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Notice: this Wiki will be going read only early in 2024 and edits will no longer be possible. Please see: https://gitlab.eclipse.org/eclipsefdn/helpdesk/-/wikis/Wiki-shutdown-plan for the plan.
About ICE Data Structures
The many different data structures built into ICE, allowing it to be flexible and support many different uses. This page will briefly summarize the most relevant packages and classes. Users who are compiling ICE from scratch know that the source code is well-documented, but for anyone just looking to understand the process a little better, this consolidation of succinct descriptions and links to the heavier pages should lend some insight.
Versions of the majority of these superclasses can be found in Eclipse's or other third-party libraries, particularly those dealing with the user interface. In an effort to make ICE more independent, these resources are used only when deemed absolutely necessary.
For a visualization and even briefer overview, see the About ICE Data Structures page.
The form is essentially the graphic user interface. Developers with the binary build can create custom forms. It's worth noting that ICE's Form class does not use any standard GUI libraries, such as swt, awt, or swing. It uses javax.persistence for persistence and object/relational mapping.
Each Entry is a value in your form. Developers using the class can regulate what kind of values are accepted, assign an acceptable range, and/or set default values. You can set parents, which creates entry dependency. You can mark a certain entry secret, which will obscure it from the user, and you can 'tag' entries, giving them secondary descriptions that won't be revealed to the user.
The primary purpose of a Listener is to monitor for the occurrence of certain events, usually something that the user has done with the mouse or keyboard. While there is a Listener interface in Eclipse's SWT library, for ICE we designed our own.
A Composite is an SWT widget. Like a Form, it can contain many elements within it, such as components. In fact, within the org.eclipse.swt.widgets package, Composite has a subclass called Form. This is not the same Form we use in ICE, but it's an option, and is intended to serve a similar purpose.
Components are the different sections that make up your form. ICE has different components based on the different needs of each user or Item. These components can act as containers for visualizing data or for accepting input from the user.
BatteryComponent models a battery per the BatML standard. DataComponent is used as a container for entries that are related to each other, and essentially behaves like a Component from the UpdateableComposite package. GeometryComponent contains shapes to help with the visualization of data. MasterDetailsComponent manages a collection of masters and a collection of details. The masters are strings, while the associated details are placed in a DataComponent. MatrixComponent is made to provide the functionality of a two-dimensional array, thus imitating a matrix. The user can add rows and/or columns, allowing both square and rectangular matrices. ResourceComponent manages a set of ICEResources. For example, it can collect output data on a Form. TableComponent is useful when you have a set of entries that are related. As the name implies, it essentially creates a table. It uses java.util.HashTable to map keys to values. All non-null object can be used as a key or as a value. contains methods for adding and deleting rows, TimeDataComponent extends DataComponent, but is specialized for dealing with time loops. There are two modes. The regular mode allows the user to specify a start time, an end time, and the number of steps needed. The second mode, explicit, allows the user to specify each time step. MeshComponent is a composite container for polygons and accompanying data. Mesh is a common term in computer graphics and solid modeling. It refers to the generation of a three-dimensional collection of vertices, edges and faces that define the shape of an object. The faces usually consist of simple convex polygons (triangles, quadrilaterals), since this simplifies rendering, but they may also be composed of more general concave polygons, or polygons with holes. This may sound limiting, but nearly every object can be graphically represented in mesh.
In ICE, when we refer to something as an 'item' within ICE, we mean the actual items you can create when running the program. Currently, this image would represent the selection of 'items'.
This item is used to analyze data produced as part of a reactor simulation. It contains one each of:
- DataComponent - contains the entries for the input and reference data
- ResourceComponent - populated by the generated artifacts
- MasterDetailsComponent - allows the user to select the types of analyses that should be performed, as well as set their properties.
It uses the interfaces IAnalysisTool and IAnalysisDocument.
VisIt is a visualization tool co-developed by the Lawrence Livermore National Laboratory and the Oak Ridge National Laboratory. More information on it can be found here.
The JobProfile will allow users to programmatically create a custom JobLauncher. A tutorial on how to use it can be found here, but it is only suitable for simple tasks. To add complexity, the user should either find a pre-made ICE Item that will better suit their needs or consider [ICE Build Instructions] and hard-coding a custom plugin.
This item simulates fuel performance. More on the AMP Fuel Performance code, a tool developed by ORNL, here.
As the name would imply, the Model class is used for simulating physical systems. From a coding perspective, it's nearly identical to the Item class from which it inherits. The only difference is that the constructor takes an IProject as a parameter; the IProject is where the Item stores files.
JobLauncher/Model Pairs in ICE
Many of the Items that can be created in ICE contain two main classes--one that extends JobLauncher, and one that extends Item, but acts as a model.
CAEBAT is an open architecture software used to computationally model batteries. See our [CAEBAT] article for more information.
[1] is an acronym for Consortium for Advanced Simulation of Light Water Reactors. ORNL acts as one of many contributors
MOOSE is a software owned by Idaho National Laboratory, but it has many contributors, including ORNL. The acronym expands to Multiphysics Object-Oriented Simulation Environment, and MOOSE's primary purpose is to simplify the process of conducting simulations. The following items use the MOOSE framework:
- BISON -used to analyze fuel performance and has applications for nuclear reactor designers. We have instructions for Creating BISON Input Files with ICE, as well as a YouTube video.
- MARMOT - it shows the microscopic responses of nuclear fuel to irradiation.
- RELAP-7 - expands to Reactor Excursion and Leak Analysis Program.
Nek5000 is actively developed at Argonne National Laboratory and is an open-source computational fluid dynamics solver based on the spectral element method. It's written in Fortran77/C and employs the MPI standard for parallelism.
While PROTEUS is still under development at Argonne National Laboratory, eventually it will be a nuclear reactor core simulator, primarily focused on sodium-cooled fast reactors, used for generating input files for launching neutronics codes, and launching that code.
SHARP, Systematic Human Action Reliability Procedure, is another tool still under development and currently only available to ORNL users. For more information, see Using_SHARP_with_ICE.
For non-programmers, an interface may best be described as a template; it cannot be instantiated as an object the way a class can be. In an interface, there are pre-labelled, but undefined, methods. A group of classes would implement the same interface if they're performing similar tasks, but with variations. This permits more flexibility than inheriting from or extending another class, where the methods have been pre-defined and must be overriden.
For developers, a crucial advantage of either of these techniques is that you can use different print statements for different classes. So if there's ever in an error in the code, checking the print statements on the console can be enough to determine exactly where things began to go awry.
The ItemBuilder interface registers an Item and builds specific Items. This is used as a pluggable service in the OSGi framework to provide the Items to ICE. For more on OSGi services, check this list of references.
The IAnalysisTool is responsible for creating the IAnalysisDocument, which we will examine soon.
- KDDAnalysisTool implements IAnalysisTool and is responsible for creating a KDDAnalysisDocument that performs and displays carious types of data clustering and anomaly detection for nuclear reactors. We have a list of references available for your viewing regarding KDD in general.
- VisItAnalysisTool implements IAnalysisTool for use with VisIt. As mentioned in the VisItViewer section, VisIt is a separate visualization software, which can work as a standalone. However, those who [it downloaded], will be able to view VisIt's images in ICE. More information on how to use it specifically within ICE can be found at our page on Using VisIt in ICE.
- KDDAnalysisDocument realizes the IAnalysisDocument interface and constructs user-specified data-mining algorithms and corresponding plots. It utilizes the Strategy pattern to decouple itself from the actual construction of individual data-mining algorithms.
- VisItAnalysisDocument
This interface describes a type of solid in the geometry editor. Each IShape is a node in the CSG tree and can affect the appearance of the final surface or volume mesh when processed with the MeshKit.
- AbstractShape
- ComplexShape
- PrimitiveShape


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- Other Federal Civil Rights Offices
- Other US Department of Education Resources
- Additional Resources
- Kids Resources
Non- Department of Education web sites linked by OCR contain information related to the OCR mission and to civil rights. Non-U.S. Department of Education web sites are linked as a public service only. The Department of Education does not control or guarantee the accuracy, relevance, timeliness, or completeness of this outside information. Inclusion of links to particular resources is not intended to reflect their relative importance, and is not intended as an endorsement of the views expressed, the products or services offered on these outside web sites, or of the organizations sponsoring the web sites.
Other Federal Civil Rights Offices
U.S. Equal Employment Opportunities Commission
Americans With Disabilities Act (ADA) Home Page
U.S. Department of Justice, Office of the Attorney General, Civil Rights Division
U.S. Commission on Civil Rights
U.S. Department of Health and Human Services, Office for Civil Rights
U.S. Department of Agriculture, Civil Rights Office
Federal Aviation Administration, Civil Rights Office
U.S. Department of Transportation, Civil Rights Office
U.S. Department of Housing
and Urban Development, Fair Housing Civil Rights
U.S. Department of Labor, Civil Rights Enforcement for Department of Labor Grant Recipients
Other U. S. Department of Education Resources
U.S. Department of Education (ED) Home Page
Office of English Language Acquisition, Language Enhancement, and Academic Achievement for Limited English Proficient Students
Office of Special Education and Rehabilitative Services
Americans With Disabilities Act (ADA) Document Center
Federal Register Online
Fed Law: Civil Rights
The Women's Educational Equity Act (WEE-A) Program
Diversity Web
The Kids.gov: Official Kid's Portal for the U.S. Government. Find links to government and other kids' sites.
The National Civil Rights Museum Virtual Tour: Civil rights movement from "Brown is Board of Education of Topeka" to current events such as "The Struggle continues". Information about civil rights heroes and heroines.
The NCES Classroom: Find out about education information and activities for students
Gear Up: College information and resources to help low-income students enter and succeed in postsecondary education.
Jobs for Kids Who Like... This is a really cool page that lets you match your interests with possible careers. Sponsored by the Department of Labor.
Explorer's Club: Lots of interesting things about recycling, plants and animals, air pollution, and the environment. Sponsored by the Environmental Protection Agency.
Ready.gov (Formerly FE-MA Kids): Floods, earthquakes, tornadoes, hurricanes, wild-fires...got your attention? Check out this site! Sponsored by the Federal Emergency Management Agency.
Forest Service Kids: The Forest Service is committed to connecting kids with nature and the outdoors by providing students, parents and teachers with youth-oriented information and resources related to natural resources and the environment.
Treasury's Kids Zone: OK - here's something we all want to know about: money! Find out about savings bonds, learn about how money is made, and even meet some of the dogs who help in drug enforcement. Sponsored by the Treasury Department.
Social Security Kids Stuff: You have heard of "social security" - right? This web site explains how it works. Sponsored by the Social Security Administration.
NASA's Multimedia Gallery : This is a great collection of photos, videos, and information about our space program. Sponsored by NASA.
Kids Links: You can ask a scientist or engineer your science questions...like how fast do butterflies fly? And how can you tell the age of a tree? Sponsored by the National Science Foundation.
Kids Page: Students can learn about, Ocean Energy, Ocean's Sand, and types of Energy and much more. Sponsored by the Bureau of Ocean Energy Management, Regulation and Enforcement.
FBI's Kids Page (Kindergarten to 5th Grade: Find out about fingerprints and lie detectors and DNA testing. Sponsored by the Federal Bureau of Investigation.
FBI's Youth Page: Orientation for youth grades 6 to 12 to the work of the Federal Bureau of Investigation.
Kids' Page: Find out why laughing is good for you. Games and puzzles and information about environmental health. Don't know what that is? Then visit this site! Sponsored by the National Institute of Environmental Health Sciences.
Learning Web: Take an electronic field trip of Glacier National Park. See maps of the world. Monitor active volcanos. Sponsored by the U.S. Geological Survey.
Air Force Link Junior: Grab your security badge and meet Steve Canyon, Air Force hero! Or send a friend an Air Force post card. Sponsored by the U.S. Air Force.
Planet Youth: Meet Native American artists and learn about Native American customs. Sponsored by the Department of Housing and Urban Development.
Just for Kids and Teachers: Visit the Maritime Administration's Video Theater to see the Ready Reserve Force and America's Marine Transportation System in action and learn about the Adopt-A-Ship program sponsored by The Propeller Club of the United States. Sponsored by the Maritime Administration.
Kids' Corner: Join the Polar Star ice breaker or read Snoopy's safe boating tips. It's all fun! Sponsored by the U.S. Coast Guard.
The National Zoo: Meet new zoo babies, play games, and see pictures of animals. Sponsored by the Smithsonian Institution.
Online Exhibit Hall: See the police plotter showing the assassination of President Abraham Lincoln. See pictures of some of the gifts that our Presidents have received. Sponsored by the National Archives and Records Administration.
Arts edge: You will have a great time looking at the art of students all over the world. Or you can read stories and visit lots of arts-related web sites. Sponsored by the Kennedy Center for Performing Arts.
Interesting Facts from NOAA: Do you know what to do if a storm approaches? Do you know what fish is the largest? Do you know what radiation is? You will learn all this, and more, at this site. Sponsored by the Department of Commerce.
Star Child: If you have ever wanted to be an astronaut, definitely check this out! You will learn about the solar system, the universe, and (ta-da!) space stuff. Sponsored by NASA.
Endorsement, Copyright, Privacy and Security of information on the ED Internet site.

subset: commoncrawl


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11 February 2013 21:00 | to | 12 February 2013 02:00 |
Belle Epoque Gran Ball
Tales of Hoffmann: The Doll Olympia
Homage to Jacques Offenbach
Monday the 11th of February 2013
Gala Dinner & Entertainment.
The Ball will be located on the first floor (the pianonobile) in an authentic 14th century Palace: Pesaro Papafava, With its precious gothic facade and its elegant quadriform gothic windows overlooking the canal of the Misericordia. The palace will be illuminated entirely with candlelights to create a memorable atmosphere.
Jacques Offenbach takes the real life German poet, E.T.A. Hoffmann, and makes him a character in some of his own, fanciful stories. Offenbach's drama placing the title character into three, fanciful stories of failed love. The result is one of the grandest and most expressive of all 19th-century French operas.
Hoffmann's first love is Olympia, an automaton created by the scientist Spalanzani. Hoffmann falls in love with her, not knowing that Olympia is a mechanical doll. The story is seen as a dream suffered: the protagonist's impossible love for a woman who turns out to be a doll.
21.15: Elegant cocktail with live music.
21.45: Seated illuminated candle lights Gala Dinner, wines included.
23.00: Performance of the most beautiful arias from the opera "The Tales of Hoffmann".
Midnight: Live music and dances.
Dress Code: costume and mask.
Cost: 290 € per person.
Do not hesitate to consult us for the rent of costumes
Our Atelier will be under your disposal for any assistance such as costumes, masks and accessories.
The Palace is reachable by 5 minutes walk from Ca D'Oro vaporetto stop: Calle Racchetta, Cannaregio 3764. Reachable also by its water door (in front of the Church of the Misericordia).
For further informations, contact our office:
Tel: +39 041 5201855, Tel: +39 041 7794559 Fax: +39 178 2263842 E-mail: email@example.com,


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The grisly spree of violence that began at the Boston Marathon this week also left a police officer dead. Law enforcement officials say the bombing suspects managed to shoot two officers as police were closing in on them.
One, transit police officer Richard Donohue, is in critical condition at Mount Auburn Hospital. The other, Sean Collier of the MIT Campus Police, was pronounced dead Thursday night.
MIT says Collier had gone to respond to a report of an altercation on campus Thursday evening. Soon, word came over the police radio that he had been shot.
Collier was taken to Massachusetts General Hospital at about 10:30 that night with multiple gunshot wounds and pronounced dead. Friday, those who knew him were still trying to make sense of a death that came all too soon. Eric Metchik was his criminal justice professor at Salem State University.
"A moment of great shock, that here was a student, who not only was a student in my classes, but who was such an outstanding student and such a great person," he says, "a student I had kept in touch with over the years and just gone in a flash."
Collier grew up in the Boston area. He was a baby-faced 26-year-old, friendly and outgoing. Metchik says he was also very serious about police work.
"He knew what he wanted to study and what he wanted to do, and he was very dedicated to the law enforcement profession," Metchik says.
He says Collier was something of a technophile, and he returned to Salem State to talk to students about the ways technology could aid police work. After college, Collier took a civilian job in the IT department in the city of Somerville, a Boston suburb.
"He was someone dedicated to his work, passionate, that had a passion for the job, full of life, extremely talented and smart," Somerville Mayor Joseph Curtatone told Boston member station WBUR Friday.
Curtatone said he had hoped to hire Collier one day as a police officer. But in the meantime, Collier took a job on the campus police at MIT.
He had been at the school just 15 months when he died. Friday, the campus set up a Tumblr account where people could post reminiscences of him.
He was remembered as someone who was easily able to mix with students. Last year, he joined the MIT Outing Club and made a dangerous mid-winter trek to Mount Washington in New Hampshire.
"[He] really just impressed me with how totally he embraced winter hiking," says Matthew Gilbertson, an officer in the club. "He wasn't afraid to really take the plunge and learn all the skills that you need to learn."
Gilbertson said the club hadn't had a police officer in recent memory, but Collier quickly assimilated into the group and became one of its more active members.
"With Sean, you just sort of forgot that he was a police officer. I mean, we all were definitely kind of proud to have him on the police force as an MIT Outing Club member," Gilbertson says.
Gilbertson said Collier grew so enthusiastic about hiking that he talked about scaling much more challenging peaks in Alaska and Africa. That will no longer be possible. Collier's family issued a statement Friday:
"Our only solace is that Sean died bravely doing what he committed his life to, serving and protecting others."
Copyright 2013 NPR. To see more, visit www.npr.org.


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Bionic Woman (2007 TV series)
Jump to navigation
Jump to search
This page is for the 2007 TV series Bionic Woman. It premiered in the USA in September 2007.
This TV article is a stub. You can help Wikiquote by expanding it. |
Season 1[edit]
Pilot [1.1][edit]
- Jaime Sommers: Last time I left you alone, you started a fire.
- Becca Sommers: The microwave was broken!
- Jaime Sommers: We don't own a microwave.
- Ruth: I'm Ruth.
- Jaime Sommers: I'm pissed.
- Ruth: Good, we're here to talk about our feelings.
- Jaime Sommers: How do you feel about me being kept here against my will?
- Ruth: I was speaking editorally. We're here to talk about your feelings.
- Jaime Sommers: Something nobody here has any regard for.
- Ruth: Curve balls will do that. You can have all the contingency plans and then someone goes and does something like this and we all has to stay after school and-
- Jaime Sommers: And talk about our feelings.
- Ruth: Your feelings.
- Jaime Sommers: Right.


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People used to open the Sunday paper, look over the real estate listings, linger over the properties with descriptive phrases like "guest house" and "horse barn," sip their coffee, and dream. Now, those with real estate envy can whet their appetites with 24-hour real estate showings on television and virtual walk-throughs online.
If you're looking to actually purchase a home, however, the ubiquity of real estate can make the prospect of a search overwhelming. The process is not friendly, regardless of who you are or how much money you have to spend. There are the typical stress points: strapping together enough cash for a down payment; figuring out the impact a purchase will have on your monthly budget; deciding where to live and in what type of dwelling; matching expectations to reality; and getting through the closing process, including the tense times of negotiations and a home inspection. Put this all together and you might think the "H" in HGTV stands for "Horror."
Navigating the process online and on-the-go can ease some of the fear and make the experience more manageable. While 88 percent of homebuyers have turned to the Internet in their home search, according to the 2011 National Association of Realtors Profile of Home Buyers and Sellers, not all have used it or relevant apps to their full potential.
When a new home is just a glimmer in your eye, you can use online and mobile tools to make sure you've got enough coin stashed away for it, learn the ins and outs of real estate, and prepare yourself for closing day. Read on for tips on how to use the Web to find the nest of your dreams.
1. Save Up
2. Get a Mortgage
3. Know Your Type
4. Find a Real Estate Agent
5. The Search Begins
6. For What It's Worth
7. Home Inspection
8. Closing Time
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Roots & Shoots Prairie Smoke
Date(s) - 07/17/2012 at 1:00 pm - 3:00 pm
Dr. Jane Goodall says, "Only if we understand will we care, only if we care shall we help, only if we help can they be saved." Roots & Shoots is a global, environmental and humanitarian education program. Kids will participate in service learning for animals, people, and the environment. It's about knowledge, compassion, and ACTION…sign up today!
Ages: 5-8
Fee: $50 + tax for all six classes


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Most Midsize Insurers Lack Mobile Device Management for BYOD: Novarica
Only a quarter of midsize insurers have implemented mobile device management (MDM) software for their employees who participate in bring-your-own-device (BYOD) access to their systems, according to a survey by analyst firm Novarica.
While allowing BYOD access to systems at about the same rate as large insurers -- defined as those with more than $1 billion in premium -- midsize carriers tend to eschew technologies such as Good Technology, MobileIron and AirWatch that help them manage those remote devices.
"We strongly recommend that all insurers carefully consider their security provisions for BYOD and consider the benefits of using an MDM platform if they are not already doing so," Novarica says in the survey, which included 22 large insurers and 64 midsize. "Companies need to have remote-wipe capabilities to delete information from lost devices or from the devices of employees who leave the company."
[Good Technology reports that financial services companies are BYOD leaders.]
That's despite the fact that in some cases, midsize insurers allowed more BYOD access than their larger counterparts: 89% reported that at least some employees could use their smartphone to access corporate systems, compared to 68% of larger companies. The percentage allowing all employees access was 32% for large companies and 31% for midsize.
The little statistical difference between midsize and large companies in terms of allowing access belies the fact that invariably, that access must at some point end -- and it is imperative that insurers build in some safeguards for their data.
"Managing security and confidential information on personal devices is an evolving practice that insurers need to stay current with," Novarica adds. "Security protocols (passwords, time-outs, not storing unencrypted information on the device, etc.) on personal devices must meet general corporate standards."
Nathan Golia is senior editor of Insurance & Technology. He joined the publication in 2010 as associate editor and covers all aspects of the nexus between insurance and information technology, including mobility, distribution, core systems, customer interaction, and risk ... View Full Bio


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Acupuncture and acupressure for thousands of years are helping people to solve numerous health problems. If you press these 4 points, you will lose weight very fast.Acupressure is not quackery and not something vague, but it is a complex medical technique.
In short, the logic is that every organ of your body, directly using the energy channels is associated with specific points on the body.So if you want to improve the function of some internal organs, it is necessary to find their particular point, and accordingly, massage it.
If you follow these instructions, your metabolism will speed up, as a result, you will be very energetic throughout the day, and the excess fat will slowly begin to eliminate because it will stop its accumulation.
You will start to control your appetite and create a completely new, healthy lifestyle.
These are the points that will help you get rid of excess weight:
1. Еar
By massaging this point you will have your metabolism accelerated, which contributes to faster weight loss in all parts of the body. It should be massaged with the thumb for a period of three minutes, three times daily, with smooth and continuous pressure on the ear.
2. Face
This point is situated right between the nose and upper lip. It is necessary to stimulate twice a day for five minutes. This massage helps in controlling hunger and anxiety. If you overeat during times of stress, then this method is perfect for you!
3. Arm
This is a key point of the body because every part of your internal energy goes through it. By massaging this point, you are releasing the body of excess body heat and contribute to improving the work of the intestine.
You need to massage this point 2-3 times daily for a period of one minute.
4. Leg
This point is most used in acupressure. It called Zu San Li. It not only improves digestion but also helps to suppress some inflammatory processes in the body.
Called point of longevity or point against hundreds of illnesses. It is located under the knee cup.
To find more accurately, cover the knee with your palm, if you chose your left leg, use your left hand, and the other way around. The point is between the end of the little and ring finger in the form of the lower recess between the bones.
Daily massage this point in the evening is suitable for loosing up to a pound a week.
This point should be massaged clockwise 9 times on each leg.
10 minutes in total (5 minutes for each leg). But do not massage directly before bed, because it can cause insomnia.
During the pressure you will experience mild discomfort, even pain, that's how it suppose to be, otherwise, it will not achieve the desired result.


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Golden ratio
Background Information
SOS Children have produced a selection of wikipedia articles for schools since 2005. Child sponsorship helps children one by one http://www.sponsor-a-child.org.uk/.
In mathematics and the arts, two quantities are in the golden ratio if the ratio of the sum of the quantities to the larger quantity is equal to the ratio of the larger quantity to the smaller one. The figure on the right illustrates the geometric relationship. Expressed algebraically:
where the Greek letter phi () represents the golden ratio. Its value is:
The golden ratio is also called the golden section (Latin: sectio aurea) or golden mean. Other names include extreme and mean ratio, medial section, divine proportion, divine section (Latin: sectio divina), golden proportion, golden cut, and golden number.
Many 20th century artists and architects have proportioned their works to approximate the golden ratio—especially in the form of the golden rectangle, in which the ratio of the longer side to the shorter is the golden ratio—believing this proportion to be aesthetically pleasing (see Applications and observations below). Mathematicians since Euclid have studied the properties of the golden ratio, including its appearance in the dimensions of a regular pentagon and in a golden rectangle, which can be cut into a square and a smaller rectangle with the same aspect ratio. The golden ratio has also been used to analyze the proportions of natural objects as well as man-made systems such as financial markets, in some cases based on dubious fits to data.
Binary | 1.1001111000110111011... |
Decimal | 1.6180339887498948482... |
Hexadecimal | 1.9E3779B97F4A7C15F39... |
Continued fraction | |
Algebraic form | |
Infinite series |
Two quantities a and b are said to be in the golden ratio φ if:
One method for finding the value of φ is to start with the left fraction. Through simplifying the fraction and substituting in b/a = 1/φ,
it is shown that
Multiplying by φ gives
which can be rearranged to
Using the quadratic formula, two solutions are obtained:
Because of the fact that φ is the ratio between length and width of a rectangle, which are non-zero, the positive solution must be chosen:
The golden ratio has fascinated Western intellectuals of diverse interests for at least 2,400 years. According to Mario Livio:
Some of the greatest mathematical minds of all ages, from Pythagoras and Euclid in ancient Greece, through the medieval Italian mathematician Leonardo of Pisa and the Renaissance astronomer Johannes Kepler, to present-day scientific figures such as Oxford physicist Roger Penrose, have spent endless hours over this simple ratio and its properties. But the fascination with the Golden Ratio is not confined just to mathematicians. Biologists, artists, musicians, historians, architects, psychologists, and even mystics have pondered and debated the basis of its ubiquity and appeal. In fact, it is probably fair to say that the Golden Ratio has inspired thinkers of all disciplines like no other number in the history of mathematics.
Ancient Greek mathematicians first studied what we now call the golden ratio because of its frequent appearance in geometry. The division of a line into "extreme and mean ratio" (the golden section) is important in the geometry of regular pentagrams and pentagons. The Greeks usually attributed discovery of this concept to Pythagoras or his followers. The regular pentagram, which has a regular pentagon inscribed within it, was the Pythagoreans' symbol.
Euclid's Elements (Greek: Στοιχεῖα) provides the first known written definition of what is now called the golden ratio: "A straight line is said to have been cut in extreme and mean ratio when, as the whole line is to the greater segment, so is the greater to the less." Euclid explains a construction for cutting (sectioning) a line "in extreme and mean ratio", i.e., the golden ratio. Throughout the Elements, several propositions (theorems in modern terminology) and their proofs employ the golden ratio. Some of these propositions show that the golden ratio is an irrational number.
The name "extreme and mean ratio" was the principal term used from the 3rd century BCE until about the 18th century.
The modern history of the golden ratio starts with Luca Pacioli's De divina proportione of 1509, which captured the imagination of artists, architects, scientists, and mystics with the properties, mathematical and otherwise, of the golden ratio.
The first known approximation of the (inverse) golden ratio by a decimal fraction, stated as "about 0.6180340", was written in 1597 by Michael Maestlin of the University of Tübingen in a letter to his former student Johannes Kepler.
Since the 20th century, the golden ratio has been represented by the Greek letter Φ or φ ( phi, after Phidias, a sculptor who is said to have employed it) or less commonly by τ ( tau, the first letter of the ancient Greek root τομή—meaning cut).
Timeline according to Priya Hemenway:
- Phidias (490–430 BC) made the Parthenon statues that seem to embody the golden ratio.
- Plato (427–347 BC), in his Timaeus, describes five possible regular solids (the Platonic solids: the tetrahedron, cube, octahedron, dodecahedron, and icosahedron), some of which are related to the golden ratio.
- Euclid (c. 325–c. 265 BC), in his Elements, gave the first recorded definition of the golden ratio, which he called, as translated into English, "extreme and mean ratio" (Greek: ἄκρος καὶ μέσος λόγος).
- Fibonacci (1170–1250) mentioned the numerical series now named after him in his Liber Abaci; the ratio of sequential elements of the Fibonacci sequence approaches the golden ratio asymptotically.
- Luca Pacioli (1445–1517) defines the golden ratio as the "divine proportion" in his Divina Proportione.
- Michael Maestlin (1550–1631) publishes the first known approximation of the (inverse) golden ratio as a decimal fraction.
- Johannes Kepler (1571–1630) proves that the golden ratio is the limit of the ratio of consecutive Fibonacci numbers, and describes the golden ratio as a "precious jewel": "Geometry has two great treasures: one is the Theorem of Pythagoras, and the other the division of a line into extreme and mean ratio; the first we may compare to a measure of gold, the second we may name a precious jewel." These two treasures are combined in the Kepler triangle.
- Charles Bonnet (1720–1793) points out that in the spiral phyllotaxis of plants going clockwise and counter-clockwise were frequently two successive Fibonacci series.
- Martin Ohm (1792–1872) is believed to be the first to use the term goldener Schnitt (golden section) to describe this ratio, in 1835.
- Édouard Lucas (1842–1891) gives the numerical sequence now known as the Fibonacci sequence its present name.
- Mark Barr (20th century) suggests the Greek letter phi (φ), the initial letter of Greek sculptor Phidias's name, as a symbol for the golden ratio.
- Roger Penrose (b.1931) discovered a symmetrical pattern that uses the golden ratio in the field of aperiodic tilings, which led to new discoveries about quasicrystals.
Applications and observations
De Divina Proportione, a three-volume work by Luca Pacioli, was published in 1509. Pacioli, a Franciscan friar, was known mostly as a mathematician, but he was also trained and keenly interested in art. De Divina Proportione explored the mathematics of the golden ratio. Though it is often said that Pacioli advocated the golden ratio's application to yield pleasing, harmonious proportions, Livio points out that the interpretation has been traced to an error in 1799, and that Pacioli actually advocated the Vitruvian system of rational proportions. Pacioli also saw Catholic religious significance in the ratio, which led to his work's title. Containing illustrations of regular solids by Leonardo da Vinci, Pacioli's longtime friend and collaborator, De Divina Proportione was a major influence on generations of artists and architects alike.
The Parthenon's façade as well as elements of its façade and elsewhere are said by some to be circumscribed by golden rectangles. Other scholars deny that the Greeks had any aesthetic association with golden ratio. For example, Midhat J. Gazalé says, "It was not until Euclid, however, that the golden ratio's mathematical properties were studied. In the Elements (308 BC) the Greek mathematician merely regarded that number as an interesting irrational number, in connection with the middle and extreme ratios. Its occurrence in regular pentagons and decagons was duly observed, as well as in the dodecahedron (a regular polyhedron whose twelve faces are regular pentagons). It is indeed exemplary that the great Euclid, contrary to generations of mystics who followed, would soberly treat that number for what it is, without attaching to it other than its factual properties." And Keith Devlin says, "Certainly, the oft repeated assertion that the Parthenon in Athens is based on the golden ratio is not supported by actual measurements. In fact, the entire story about the Greeks and golden ratio seems to be without foundation. The one thing we know for sure is that Euclid, in his famous textbook Elements, written around 300 BC, showed how to calculate its value." Near-contemporary sources like Vitruvius exclusively discuss proportions that can be expressed in whole numbers, i.e. commensurate as opposed to irrational proportions.
A 2004 geometrical analysis of earlier research into the Great Mosque of Kairouan reveals a consistent application of the golden ratio throughout the design, according to Boussora and Mazouz. They found ratios close to the golden ratio in the overall proportion of the plan and in the dimensioning of the prayer space, the court, and the minaret. The authors note, however, that the areas where ratios close to the golden ratio were found are not part of the original construction, and theorize that these elements were added in a reconstruction.
The Swiss architect Le Corbusier, famous for his contributions to the modern international style, centered his design philosophy on systems of harmony and proportion. Le Corbusier's faith in the mathematical order of the universe was closely bound to the golden ratio and the Fibonacci series, which he described as "rhythms apparent to the eye and clear in their relations with one another. And these rhythms are at the very root of human activities. They resound in man by an organic inevitability, the same fine inevitability which causes the tracing out of the Golden Section by children, old men, savages and the learned."
Le Corbusier explicitly used the golden ratio in his Modulor system for the scale of architectural proportion. He saw this system as a continuation of the long tradition of Vitruvius, Leonardo da Vinci's " Vitruvian Man", the work of Leon Battista Alberti, and others who used the proportions of the human body to improve the appearance and function of architecture. In addition to the golden ratio, Le Corbusier based the system on human measurements, Fibonacci numbers, and the double unit. He took suggestion of the golden ratio in human proportions to an extreme: he sectioned his model human body's height at the navel with the two sections in golden ratio, then subdivided those sections in golden ratio at the knees and throat; he used these golden ratio proportions in the Modulor system. Le Corbusier's 1927 Villa Stein in Garches exemplified the Modulor system's application. The villa's rectangular ground plan, elevation, and inner structure closely approximate golden rectangles.
Another Swiss architect, Mario Botta, bases many of his designs on geometric figures. Several private houses he designed in Switzerland are composed of squares and circles, cubes and cylinders. In a house he designed in Origlio, the golden ratio is the proportion between the central section and the side sections of the house.
In a recent book, author Jason Elliot speculated that the golden ratio was used by the designers of the Naqsh-e Jahan Square and the adjacent Lotfollah mosque.
The 16th-century philosopher Heinrich Agrippa drew a man over a pentagram inside a circle, implying a relationship to the golden ratio.
Leonardo da Vinci's illustrations of polyhedra in De divina proportione (On the Divine Proportion) and his views that some bodily proportions exhibit the golden ratio have led some scholars to speculate that he incorporated the golden ratio in his paintings. But the suggestion that his Mona Lisa, for example, employs golden ratio proportions, is not supported by anything in Leonardo's own writings. Similarly, although the Vitruvian Man is often shown in connection with the golden ratio, the proportions of the figure do not actually match it, and the text only mentions whole number ratios.
Salvador Dalí, influenced by the works of Matila Ghyka, explicitly used the golden ratio in his masterpiece, The Sacrament of the Last Supper. The dimensions of the canvas are a golden rectangle. A huge dodecahedron, in perspective so that edges appear in golden ratio to one another, is suspended above and behind Jesus and dominates the composition.
Mondrian has been said to have used the golden section extensively in his geometrical paintings, though other experts (including critic Yve-Alain Bois) have disputed this claim.
A statistical study on 565 works of art of different great painters, performed in 1999, found that these artists had not used the golden ratio in the size of their canvases. The study concluded that the average ratio of the two sides of the paintings studied is 1.34, with averages for individual artists ranging from 1.04 (Goya) to 1.46 (Bellini). On the other hand, Pablo Tosto listed over 350 works by well-known artists, including more than 100 which have canvasses with golden rectangle and root-5 proportions, and others with proportions like root-2, 3, 4, and 6.
Book design
According to Jan Tschichold,
There was a time when deviations from the truly beautiful page proportions 2:3, 1:√3, and the Golden Section were rare. Many books produced between 1550 and 1770 show these proportions exactly, to within half a millimeter.
Industrial design
Some sources claim that the golden ratio is commonly used in everyday design, for example in the shapes of postcards, playing cards, posters, wide-screen televisions, photographs, and light switch plates.
Ernő Lendvaï analyzes Béla Bartók's works as being based on two opposing systems, that of the golden ratio and the acoustic scale, though other music scholars reject that analysis. In Bartok's Music for Strings, Percussion and Celesta the xylophone progression occurs at the intervals 1:2:3:5:8:5:3:2:1. French composer Erik Satie used the golden ratio in several of his pieces, including Sonneries de la Rose+Croix. The golden ratio is also apparent in the organization of the sections in the music of Debussy's Reflets dans l'eau (Reflections in Water), from Images (1st series, 1905), in which "the sequence of keys is marked out by the intervals 34, 21, 13 and 8, and the main climax sits at the phi position."
The musicologist Roy Howat has observed that the formal boundaries of La Mer correspond exactly to the golden section. Trezise finds the intrinsic evidence "remarkable," but cautions that no written or reported evidence suggests that Debussy consciously sought such proportions.
Pearl Drums positions the air vents on its Masters Premium models based on the golden ratio. The company claims that this arrangement improves bass response and has applied for a patent on this innovation.
Though Heinz Bohlen proposed the non-octave-repeating 833 cents scale based on combination tones, the tuning features relations based on the golden ratio. As a musical interval the ratio 1.618... is 833.090... cents (Play).
Adolf Zeising, whose main interests were mathematics and philosophy, found the golden ratio expressed in the arrangement of branches along the stems of plants and of veins in leaves. He extended his research to the skeletons of animals and the branchings of their veins and nerves, to the proportions of chemical compounds and the geometry of crystals, even to the use of proportion in artistic endeavors. In these phenomena he saw the golden ratio operating as a universal law. In connection with his scheme for golden-ratio-based human body proportions, Zeising wrote in 1854 of a universal law "in which is contained the ground-principle of all formative striving for beauty and completeness in the realms of both nature and art, and which permeates, as a paramount spiritual ideal, all structures, forms and proportions, whether cosmic or individual, organic or inorganic, acoustic or optical; which finds its fullest realization, however, in the human form."
In 2010, the journal Science reported that the golden ratio is present at the atomic scale in the magnetic resonance of spins in cobalt niobate crystals.
Several researchers have proposed connections between the golden ratio and human genome DNA.
However, some have argued that many of the apparent manifestations of the golden mean in nature, especially in regard to animal dimensions, are in fact fictitious.
The golden ratio is key to the golden section search.
Perceptual studies
Studies by psychologists, starting with Fechner, have been devised to test the idea that the golden ratio plays a role in human perception of beauty. While Fechner found a preference for rectangle ratios centered on the golden ratio, later attempts to carefully test such a hypothesis have been, at best, inconclusive.
Golden ratio conjugate
The negative root of the quadratic equation for φ (the "conjugate root") is
The absolute value of this quantity (≈ 0.618) corresponds to the length ratio taken in reverse order (shorter segment length over longer segment length, b/a), and is sometimes referred to as the golden ratio conjugate. It is denoted here by the capital Phi (Φ):
Alternatively, Φ can be expressed as
This illustrates the unique property of the golden ratio among positive numbers, that
or its inverse:
This means 0.61803...:1 = 1:1.61803....
Short proofs of irrationality
Contradiction from an expression in lowest terms
Recall that:
- the whole is the longer part plus the shorter part;
- the whole is to the longer part as the longer part is to the shorter part.
If we call the whole n and the longer part m, then the second statement above becomes
- n is to m as m is to n − m,
or, algebraically
To say that φ is rational means that φ is a fraction n/m where n and m are integers. We may take n/m to be in lowest terms and n and m to be positive. But if n/m is in lowest terms, then the identity labeled (*) above says m/(n − m) is in still lower terms. That is a contradiction that follows from the assumption that φ is rational.
Derivation from irrationality of √5
Another short proof—perhaps more commonly known—of the irrationality of the golden ratio makes use of the closure of rational numbers under addition and multiplication. If is rational, then is also rational, which is a contradiction if it is already known that the square root of a non- square natural number is irrational.
Alternative forms
The formula φ = 1 + 1/φ can be expanded recursively to obtain a continued fraction for the golden ratio:
and its reciprocal:
The convergents of these continued fractions (1/1, 2/1, 3/2, 5/3, 8/5, 13/8, ..., or 1/1, 1/2, 2/3, 3/5, 5/8, 8/13, ...) are ratios of successive Fibonacci numbers.
The equation φ2 = 1 + φ likewise produces the continued square root, or infinite surd, form:
An infinite series can be derived to express phi:
These correspond to the fact that the length of the diagonal of a regular pentagon is φ times the length of its side, and similar relations in a pentagram.
The number φ turns up frequently in geometry, particularly in figures with pentagonal symmetry. The length of a regular pentagon's diagonal is φ times its side. The vertices of a regular icosahedron are those of three mutually orthogonal golden rectangles.
There is no known general algorithm to arrange a given number of nodes evenly on a sphere, for any of several definitions of even distribution (see, for example, Thomson problem). However, a useful approximation results from dividing the sphere into parallel bands of equal area and placing one node in each band at longitudes spaced by a golden section of the circle, i.e. 360°/φ ≅ 222.5°. This method was used to arrange the 1500 mirrors of the student-participatory satellite Starshine-3.
Dividing a line segment
The following algorithm produces a geometric construction that divides a line segment into two line segments where the ratio of the longer to the shorter line segment is the golden ratio:
- Having a line segment AB, construct a perpendicular BC at point B, with BC half the length of AB. Draw the hypotenuse AC.
- Draw a circle with centre C and radius BC. This circle intersects the hypotenuse AC at point D.
- Draw a circle with centre A and radius AD. This circle intersects the original line segment AB at point S. Point S divides the original segment AB into line segments AS and SB with lengths in the golden ratio.
Golden triangle, pentagon and pentagram
Golden triangle
The golden triangle can be characterized as an isosceles triangle ABC with the property that bisecting the angle C produces a new triangle CXB which is a similar triangle to the original.
If angle BCX = α, then XCA = α because of the bisection, and CAB = α because of the similar triangles; ABC = 2α from the original isosceles symmetry, and BXC = 2α by similarity. The angles in a triangle add up to 180°, so 5α = 180, giving α = 36°. So the angles of the golden triangle are thus 36°-72°-72°. The angles of the remaining obtuse isosceles triangle AXC (sometimes called the golden gnomon) are 36°-36°-108°.
Suppose XB has length 1, and we call BC length φ. Because of the isosceles triangles XC=XA and BC=XC, so these are also length φ. Length AC = AB, therefore equals φ + 1. But triangle ABC is similar to triangle CXB, so AC/BC = BC/BX, and so AC also equals φ2. Thus φ2 = φ + 1, confirming that φ is indeed the golden ratio.
Similarly, the ratio of the area of the larger triangle AXC to the smaller CXB is equal to φ, while the inverse ratio is φ − 1.
In a regular pentagon the ratio between a side and a diagonal is (i.e. 1/φ), while intersecting diagonals section each other in the golden ratio.
Odom's construction
George Odom has given a remarkably simple construction for φ involving an equilateral triangle: if an equilateral triangle is inscribed in a circle and the line segment joining the midpoints of two sides is produced to intersect the circle in either of two points, then these three points are in golden proportion. This result is a straightforward consequence of the intersecting chords theorem and can be used to construct a regular pentagon, a construction that attracted the attention of the noted Canadian geometer H. S. M. Coxeter who published it in Odom's name as a diagram in the American Mathematical Monthly accompanied by the single word "Behold!"
The golden ratio plays an important role in the geometry of pentagrams. Each intersection of edges sections other edges in the golden ratio. Also, the ratio of the length of the shorter segment to the segment bounded by the two intersecting edges (a side of the pentagon in the pentagram's center) is φ, as the four-colour illustration shows.
The pentagram includes ten isosceles triangles: five acute and five obtuse isosceles triangles. In all of them, the ratio of the longer side to the shorter side is φ. The acute triangles are golden triangles. The obtuse isosceles triangles are golden gnomons.
Ptolemy's theorem
The golden ratio properties of a regular pentagon can be confirmed by applying Ptolemy's theorem to the quadrilateral formed by removing one of its vertices. If the quadrilateral's long edge and diagonals are b, and short edges are a, then Ptolemy's theorem gives b2 = a2 + ab which yields
Scalenity of triangles
Consider a triangle with sides of lengths a, b, and c in decreasing order. Define the "scalenity" of the triangle to be the smaller of the two ratios a/b and b/c. The scalenity is always less than φ and can be made as close as desired to φ.
Triangle whose sides form a geometric progression
If the side lengths of a triangle form a geometric progression and are in the ratio 1 : r : r2, where r is the common ratio, then r must lie in the range φ−1 < r < φ, which is a consequence of the triangle inequality (the sum of any two sides of a triangle must be strictly bigger than the length of the third side). If r = φ then the shorter two sides are 1 and φ but their sum is φ2, thus r < φ. A similar calculation shows that r > φ−1. A triangle whose sides are in the ratio 1 : √φ : φ is a right triangle (because 1 + φ = φ2) known as a Kepler triangle.
Golden triangle, rhombus, and rhombic triacontahedron
A golden rhombus is a rhombus whose diagonals are in the golden ratio. The rhombic triacontahedron is a convex polytope that has a very special property: all of its faces are golden rhombi. In the rhombic triacontahedron the dihedral angle between any two adjacent rhombi is 144°, which is twice the isosceles angle of a golden triangle and four times its most acute angle.
Relationship to Fibonacci sequence
The mathematics of the golden ratio and of the Fibonacci sequence are intimately interconnected. The Fibonacci sequence is:
- 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, ....
The closed-form expression (known as Binet's formula, even though it was already known by Abraham de Moivre) for the Fibonacci sequence involves the golden ratio:
The golden ratio is the limit of the ratios of successive terms of the Fibonacci sequence (or any Fibonacci-like sequence), as originally shown by Kepler:
Therefore, if a Fibonacci number is divided by its immediate predecessor in the sequence, the quotient approximates φ; e.g., 987/610 ≈ 1.6180327868852. These approximations are alternately lower and higher than φ, and converge on φ as the Fibonacci numbers increase, and:
More generally:
where above, the ratios of consecutive terms of the Fibonacci sequence, is a case when .
Furthermore, the successive powers of φ obey the Fibonacci recurrence:
This identity allows any polynomial in φ to be reduced to a linear expression. For example:
However, this is no special property of φ, because polynomials in any solution x to a quadratic equation can be reduced in an analogous manner, by applying:
for given coefficients a, b such that x satisfies the equation. Even more generally, any rational function (with rational coefficients) of the root of an irreducible nth-degree polynomial over the rationals can be reduced to a polynomial of degree n ‒ 1. Phrased in terms of field theory, if α is a root of an irreducible nth-degree polynomial, then has degree n over , with basis .
The golden ratio and inverse golden ratio have a set of symmetries that preserve and interrelate them. They are both preserved by the fractional linear transformations – this fact corresponds to the identity and the definition quadratic equation. Further, they are interchanged by the three maps – they are reciprocals, symmetric about , and (projectively) symmetric about 2.
More deeply, these maps form a subgroup of the modular group isomorphic to the symmetric group on 3 letters, corresponding to the stabilizer of the set of 3 standard points on the projective line, and the symmetries correspond to the quotient map – the subgroup consisting of the 3-cycles and the identity fixes the two numbers, while the 2-cycles interchange these, thus realizing the map.
Other properties
The golden ratio has the simplest expression (and slowest convergence) as a continued fraction expansion of any irrational number (see Alternate forms above). It is, for that reason, one of the worst cases of Lagrange's approximation theorem and it is an extremal case of the Hurwitz inequality for Diophantine approximations. This may be why angles close to the golden ratio often show up in phyllotaxis (the growth of plants).
The defining quadratic polynomial and the conjugate relationship lead to decimal values that have their fractional part in common with φ:
The sequence of powers of φ contains these values 0.618..., 1.0, 1.618..., 2.618...; more generally, any power of φ is equal to the sum of the two immediately preceding powers:
As a result, one can easily decompose any power of φ into a multiple of φ and a constant. The multiple and the constant are always adjacent Fibonacci numbers. This leads to another property of the positive powers of φ:
If , then:
When the golden ratio is used as the base of a numeral system (see Golden ratio base, sometimes dubbed phinary or φ-nary), every integer has a terminating representation, despite φ being irrational, but every fraction has a non-terminating representation.
The golden ratio is a fundamental unit of the algebraic number field and is a Pisot–Vijayaraghavan number. In the field we have , where is the -th Lucas number.
The golden ratio also appears in hyperbolic geometry, as the maximum distance from a point on one side of an ideal triangle to the closer of the other two sides: this distance, the side length of the equilateral triangle formed by the points of tangency of a circle inscribed within the ideal triangle, is 4 ln φ.
Decimal expansion
The golden ratio's decimal expansion can be calculated directly from the expression
with √5 ≈ 2.2360679774997896964. The square root of 5 can be calculated with the Babylonian method, starting with an initial estimate such as xφ = 2 and iterating
for n = 1, 2, 3, ..., until the difference between xn and xn−1 becomes zero, to the desired number of digits.
The Babylonian algorithm for √5 is equivalent to Newton's method for solving the equation x2 − 5 = 0. In its more general form, Newton's method can be applied directly to any algebraic equation, including the equation x2 − x − 1 = 0 that defines the golden ratio. This gives an iteration that converges to the golden ratio itself,
for an appropriate initial estimate xφ such as xφ = 1. A slightly faster method is to rewrite the equation as x − 1 − 1/x = 0, in which case the Newton iteration becomes
These iterations all converge quadratically; that is, each step roughly doubles the number of correct digits. The golden ratio is therefore relatively easy to compute with arbitrary precision. The time needed to compute n digits of the golden ratio is proportional to the time needed to divide two n-digit numbers. This is considerably faster than known algorithms for the transcendental numbers π and e.
An easily programmed alternative using only integer arithmetic is to calculate two large consecutive Fibonacci numbers and divide them. The ratio of Fibonacci numbers F 25001 and F 25000, each over 5000 digits, yields over 10,000 significant digits of the golden ratio.
The golden ratio φ has been calculated to an accuracy of several millions of decimal digits (sequence A001622 in OEIS). Alexis Irlande performed computations and verification of the first 17,000,000,000 digits.
Both Egyptian pyramids and those mathematical regular square pyramids that resemble them can be analyzed with respect to the golden ratio and other ratios.
Mathematical pyramids and triangles
A pyramid in which the apothem (slant height along the bisector of a face) is equal to φ times the semi-base (half the base width) is sometimes called a golden pyramid. The isosceles triangle that is the face of such a pyramid can be constructed from the two halves of a diagonally split golden rectangle (of size semi-base by apothem), joining the medium-length edges to make the apothem. The height of this pyramid is times the semi-base (that is, the slope of the face is ); the square of the height is equal to the area of a face, φ times the square of the semi-base.
The medial right triangle of this "golden" pyramid (see diagram), with sides is interesting in its own right, demonstrating via the Pythagorean theorem the relationship or . This " Kepler triangle" is the only right triangle proportion with edge lengths in geometric progression, just as the 3–4–5 triangle is the only right triangle proportion with edge lengths in arithmetic progression. The angle with tangent corresponds to the angle that the side of the pyramid makes with respect to the ground, 51.827... degrees (51° 49' 38").
A nearly similar pyramid shape, but with rational proportions, is described in the Rhind Mathematical Papyrus (the source of a large part of modern knowledge of ancient Egyptian mathematics), based on the 3:4:5 triangle; the face slope corresponding to the angle with tangent 4/3 is 53.13 degrees (53 degrees and 8 minutes). The slant height or apothem is 5/3 or 1.666... times the semi-base. The Rhind papyrus has another pyramid problem as well, again with rational slope (expressed as run over rise). Egyptian mathematics did not include the notion of irrational numbers, and the rational inverse slope (run/rise, multiplied by a factor of 7 to convert to their conventional units of palms per cubit) was used in the building of pyramids.
Another mathematical pyramid with proportions almost identical to the "golden" one is the one with perimeter equal to 2π times the height, or h:b = 4:π. This triangle has a face angle of 51.854° (51°51'), very close to the 51.827° of the Kepler triangle. This pyramid relationship corresponds to the coincidental relationship .
Egyptian pyramids very close in proportion to these mathematical pyramids are known.
Egyptian pyramids
In the mid-nineteenth century, Röber studied various Egyptian pyramids including Khafre, Menkaure and some of the Giza, Sakkara, and Abusir groups, and was interpreted as saying that half the base of the side of the pyramid is the middle mean of the side, forming what other authors identified as the Kepler triangle; many other mathematical theories of the shape of the pyramids have also been explored.
One Egyptian pyramid is remarkably close to a "golden pyramid"—the Great Pyramid of Giza (also known as the Pyramid of Cheops or Khufu). Its slope of 51° 52' is extremely close to the "golden" pyramid inclination of 51° 50' and the π-based pyramid inclination of 51° 51'; other pyramids at Giza (Chephren, 52° 20', and Mycerinus, 50° 47') are also quite close. Whether the relationship to the golden ratio in these pyramids is by design or by accident remains open to speculation. Several other Egyptian pyramids are very close to the rational 3:4:5 shape.
Adding fuel to controversy over the architectural authorship of the Great Pyramid, Eric Temple Bell, mathematician and historian, claimed in 1950 that Egyptian mathematics would not have supported the ability to calculate the slant height of the pyramids, or the ratio to the height, except in the case of the 3:4:5 pyramid, since the 3:4:5 triangle was the only right triangle known to the Egyptians and they did not know the Pythagorean theorem, nor any way to reason about irrationals such as π or φ.
Michael Rice asserts that principal authorities on the history of Egyptian architecture have argued that the Egyptians were well acquainted with the golden ratio and that it is part of mathematics of the Pyramids, citing Giedon (1957). Historians of science have always debated whether the Egyptians had any such knowledge or not, contending rather that its appearance in an Egyptian building is the result of chance.
In 1859, the pyramidologist John Taylor claimed that, in the Great Pyramid of Giza, the golden ratio is represented by the ratio of the length of the face (the slope height), inclined at an angle θ to the ground, to half the length of the side of the square base, equivalent to the secant of the angle θ. The above two lengths were about 186.4 and 115.2 meters respectively. The ratio of these lengths is the golden ratio, accurate to more digits than either of the original measurements. Similarly, Howard Vyse, according to Matila Ghyka, reported the great pyramid height 148.2 m, and half-base 116.4 m, yielding 1.6189 for the ratio of slant height to half-base, again more accurate than the data variability.
Disputed observations
Examples of disputed observations of the golden ratio include the following:
- Historian John Man states that the pages of the Gutenberg Bible were "based on the golden section shape". However, according to Man's own measurements, the ratio of height to width was 1.45.
- Some specific proportions in the bodies of many animals (including humans) and parts of the shells of mollusks and cephalopods are often claimed to be in the golden ratio. There is a large variation in the real measures of these elements in specific individuals, however, and the proportion in question is often significantly different from the golden ratio. The ratio of successive phalangeal bones of the digits and the metacarpal bone has been said to approximate the golden ratio. The nautilus shell, the construction of which proceeds in a logarithmic spiral, is often cited, usually with the idea that any logarithmic spiral is related to the golden ratio, but sometimes with the claim that each new chamber is proportioned by the golden ratio relative to the previous one; however, measurements of nautilus shells do not support this claim.
- The proportions of different plant components (numbers of leaves to branches, diameters of geometrical figures inside flowers) are often claimed to show the golden ratio proportion in several species. In practice, there are significant variations between individuals, seasonal variations, and age variations in these species. While the golden ratio may be found in some proportions in some individuals at particular times in their life cycles, there is no consistent ratio in their proportions.
- In investing, some practitioners of technical analysis use the golden ratio to indicate support of a price level, or resistance to price increases, of a stock or commodity; after significant price changes up or down, new support and resistance levels are supposedly found at or near prices related to the starting price via the golden ratio. The use of the golden ratio in investing is also related to more complicated patterns described by Fibonacci numbers (e.g. Elliott wave principle and Fibonacci retracement). However, other market analysts have published analyses suggesting that these percentages and patterns are not supported by the data.


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A question I am often asked when people see one of my paintings is, how long has it taken to do it. The short is answer is ' well actually, most of my life ' ! but this really poses a fundamental dilemma that seems to confront most artists I talk to, that is, how to decide when is a painting finished. For me it's when I reach the point where I've achieved what I set out to do, and when adding more detail or refinement becomes irrelevant. This helps me define in my own mind the object of the painting, and what I'm trying to convey before I start. The more I paint the more I realize that I am constantly trying to capture the essence of the moment or the subject clearly and concisely, which is probably what drew me to painting in the first place.
I hope you enjoy the results!
Peter Rocklin.
He is represented by Plus One Gallery in London . His paintings are also at Soho Hotel, Haymarket Hotel, Dorset Square Hotel and Ham Yard Hotel in London and also Crosby Street Hotel in New York and in numerous corporate and private collections through out the world.


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By Michael Lucibella
Scientists receiving federal funds will soon have to include plans for the public access of much of their raw data. This requirement was spelled out in February, in the same memo from the executive branch's Office of Science and Technology Policy (OSTP) that dealt with the open availability of journal papers derived from federally funded research.
Though there has been no official statement on the issue, scientists applying for federal grants will likely start seeing requirements for a data management plan in the coming months. Michael Lubell, APS Director of Public Affairs, said that after meetings with representatives from various funding agencies, including the NSF and the DOE, it's clear that the beginning of a framework is just starting to take shape.
Many of the details of how and where this data will be stored are still unclear, and the timeframe is still uncertain. The enormous amount and huge diversity of different kinds of data across all disciplines of science poses a huge challenge to anyone trying to put together a single centralized database of research data. It's also possible that individual agencies, or even publishers, might be the stewards of the raw data files.
Who will store the data will have to be worked out on a field by field or even discipline by discipline basis.
"What they're looking for is not something that would be burdensome but something that will enable readers to assess how important that result is in terms of their own work," Lubell said.
Generally speaking the data that would have to be included are the individual data points used in preparation of a published paper. Data points that have been expunged from the final analysis will likely have to be included, the idea being that scientists can evaluate why those points were eliminated.
However, the policy would not extend to objects or lab notebooks. It would likely not extend also to computer codes, though talks are continuing over this point.
Victoria Stodden, a statistician at Columbia University and an expert on open data, expressed concern at the prospect that computer code might not be included in the requirements. She said that computers have dramatically changed the way that scientists process their data, and knowing how is as important as knowing the raw data points.
"Now things have changed, computation adds this extra level of complexity," Stodden said, adding that without codes, "results are typically not replicable."
The February memorandum from OSTP called for a road map to make all scientific journal articles based on federally funded research freely available for everyone to see after a year. The memo also stipulated that "scientific data resulting from unclassified research supported wholly or in part by Federal funding should be stored and publicly accessible to search, retrieve, and analyze."
The memo set an August 22 deadline for when the funding agencies needed to submit a plan for their data management. Several agencies have received extensions and no plans have been publicly released.
When reached for comment, OSTP spokesperson Rick Weiss said that "[The] OSTP will be working with the agencies to get the various submitted plans finalized."
In June, APS announced that along with 75 other publishers and organizations, they will participate in the Clearinghouse for the Open Research of the United States, or CHORUS, which would be an online platform that links to open access journal articles stored on publishers' servers. However, the service focuses solely on research articles."
The concept of CHORUS is to maximize existing infrastructure, standards and processes," said Andi Sporkin, spokesperson for CHORUS. "The maintenance of raw data requires a new infrastructure."
Though policies and guidelines are still forthcoming, Lubell encouraged researchers to start thinking ahead about raw data management.
"Everyone needs to start thinking about 'How am I going to manage my data?'…'What is the plan, and how do I ensure a long life for this so it doesn't get destroyed?'" Lubell said. "That is what the community will have to start thinking about right now."
OSTP Memo Sets Goal of Public Access – APS News
APS to Participate in Multi-Publisher Open Access Research Clearinghouse - APS News
APS encourages the redistribution of the materials included in this newspaper provided that attribution to the source is noted and the materials are not truncated or changed.


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Santiago, Chile (CNN) -- As the sun set in Chile on Saturday, a picture of the immense structural damage wrought by an early morning earthquake had come clearly into focus, with the nation's president estimating that 2 million people had been affected in some way.
More than 300 people were killed, according to Chile's Office of Emergency Management, and 15 are missing.
The carnage from the 8.8-magnitude quake didn't begin to approach that unleashed by January's earthquake in Haiti, which left 212,000 people dead and more than a million homeless, even though it was considerably less forceful, with a 7.0 magnitude.
Saturday's quake was 700 to 800 times stronger, but at a greater depth -- 21.7 miles -- compared to the shallow 8.1-mile depth of the Haiti quake, which contributed to much of the damage there.
Coastal Chile has a history of deadly earthquakes, with 13 quakes of magnitude 7.0 or higher since 1973, the U.S. Geological Survey said. As a result, experts said that newer buildings are constructed to help withstand the shocks.
Still, the damage from Chile's earthquake was widespread. A 15-story high rise near the southern city of Concepcion collapsed; the country's major north-south highway was severed at multiple points; and the capital city's airport was closed after its terminal sustained major damage.
Chilean President Michelle Bachelet announced that all public events would be canceled for the next 72 hours and that the start of the the school year -- originally scheduled for Monday -- would be delayed until March 8.
"The forces of nature have hurt our country greatly," Bachelet said in a nationally televised message Saturday night. "We are now having to face adversity and stand again."
The quake struck at 3:34 a.m. (1:34 a.m. ET) off the Pacific coast at a depth of nearly 22 miles (35 km) and about 60 miles (100 km) northwest of Chillan, Chile, the USGS said. Santiago, the capital, is 200 miles (325 km) northeast of the epicenter.
Saturday's epicenter was just a few miles north of the largest earthquake recorded in the world: a magnitude 9.5 quake in May 1960 that killed 1,655 and unleashed a tsunami that crossed the Pacific.
The quake was followed by 76 aftershocks of 4.9 magnitude or greater, according to the USGS. That includes a 6.1-magnitude temblor in Argentina that killed a 58-year-old man and an 8-year-old boy in separate towns, the government-run Telam news agency said. Some buildings in the Argentine capital, Buenos Aires, were evacuated, though the city is 690 miles (1,111 kilometers) from Santiago.
Earlier Saturday, a large wave killed three people and 10 were missing on the island of Juan Fernandez, 400 miles (643 km) off the coast of Chile, said Provincial Governor Ivan De La Maza.
Across Chile, desperate relatives spent the day searching for missing loved ones. Many used the Internet to ask for help in finding relatives.
Millions of other Chileans began swapping tales of fear and confusion in the early morning hours, soon after the quake struck.
CNN iReporter Matias de Cristobal said many homes in her Santiago neighborhood were destroyed.
Cristobal tried to climb upstairs to check on her three children after she began feeling tremors Saturday, but she was slowed by shifting ground and falling objects.
Mirko Vukasovic, a 25-year-old illustrator in Santiago, had been dancing at a club early Saturday when the disco ball began swinging wildly. A chaotic evacuation was already under way when the lights went out, and everyone managed to escape, Vukasovic said.
"Broken windows and falling building parts was what welcomed us in the streets," he said.
Many initially greeted the quake with disbelief.
"It was 3 or 4 in the morning and I had come home late," said Aneya Fernando, an American who teaches English in Santiago. "Suddenly my bed was moving so violently that it woke me up."
"I'm on the 10th floor of a building and it was swaying and shaking," Fernando, 23, said. "Suddenly [the shaking] was just gone and I was confused. I thought it was in my head."
When Fernando's electricity returned 30 minutes later, she learned of the earthquake on TV.
The task of trying to rescue survivors and recover the dead continued into the night. Buildings lay in rubble, bridges and highway overpasses were toppled and roads buckled like rumpled paper. Mangled cars were strewn on highways, many of them resting on their roofs.
Santiago, the capital, lost electricity and basic services, including water and telephones. A chemical fire in the city that was spreading from one building to others forced the evacuation of everyone within 500 meters.
Chilean television showed buildings in tatters in Concepcion, in coastal central Chile. Whole sides of buildings were torn off, and at least two structures were engulfed in flames. Emergency teams rescued 30 people from one collapsed building in Concepcion.
iReport.com: Did you feel it? Share information, images with CNN
President-elect Sebastian Pinera, who will take office in March, also was monitoring the situation and warned, "The number of victims could get higher."
Bachelet declared areas of catastrophe, similar to a state of emergency, which will allow her to rush in aid. She noted that two of the nation's largest hospitals had suffered structural damage and patients were taken to other facilities.
Other public institutions also were affected.
"There were reports of riots at one of the jails," Bachelet said. "The jails have, of course, received significant damage... We are looking into possibly moving some of these inmates."
Two airlines, LAN and Cencosud, announced they were temporarily suspending services.
Several international humanitarian groups pledged help for Chile's relief effort, with AmeriCares announcing it was sending medical aid and an emergency response team to Chile. Oxfam said it's sending a team of water engineers and logisticians from Colombia and senior humanitarian staff from Mexico to help in relief efforts.
In a televised address Saturday, President Obama said that the United States has resources positioned to assist Chile if it requests help. Secretary of State Hillary Clinton said she will proceed Sunday with her planned trip to five Latin American countries, including Chile.
Meanwhile, the Japan Meteorological Agency issued a major tsunami warning for parts of its coastline, indicating the possibility of waves 9 feet or higher. Tens of thousands of coastal residents were evacuated ahead of the potential surge.
Follow tsunami warning information
The Philippines Institute of Volcanology and Seismology also issued a tsunami alert, with the first waves expected in the Philippines around 1 p.m. on Sunday (midnight Saturday ET).
In Hawaii, a tsunami warning was lifted around 1:45 p.m. (6:45 p.m. ET), the Pacific Tsunami Warning Center said.
Check out the world's biggest earthquakes since 1900
Small waves from the tsunami also reached Tasmania, an island about 150 miles (240 km) east of Australia, said Chris Ryan co-director of the Joint Australian Tsunami Warning Center in Melbourne, Australia.
No damage was expected from possibly stronger waves to follow, Ryan said.
"We have a two-level warning system," he said. "It's at the lower warning level. ... We expect some danger for people on the beach or close to water's edge ... but not to buildings or structures."
CNN's Rolando Santos, Brian Byrnes and Patty Lane contributed to this report.


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VIDEO: The trailer for Slumdog Millionaire
Slumdog Millionaire | Directed by Danny Boyle And Loveleen Tandan | Written by Simon Beaufoy based on the novel Q & A by Vikas Swarup | with Dev Patel, Freida Pinto, Madhur Mittal, Anil Kapoor, and Irrfan Khan | Warner Bros. | English + Hindi | 120 minutes
Interview: Danny Boyle. By Peter Keough.
The young man getting the third degree is 18-year-old Jamal Malik (Dev Patel), the slumdog of the title and the unlikely winner of the top 20-million-rupee prize in the Indian version of Who Wants To Be a Millionaire. The host of the show (Anil Kapoor), no Regis Philbin, wonders how an uneducated ragamuffin could achieve what PhDs have failed to do; he may also fear that the contestant was getting more popular than the host. In any case, he turns Jamal over to the cops. After rougher treatment fails to produce a confession of cheating, the police inspector (Irrfan Khan) just asks Jamal to explain how he arrived at each answer.
And so a simple but exhilarating structure falls into place as each question proves a talisman that whirls the film into Jamal's sometimes hideous, sometimes wondrous, always photogenic past. It's like an MTV version of The Arabian Nights by way of Mira Nair's Salaam Bombay. The first question (about the star of a popular Bollywood movie) sets off a raucous chase scene with potbellied cops pursuing an army of urchins through the parti-colored squalor of Mumbai's Dharavi slum. It includes an astounding aerial shot of the tiny figures sprinting through the endless vista of hovels (Boyle has a knack for urban desolation, as in 28 Days Later), and it culminates in a slapsticky immersion of the hero in a cesspit.
But the shit hits the fan for real as the questions get more difficult and the autobiography follows suit. Horrific images — of the anti-Muslim riots that orphan Jamal and his tougher, more ruthless brother, Salim (Madhur Mittal), and of the cruelties suffered by children enlisted as professional beggars — strain Boyle's whimsy. At this point a Dickensian mode emerges (screenwriter Simon Beaufoy's previous credit is The Full Monty), with a villain who makes Fagin look like Mother Teresa, a loyalty/rivalry dynamic established between Jamal and Salim, and an elusive beloved, fellow urchin and latter-day beauty Latika (Freida Pinto). If only Jamal can somehow rescue her and make her his, then all the suffering will have been worth it.
No wonder then, that the Bollywood musical number that makes the concluding credits worth sitting through doesn't require such a difficult suspension of disbelief. But the willing suspension of outrage at the injustice and misery on display for the entertainment of audiences is another matter.
See all articles by: PETER KEOUGH
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D.A.R.E. Program
The D.A.R.E. (Drug Abuse Resistance Education) Program, founded in 1983 by former Los Angeles Police Department Chief Daryl Gates, has evolved into an international education program that seeks to prevent the use of controlled dangerous substances, membership in gangs and violent behavior. Starting in 5th grade, elementary students are educated about acting in their own best interest when facing high-risk, low-gain choices and resisting peer pressure and other influences when making personal choices regarding tobacco smoking and advertising, drug abuse, use of inhalants, alcohol consumption and health and peer pressure in social networks.
Classroom Environment
The D.A.R.E. Program enables students to interact with police officers or sheriffs in a controlled, safe, classroom environment. This helps students and officers meet and understand each other in a friendly manner, rather than meeting when a student commits a crime, or when officers must intervene in domestic disputes and severe family problems. D.A.R.E. is also an important tertiary crime and violence prevention education program.
D.A.R.E. curriculum instructors are local police officers who must undergo 80 hours of specialized training in areas including child development, classroom management, teaching techniques and communication skills. Police officers are invited by the local school districts to speak to and work with students. Different programs are presented to different age groups. Working with classroom teachers, the officers lead students through workbooks and conduct interactive discussions.
Participating Schools
The Park Police Division has partnered with the Prince George's County School system since 1995 and has seven certified D.A.R.E. officers participating in the program. Currently, Park Police offer D.A.R.E. programs in Prince George's County at the following schools:
Beacon Heights Elementary
Glassmanor Elementary
Kingsford Elementary
Perwood Elementary
Samuel P. Massey Academy
William Hall Academy
Additional Information
For more information about the program,
visit the D.A.R.E website
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Bicycle Safety Education Program
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D.A.R.E. Program
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More Family Voices Needed in Immigration Hearings
by Community Change | April 24, 2013 12:00 am
The Senate Judiciary Committee has held three hearings so far on the Gang of 8's proposed immigration reform bill. So far, there has been only one undocumented immigrant who has been invited to testify.
On Monday, Gaby Pacheco told her story of immigrating to the United States from Ecuador at the age of eight. In her testimony, she talked about her mixed status family and their struggles under our current immigration system. She also spoke about her work as an immigrant rights activist, including her participation in the Trail of Dreams, a 1,500 mile walk from Miami to Washington, D.C. that she and three other activists embarked on in 2010 to shed light on the plight of undocumented immigrants everywhere.
Instead of using tactics to delay and derail this important piece of legislation, lawmakers in Washington should hear more stories from people like Pacheco. Each day that this bill has not become a law, 1,100 people are deported, and 1,100 families are destroyed in the process.
"These people are mothers, fathers, children, and neighbors," Pacheco said. "Their dreams are held in the hands of this committee and the rest of Congress. Their dreams now lie in the Senate bipartisan bill, S.744."
The media should focus on testimony like Gaby's because she illustrated the problems of our current broken immigration system. Instead, they focus on comments from lawmakers who try to derail the conversation.
Fortunately, the voices of the naysayers have been somewhat quieted by members of their own party. Even Republican Rep. Paul Ryan has said immigration reform is needed now.


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Hal Trosky, Jr. grew up with a great model to emulate while dreaming of becoming a big league player. His father, Hal Trosky, Sr. was a major league star, who, if not for World War II may have made a very strong case for enshrinement in the Baseball Hall of Fame. As it was, Senior had a star career that ended after the 1946 season when Junior was 10 years old. By that time the younger Trosky had seen enough to know what he wanted to do with his life- play baseball.
By the time he was in high school, Trosky, Jr. had become a talented player and was drawing a lot of interest from professional teams. As a senior in Cedar Rapids, Iowa he hit .667 and had scouts from nearly half the major league teams in attendance at his games. The connections his father had made during his time in the game helped guide the young man's decision making, and in 1954 he settled on signing with the Chicago White Sox after making a good connection with team owner Charlie Comiskey, Jr., who shared the commonality of being baseball progeny.
Like his father, Trosky was a slugging first baseman, with the only difference being that he hit right-handed, unlike his dad's lefty approach. He hit a home run in his first at bat in the minors, but was constantly hobbled by injuries. Wanting to get as much as they could out of their prized prospect, the White Sox suggested in 1956 that he try pitching as a way to possibly keep him on the field. Trosky was amenable to the idea and experienced immediate success, going 9-5, with a 3.95 ERA his first year.
Throwing hard, yet with inconsistent control, Trosky developed almost immediately into a top pitching prospect. In the minors he posted 14 wins in 1957 and another 13 in 1958, fueling speculation that it was only a matter of time before he would be summoned to help out an aging White Sox pitching staff.
Trosky earned an end of season call-up to Chicago in September of 1958. The White Sox were on their way to a second place finish, but well behind the first place Yankees, and wanted to see what they had in their young pitcher. He was given a two relief appearance audition. The first came against the Tigers, and he pitched a scoreless inning. He gave up a single to Billy Martin, the first major league hitter he faced, but got the next batter, Charlie Maxwell, to strikeout into a double play when Martin attempted a stolen base. His second and final major league game was the final contest of the season, on September 28, 1958 against the Kansas City Athletics. Although he gave up 4 hits and 3 runs in two innings, he was able to earn the win in an 11-4 shootout.
The following season Trosky seemed poised to make the White Sox out of spring training, but was sent down on the final day of cuts. He continued to pitch well, but was never brought up again to the big leagues. Feeling that he had no future with Chicago, Trosky refused to sign with the organization for the 1961 season and asked for his release. The team would not release or trade him, so Trosky quit the game for good and began a lengthy career in insurance. Interestingly the White Sox finally did grant his request for a release, but it occurred in 1972, when he was 36 and had been out of professional baseball for over a decade.
Trosky went 44-30, with a 3.53 ERA in five minor league seasons. Although he only appeared in two major league games, he is able to say that he did earn a win during that time. More information about his career statistics is available at http://www.baseball-reference.com/players/t/troskha02.shtml.
I think that Trosky and how his baseball career played out is a fascinating story. This past year I had the opportunity to exchange letters with him and asked him a few questions about his experience with the game.
Hal Trosky, Jr. Questionnaire:
If you could do anything different about your career, what would that be?: Try earlier to get out of the White Sox organization.
Who was your coach or manager?: Luke Appling at Memphis and Jim Turner at Nashville.
What current player reminds you the most of players from your era?: Quite frankly I've all but ceased watching professional sports. The attitudes and intensity are sad.
You can follow me on Facebook by going to http://www.facebook.com/pages/The-Baseball-Historian/138174109591660 or follow me on Twitter @historianandrew


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Two-time Olympic medalist and openly gay athlete Caitlin Cahow appeared on the "Today" show on Thursday and said she is "very proud" to be part of the U.S. delegation for the Sochi Games selected by the White House earlier this week.
"I am going to Sochi to represent a country that has made the most dramatic shifts on some of these issues in the last few years and I am very proud to be representing that kind of diversity," Cahow said, referring to recent strides made in gay rights in the U.S.
Cahow, who medaled in ice hockey in Turin and Vancouver, received a call from the White House with an invitation to join a delegation that includes another openly-gay athlete, tennis great Billie Jean King. 1998 Olympic figure skating gold medalist Brian Boitano was also added to the delegation. On Thursday, Boitano announced in a statement that he is gay, saying that his sexual orientation is "just one part of who I am."
The delegation selections come amid much public conversation about Russia's anti-gay laws, even though President Vladimir Putin insists his country's first priority as host is to provide "equal terms" for all athletes.
Cahow told host Matt Lauer that mixing politics and sports is inevitable at the Olympics and hopes she can make the best of what she perceives as her "John Carlos moment," a nod to the U.S. track and field Olympian who, along with fellow athlete Tommie Smith, raised their fists in a Black Power salute on the podium during their medal ceremony in 1968 in Mexico City.
"Honestly, I think that my John Carlos moment right now is going to Russia and being present and representing the United States," she told Lauer. "This delegation represents so much more than just LGBT diversity."
President Barack Obama will not attend the games in February, but the White House said in a statement that the delegates will "showcase to the world the best of America -- diversity, determination and teamwork." This marks the first Olympics since the Sydney games in 2000 that a U.S. president, vice president, first lady or former president is not part of the U.S delegation.
U.S. & World
Cahow and King will be accompanied by former Homeland Security Secretary and current president of the University of California Janet Napolitano, and speed skater Bonnie Flair.