How to Compute Pi
Pi uses the Greek symbol "π", which is the lowercase equivalent to the Cyrillic letter "p." That's pretty straightforward. But what is pi? It is the ratio of the circumference to the diameter of a circle; approximately equal to 3.14159265358979323846... Find out how to compute that number and what it represents.
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Instructions
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Know that pi is defined as the ratio of the circumference of a circle to its diameter. That means that the number 3.14159..., is in truth a number that comes from taking the length of the distance around the outside of a circle divided by a line that goes through the middle of the circle extending from one side of the circle to the other.
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Go to a website like mathforum.org (see Resources below) or buy a book like "Pi: A Biography of the World's most Mysterious Number" by Alfred Posamentier and Ingmar Lehman and read about pi's long history, how there were many efforts to compute it, and that it has some bizarre characteristics.
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Learn that there are actually people who have used measurements of circles and their diameters to arrive at the number pi. Check out a description of such an effort, made by H.G. Smythe in 1993.
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Realize that 22/7 is a rough approximation of pi, but only a rough approximation. This is easily demonstrated by carrying out division to 6 places. 22/7=3.142857...and pi=3.141592... Archimedes first offered a proof of this by proving that 22/7 is greater than the ratio of the perimeter of a circumscribed regular polygon with 96 sides to the diameter of a circle.
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Grasp that the mathematics involved in computing pi can be very laborious and that computer programs have been designed to accomplish the task. In fact, the speed at which pi can be computed is sometimes used as an estimation of a computer's power. Check out one of the programs that does the mathematics.
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Be aware that pi has a huge number of everyday uses including basic geometry used in engineering, any process that uses sine waves since the fundamental period of a sign wave is 2*pi, in probability since Gaussian distribution has pi in its formula, in navigation since long flights are actually an arc and pi must be used in computing it, and even in computer games to simulate "white noise" variation.
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