philosophical Society
Category:Members of the Norwegian Academy of Science and Letters
Category:Members of the Pontifical Academy of Sciences
Category:Members of the Royal Swedish Academy of Sciences
Aage
Category:Nobel laureates in Physics
Category:Scientists from Copenhagen
Category:University of Copenhagen alumni
Category:Fellows of the American Academy of Arts and Sciences
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Aage Bohr
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Table of Content
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Short description, Early life and education, Career, Notes, References, External links
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Analytic geometry
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short description
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In mathematics, analytic geometry, also known as coordinate geometry or Cartesian geometry, is the study of geometry using a coordinate system. This contrasts with synthetic geometry.
Analytic geometry is used in physics and engineering, and also in aviation, rocketry, space science, and spaceflight. It is the foundation of most modern fields of geometry, including algebraic, differential, discrete and computational geometry.
Usually the Cartesian coordinate system is applied to manipulate equations for planes, straight lines, and circles, often in two and sometimes three dimensions. Geometrically, one studies the Euclidean plane (two dimensions) and Euclidean space. As taught in school books, analytic geometry can be explained more simply: it is concerned with defining and representing geometric shapes in a numerical way and extracting numerical information from shapes' numerical definitions and representations. That the algebra of the real numbers can be employed to yield results about the linear continuum of geometry relies on the Cantor–Dedekind axiom.
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Analytic geometry
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History
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History
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Analytic geometry
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Ancient Greece
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Ancient Greece
The Greek mathematician Menaechmus solved problems and proved theorems by using a method that had a strong resemblance to the use of coordinates and it has sometimes been maintained that he had introduced analytic geometry.
Apollonius of Perga, in On Determinate Section, dealt with problems in a manner that may be called an analytic geometry of one dimension; with the question of finding points on a line that were in a ratio to the others. Apollonius in the Conics further developed a method that is so similar to analytic geometry that his work is sometimes thought to have anticipated the work of Descartes by some 1800 years. His application of reference lines, a diameter and a tangent is essentially no different from our modern use of a coordinate frame, where the distances measured along the diameter from the point of tangency are the abscissas, and the segments parallel to the tangent and intercepted between the axis and the curve are the ordinates. He further developed relations between the abscissas and the corresponding ordinates that are equivalent to rhetorical equations (expressed in words) of curves. However, although Apollonius came close to developing analytic geometry, he did not manage to do so since he did not take into account negative magnitudes and in every case the coordinate system was superimposed upon a given curve a posteriori instead of a priori. That is, equations were determined by curves, but curves were not determined by equations. Coordinates, variables, and equations were subsidiary notions applied to a specific geometric situation.
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Analytic geometry
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Persia
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Persia
The 11th-century Persian mathematician Omar Khayyam saw a strong relationship between geometry and algebra and was moving in the right direction when he helped close the gap between numerical and geometric algebra with his geometric solution of the general cubic equations, but the decisive step came later with Descartes. Omar Khayyam is credited with identifying the foundations of algebraic geometry, and his book Treatise on Demonstrations of Problems of Algebra (1070), which laid down the principles of analytic geometry, is part of the body of Persian mathematics that was eventually transmitted to Europe.Mathematical Masterpieces: Further Chronicles by the Explorers, p. 92 Because of his thoroughgoing geometrical approach to algebraic equations, Khayyam can be considered a precursor to Descartes in the invention of analytic geometry.Cooper, G. (2003). Journal of the American Oriental Society,123(1), 248-249.
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Analytic geometry
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Western Europe
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Western Europe
Analytic geometry was independently invented by René Descartes and Pierre de Fermat, although Descartes is sometimes given sole credit. Cartesian geometry, the alternative term used for analytic geometry, is named after Descartes.
Descartes made significant progress with the methods in an essay titled La Géométrie (Geometry), one of the three accompanying essays (appendices) published in 1637 together with his Discourse on the Method for Rightly Directing One's Reason and Searching for Truth in the Sciences, commonly referred to as Discourse on Method.
La Geometrie, written in his native French tongue, and its philosophical principles, provided a foundation for calculus in Europe. Initially the work was not well received, due, in part, to the many gaps in arguments and complicated equations. Only after the translation into Latin and the addition of commentary by van Schooten in 1649 (and further work thereafter) did Descartes's masterpiece receive due recognition.
Pierre de Fermat also pioneered the development of analytic geometry. Although not published in his lifetime, a manuscript form of Ad locos planos et solidos isagoge (Introduction to Plane and Solid Loci) was circulating in Paris in 1637, just prior to the publication of Descartes' Discourse.Pierre de Fermat, Varia Opera Mathematica d. Petri de Fermat, Senatoris Tolosani (Toulouse, France: Jean Pech, 1679), "Ad locos planos et solidos isagoge," pp. 91–103. "Eloge de Monsieur de Fermat" (Eulogy of Mr. de Fermat), Le Journal des Scavans, 9 February 1665, pp. 69–72. From p. 70: "Une introduction aux lieux, plans & solides; qui est un traité analytique concernant la solution des problemes plans & solides, qui avoit esté veu devant que M. des Cartes eut rien publié sur ce sujet." (An introduction to loci, plane and solid; which is an analytical treatise concerning the solution of plane and solid problems, which was seen before Mr. des Cartes had published anything on this subject.) Clearly written and well received, the Introduction also laid the groundwork for analytical geometry. The key difference between Fermat's and Descartes' treatments is a matter of viewpoint: Fermat always started with an algebraic equation and then described the geometric curve that satisfied it, whereas Descartes started with geometric curves and produced their equations as one of several properties of the curves. As a consequence of this approach, Descartes had to deal with more complicated equations and he had to develop the methods to work with polynomial equations of higher degree. It was Leonhard Euler who first applied the coordinate method in a systematic study of space curves and surfaces.
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Analytic geometry
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Coordinates
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Coordinates
thumb|right|250px|Illustration of a Cartesian coordinate plane. Four points are marked and labeled with their coordinates: (2,3) in green, (−3,1) in red, (−1.5,−2.5) in blue, and the origin (0,0) in purple.
In analytic geometry, the plane is given a coordinate system, by which every point has a pair of real number coordinates. Similarly, Euclidean space is given coordinates where every point has three coordinates. The value of the coordinates depends on the choice of the initial point of origin. There are a variety of coordinate systems used, but the most common are the following:Stewart, James (2008). Calculus: Early Transcendentals, 6th ed., Brooks Cole Cengage Learning.
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Analytic geometry
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Cartesian coordinates (in a plane or space)
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Cartesian coordinates (in a plane or space)
The most common coordinate system to use is the Cartesian coordinate system, where each point has an x-coordinate representing its horizontal position, and a y-coordinate representing its vertical position. These are typically written as an ordered pair (x, y). This system can also be used for three-dimensional geometry, where every point in Euclidean space is represented by an ordered triple of coordinates (x, y, z).
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Analytic geometry
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Polar coordinates (in a plane)
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Polar coordinates (in a plane)
In polar coordinates, every point of the plane is represented by its distance r from the origin and its angle θ, with θ normally measured counterclockwise from the positive x-axis. Using this notation, points are typically written as an ordered pair (r, θ). One may transform back and forth between two-dimensional Cartesian and polar coordinates by using these formulae: This system may be generalized to three-dimensional space through the use of cylindrical or spherical coordinates.
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Analytic geometry
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Cylindrical coordinates (in a space)
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Cylindrical coordinates (in a space)
In cylindrical coordinates, every point of space is represented by its height z, its radius r from the z-axis and the angle θ its projection on the xy-plane makes with respect to the horizontal axis.
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Analytic geometry
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Spherical coordinates (in a space)
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Spherical coordinates (in a space)
In spherical coordinates, every point in space is represented by its distance ρ from the origin, the angle θ its projection on the xy-plane makes with respect to the horizontal axis, and the angle φ that it makes with respect to the z-axis. The names of the angles are often reversed in physics.
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Analytic geometry
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Equations and curves
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Equations and curves
In analytic geometry, any equation involving the coordinates specifies a subset of the plane, namely the solution set for the equation, or locus. For example, the equation y = x corresponds to the set of all the points on the plane whose x-coordinate and y-coordinate are equal. These points form a line, and y = x is said to be the equation for this line. In general, linear equations involving x and y specify lines, quadratic equations specify conic sections, and more complicated equations describe more complicated figures.Percey Franklyn Smith, Arthur Sullivan Gale (1905)Introduction to Analytic Geometry, Athaeneum Press
Usually, a single equation corresponds to a curve on the plane. This is not always the case: the trivial equation x = x specifies the entire plane, and the equation x2 + y2 = 0 specifies only the single point (0, 0). In three dimensions, a single equation usually gives a surface, and a curve must be specified as the intersection of two surfaces (see below), or as a system of parametric equations.William H. McCrea, Analytic Geometry of Three Dimensions
Courier Dover Publications, Jan 27, 2012 The equation x2 + y2 = r2 is the equation for any circle centered at the origin (0, 0) with a radius of r.
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Analytic geometry
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Lines and planes
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Lines and planes
Lines in a Cartesian plane, or more generally, in affine coordinates, can be described algebraically by linear equations. In two dimensions, the equation for non-vertical lines is often given in the slope-intercept form:
where:
m is the slope or gradient of the line.
b is the y-intercept of the line.
x is the independent variable of the function y = f(x).
In a manner analogous to the way lines in a two-dimensional space are described using a point-slope form for their equations, planes in a three dimensional space have a natural description using a point in the plane and a vector orthogonal to it (the normal vector) to indicate its "inclination".
Specifically, let be the position vector of some point , and let be a nonzero vector. The plane determined by this point and vector consists of those points , with position vector , such that the vector drawn from to is perpendicular to . Recalling that two vectors are perpendicular if and only if their dot product is zero, it follows that the desired plane can be described as the set of all points such that
(The dot here means a dot product, not scalar multiplication.)
Expanded this becomes
This is just a linear equation:
Conversely, it is easily shown that if a, b, c and d are constants and a, b, and c are not all zero, then the graph of the equation
This familiar equation for a plane is called the general form of the equation of the plane.
In three dimensions, lines can not be described by a single linear equation, so they are frequently described by parametric equations:
where:
x, y, and z are all functions of the independent variable t which ranges over the real numbers.
(x0, y0, z0) is any point on the line.
a, b, and c are related to the slope of the line, such that the vector (a, b, c) is parallel to the line.
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Analytic geometry
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Conic sections
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Conic sections
thumb|right|250px|A hyperbola and its conjugate hyperbola
In the Cartesian coordinate system, the graph of a quadratic equation in two variables is always a conic section – though it may be degenerate, and all conic sections arise in this way. The equation will be of the form
As scaling all six constants yields the same locus of zeros, one can consider conics as points in the five-dimensional projective space
The conic sections described by this equation can be classified using the discriminant, Section 3.2, page 45
If the conic is non-degenerate, then:
if , the equation represents an ellipse;
if and , the equation represents a circle, which is a special case of an ellipse;
if , the equation represents a parabola;
if , the equation represents a hyperbola;
if we also have , the equation represents a rectangular hyperbola.
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Analytic geometry
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Quadric surfaces
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Quadric surfaces
A quadric, or quadric surface, is a 2-dimensional surface in 3-dimensional space defined as the locus of zeros of a quadratic polynomial. In coordinates , the general quadric is defined by the algebraic equationSilvio Levy Quadrics in "Geometry Formulas and Facts", excerpted from 30th Edition of CRC Standard Mathematical Tables and Formulas, CRC Press, from The Geometry Center at University of Minnesota
Quadric surfaces include ellipsoids (including the sphere), paraboloids, hyperboloids, cylinders, cones, and planes.
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Analytic geometry
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Distance and angle
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Distance and angle
thumb|right|250px|The distance formula on the plane follows from the Pythagorean theorem.
In analytic geometry, geometric notions such as distance and angle measure are defined using formulas. These definitions are designed to be consistent with the underlying Euclidean geometry. For example, using Cartesian coordinates on the plane, the distance between two points (x1, y1) and (x2, y2) is defined by the formula
which can be viewed as a version of the Pythagorean theorem. Similarly, the angle that a line makes with the horizontal can be defined by the formula
where m is the slope of the line.
In three dimensions, distance is given by the generalization of the Pythagorean theorem:
while the angle between two vectors is given by the dot product. The dot product of two Euclidean vectors A and B is defined by
where θ is the angle between A and B.
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Analytic geometry
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Transformations
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Transformations
thumb|400px|a) y = f(x) = |x| b) y = f(x+3) c) y = f(x)-3 d) y = 1/2 f(x)
Transformations are applied to a parent function to turn it into a new function with similar characteristics.
The graph of is changed by standard transformations as follows:
Changing to moves the graph to the right units.
Changing to moves the graph up units.
Changing to stretches the graph horizontally by a factor of . (think of the as being dilated)
Changing to stretches the graph vertically.
Changing to and changing to rotates the graph by an angle .
There are other standard transformation not typically studied in elementary analytic geometry because the transformations change the shape of objects in ways not usually considered. Skewing is an example of a transformation not usually considered.
For more information, consult the Wikipedia article on affine transformations.
For example, the parent function has a horizontal and a vertical asymptote, and occupies the first and third quadrant, and all of its transformed forms have one horizontal and vertical asymptote, and occupies either the 1st and 3rd or 2nd and 4th quadrant. In general, if , then it can be transformed into . In the new transformed function, is the factor that vertically stretches the function if it is greater than 1 or vertically compresses the function if it is less than 1, and for negative values, the function is reflected in the -axis. The value compresses the graph of the function horizontally if greater than 1 and stretches the function horizontally if less than 1, and like , reflects the function in the -axis when it is negative. The and values introduce translations, , vertical, and horizontal. Positive and values mean the function is translated to the positive end of its axis and negative meaning translation towards the negative end.
Transformations can be applied to any geometric equation whether or not the equation represents a function.
Transformations can be considered as individual transactions or in combinations.
Suppose that is a relation in the plane. For example,
is the relation that describes the unit circle.
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Analytic geometry
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Finding intersections of geometric objects {{anchor
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Finding intersections of geometric objects
For two geometric objects P and Q represented by the relations and the intersection is the collection of all points which are in both relations.While this discussion is limited to the xy-plane, it can easily be extended to higher dimensions.
For example, might be the circle with radius 1 and center : and might be the circle with radius 1 and center . The intersection of these two circles is the collection of points which make both equations true. Does the point make both equations true? Using for , the equation for becomes or which is true, so is in the relation . On the other hand, still using for the equation for becomes or which is false. is not in so it is not in the intersection.
The intersection of and can be found by solving the simultaneous equations:
Traditional methods for finding intersections include substitution and elimination.
Substitution: Solve the first equation for in terms of and then substitute the expression for into the second equation:
We then substitute this value for into the other equation and proceed to solve for :
Next, we place this value of in either of the original equations and solve for :
So our intersection has two points:
Elimination: Add (or subtract) a multiple of one equation to the other equation so that one of the variables is eliminated. For our current example, if we subtract the first equation from the second we get . The in the first equation is subtracted from the in the second equation leaving no term. The variable has been eliminated. We then solve the remaining equation for , in the same way as in the substitution method:
We then place this value of in either of the original equations and solve for :
So our intersection has two points:
For conic sections, as many as 4 points might be in the intersection.
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Analytic geometry
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Finding intercepts
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Finding intercepts
One type of intersection which is widely studied is the intersection of a geometric object with the and coordinate axes.
The intersection of a geometric object and the -axis is called the -intercept of the object.
The intersection of a geometric object and the -axis is called the -intercept of the object.
For the line , the parameter specifies the point where the line crosses the axis. Depending on the context, either or the point is called the -intercept.
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Analytic geometry
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Geometric axis
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Geometric axis
Axis in geometry is the perpendicular line to any line, object or a surface.
Also for this may be used the common language use as a: normal (perpendicular) line, otherwise in engineering as axial line.
In geometry, a normal is an object such as a line or vector that is perpendicular to a given object. For example, in the two-dimensional case, the normal line to a curve at a given point is the line perpendicular to the tangent line to the curve at the point.
In the three-dimensional case a surface normal, or simply normal, to a surface at a point P is a vector that is perpendicular to the tangent plane to that surface at P. The word "normal" is also used as an adjective: a line normal to a plane, the normal component of a force, the normal vector, etc. The concept of normality generalizes to orthogonality.
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Analytic geometry
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Spherical and nonlinear planes and their tangents
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Spherical and nonlinear planes and their tangents
Tangent is the linear approximation of a spherical or other curved or twisted line of a function.
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Analytic geometry
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Tangent lines and planes
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Tangent lines and planes
In geometry, the tangent line (or simply tangent) to a plane curve at a given point is the straight line that "just touches" the curve at that point. Informally, it is a line through a pair of infinitely close points on the curve. More precisely, a straight line is said to be a tangent of a curve at a point on the curve if the line passes through the point on the curve and has slope where f is the derivative of f. A similar definition applies to space curves and curves in n-dimensional Euclidean space.
As it passes through the point where the tangent line and the curve meet, called the point of tangency, the tangent line is "going in the same direction" as the curve, and is thus the best straight-line approximation to the curve at that point.
Similarly, the tangent plane to a surface at a given point is the plane that "just touches" the surface at that point. The concept of a tangent is one of the most fundamental notions in differential geometry and has been extensively generalized; see Tangent space.
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Analytic geometry
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See also
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See also
Applied geometry
Cross product
Rotation of axes
Translation of axes
Vector space
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Analytic geometry
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Notes
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Notes
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Analytic geometry
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References
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References
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Analytic geometry
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Books
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Books
John Casey (1885) Analytic Geometry of the Point, Line, Circle, and Conic Sections, link from Internet Archive.
Mikhail Postnikov (1982) Lectures in Geometry Semester I Analytic Geometry via Internet Archive
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Analytic geometry
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Articles
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Articles
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Analytic geometry
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External links
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External links
Coordinate Geometry topics with interactive animations
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Analytic geometry
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Table of Content
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short description, History, Ancient Greece, Persia, Western Europe, Coordinates, Cartesian coordinates (in a plane or space), Polar coordinates (in a plane), Cylindrical coordinates (in a space), Spherical coordinates (in a space), Equations and curves, Lines and planes, Conic sections, Quadric surfaces, Distance and angle, Transformations, Finding intersections of geometric objects {{anchor, Finding intercepts, Geometric axis, Spherical and nonlinear planes and their tangents, Tangent lines and planes, See also, Notes, References, Books, Articles, External links
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Arabic alphabet
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Short description
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thumb|270x270px|Countries and regions that use the Arabic script:
The Arabic alphabet, or the Arabic abjad, is the Arabic script as specifically codified for writing the Arabic language. It is a unicameral script written from right-to-left in a cursive style, and includes 28 letters, of which most have contextual letterforms. Unlike the modern Latin alphabet, the script has no concept of letter case. The Arabic alphabet is an abjad, with only consonants required to be written (though the long vowels – ā ī ū – are also written, with letters used for consonants); due to its optional use of diacritics to notate vowels, it is considered an impure abjad.
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Arabic alphabet
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Letters
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Letters
The basic Arabic alphabet contains 28 letters. Forms using the Arabic script to write other languages added and removed letters: for example ⟨پ⟩ is often used to represent in adaptations of the Arabic script. Unlike Greek-derived alphabets, Arabic has no distinct upper and lower case letterforms.
Many letters look similar but are distinguished from one another by dots () above or below their central part (). These dots are an integral part of a letter, since they distinguish between letters that represent different sounds. For example, the Arabic letters , , and have the same basic shape, but with one dot added below, two dots added above, and three dots added above respectively. The letter also has the same form in initial and medial forms, with one dot added above, though it is somewhat different in its isolated and final forms. Historically, they were often omitted, in a writing style called rasm.
Both printed and written Arabic are cursive, with most letters within a word directly joined to adjacent letters.
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Arabic alphabet
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Alphabetical order
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Alphabetical order
There are two main collating sequences ('alphabetical orderings') for the Arabic alphabet: , and .
The Hija'i order ( ) is the more common order and it is used when sorting lists of words and names, such as in phonebooks, classroom lists, and dictionaries.
The original order ( ) derives from that used by the Phoenician alphabet and therefore resembles the sequence of letters in Hebrew and Greek. Letters are also assigned numerical values (abjad numerals) for purposes of numerology, as is done in Hebrew gematria and Greek isopsephy. Letters in the Hija'i order are not considered to have numerical values.
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Arabic alphabet
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Hijaʼi
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Hijaʼi
Modern dictionaries and reference books use the alphabetical order instead of the Abjadi alphabetical order, in which letters are arranged mainly by similarity of shape. The hijaʼi order is never used for numerals.
+ Common order ʾ
A different hijaʼi order was used in the Maghreb but is now considered obsolete. The sequence is:
+ Maghrebian order (obsolete) ʾ The colors indicate which letters have different positions from the previous table
The al-iklīl order, now obsolete, also arranged letters mainly by shape. It was first used in the 10th-century work Kitāb al-Iklīl. The sequence is:
+ Al-iklīl order (obsolete) ʾ
thumb|320px|hijāʾī collation compared to Hebrew, Syriac, and Greek
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Arabic alphabet
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Abjadi
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Abjadi
The Abjadi order is not a simple correspondence with the earlier north Semitic alphabetic order, as it has a position corresponding to the Aramaic letter samek , which has no cognate letter in the Arabic alphabet historically. The abjadi order is the usual Arabic order in dictionaries and reference books of the late 1st millennium to the early 2nd millennium.
The loss of was compensated for by:
In the Mashriqi abjad sequence, the letter took the place of , and the letter took place of šīn .
In the Maghrebi abjad sequence, the letter ṣāḏē was split into two independent Arabic letters, and , with the latter taking the place of .
The six other letters that do not correspond to any north Semitic letter are placed at the end.
+Common sequenceʾ123456789101112131415161718192021222324252627281234567891020304050607080901002003004005006007008009001000
This is commonly vocalized as follows:
.
Another vocalization is:
+Maghrebian sequence (quoted in apparently earliest authorities & considered older) Alyaseer.net Ordering entries and cards in subject indexes Discussion thread (Accessed 2009-October–06)ʾ123456789101112131415161718192021222324252627281234567891020304050607080901002003004005006007008009001000The colors indicate which letters have different positions from the previous table
This can be vocalized as:
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