Pi. Pi, Greek letter (p) used in mathematics as the symbol
Publié le 12/05/2013
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Pi. Pi, Greek letter (p) used in mathematics as the symbol for the ratio of the circumference of a circle to its diameter. This ratio is a universal constant, meaning that it is always the same for any size circle. Many important mathematical and physical equations contain pi. Finding the area of a circle (A = pr2 where r is the circle's radius) or the volume of a sphere (V = ? pr3), for instance, both require knowledge of the value of pi. The approximate value of pi to eight decimal places is 3.14159265. The ratio is actually an irrational number, meaning that its decimal places go on infinitely without repeating or ending in zeros. Mathematicians have found many unending equations with solutions equal to pi; one of the simplest is p = 4(1 - ?+ ?- ?+ ?...). Computers can use such equations to quickly estimate pi with great accuracy; in this way the value of p has been figured to more than 1.2 trillion (1,200,000,000,000) decimal places. The ratio pi was known in ancient times, and various approximations of its numerical value were used. In the Bible, the value of pi was taken to be 3. The Greek mathematician Archimedes correctly asserted that the value was between 3 10/70 and 3 10/71. The symbol p for the ratio was first used in 1706 by the Welsh mathematician William Jones, but it became popular only after its adoption by the Swiss mathematician Leonhard Euler in 1737. In 1882 the German mathematician Ferdinand Lindemann proved that p is a transcendental number--that is, it is not the root of any polynomial equation with rational coefficients (for example, ? x3 - ? x2 21x + 17 = 0). Consequently, Lindemann was able to demonstrate that it is impossible to square the circle (construct a square whose area equals that of a given circle) using algebra or a ruler and compass because the area of a square can always be expressed as a polynomial equation with rational coefficients. Contributed By: James Singer Reviewed By: J. Lennart Berggren Microsoft ® Encarta ® 2009. © 1993-2008 Microsoft Corporation. All rights reserved.
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