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Pi

π (or pi) is a mathematical constant that is the ratio of a circle's circumference to its diameter. It is approximately equal to 3.14159. π is an irrational number, which means that it cannot be expressed exactly as a ratio of two integers, although it is roughly approximated by 22/7. It is a transcendental number – a number that cannot be produced with a finite sequence of algebraic operations (sums, products, powers, and roots). The transcendence of π implies that it is impossible to solve the ancient challenge of squaring the circle with a compass and straightedge. The digits in the decimal representation of π appear to be random. Because its definition relates to the circle, π is found in many formulae in trigonometry and geometry, such as Euler's identity, e + 1 = 0. It is also found in formulae from other branches of science, such as cosmology, number theory, statistics, fractals, thermodynamics, mechanics, and electromagnetism. (more...)

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Did you know...

From Wikipedia's newest content:

  • ... that until 1999, Queen Elizabeth II was the only woman allowed into the Lord's Pavilion (pictured)?
  • ... that anthropologist Alice G. Dewey was dissertation advisor for Barack Obama's mother Ann Dunham at the University of Hawaiʻi?
  • ... that Serbia's first known "čelnik", Gradislav Vojšić, served King Milutin in 1284 and King Uroš III in 1327?
  • ... that Helen Desha Beamer and Sam Kapu made the first commercial recording of the Hawaiian Wedding Song in 1928?
  • ... that Rabbi Alexander Zusia Friedman alerted world Jewry to the start of deportations from the Warsaw Ghetto to the death camps in a coded message referring to "Mr. Amos"?
  • ... that EthicalWiki advises public relations professionals to engage with Wikipedia's editors in the same way they do with journalists?
  • ... that 2012 Australian Paralympic swimmer Esther Overton once broke her arm trying to get into a swimsuit?
  • In the news

    Century 16 theater

  • A gunman kills 12 people and injures more than 50 others during a midnight film screening (location pictured) in the U.S. state of Colorado.
  • Bollywood actor and film producer Rajesh Khanna dies at the age of 69.
  • Syrian defense minister Dawoud Rajiha and deputy defense minister Assef Shawkat are killed in a bomb attack on the Military Intelligence Directorate headquarters in Damascus.
  • At least seven people are killed in an attack on a bus carrying Israeli tourists in Burgas, Bulgaria.
  • The National Forces Alliance, led by Mahmoud Jibril, gains a plurality in the Libyan General National Congress election, the first election since the deposition of Muammar Gaddafi.
  • On this day...

    July 22: Feast day of Mary Magdalene; Parents' Day in the United States (2012); Pi Approximation Day

    John Dillinger

  • 1793 – Two days after becoming the first recorded person to complete a transcontinental crossing of North America north of Mexico, Scottish-Canadian explorer Alexander Mackenzie reached the westernmost point of his journey and inscribed his name on a rock.
  • 1802Gia Long conquered Hanoi and unified modern-day Vietnam, which had experienced centuries of feudal warfare.
  • 1934 – Bank robber John Dillinger (pictured), whose exploits were sensationalized across the United States, was shot dead by police in an ambush outside the Biograph Theater in Chicago.
  • 1991 – American serial killer Jeffrey Dahmer was arrested in Milwaukee, Wisconsin, after police discovered human remains in his apartment.
  • 2002 – The Israeli Defense Forces dropped a bomb on the home of Salah Shehade, the leader of the military arm of Hamas, killing him and his family.
  • More anniversaries: July 21 July 22 July 23

    It is now July 22, 2012 (UTC) – Refresh this page
    Simulated depth of field

    A 3D ray tracing of a glass molecular model, demonstrating the algorithm's ability in simulating depth of field (DOF), which is the distance between the nearest and farthest objects in a scene that appear acceptably sharp in an image. When much of the foreground and background of an image is sharp, its DOF is deep. The opposite is called shallow focus.

    Image: Purpy Pupple

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