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Pi is the ratio of the circumference of a circle to its diameter.  This ratio has been useful not only for computation of circumference of circles, but in many other geometric and mathematical computations.  These include areas of circles and ellipse, as well as volumes of spheres and ellipsoids.

Approximation of pi has began as early as the ancient times.  One of the well-known one was by the great Greek mathematician Archimedes, who started approximating Pi by inscribing a hexagon into a circle.  With the hexagon, pi was calculated to have a value of 3. Doubling the number of sides and inscribing a dodecagon in the same circle, his new value became closer to pi. He continued until he used a 96-gon, and found a better approximation of 3.1419.  A Chinese mathematician Lui Hui took Archemedes' method farther.  He used a 3,072-gon and approximated pi to have a value of 3.1416, a very good approximation.

The value of Pi to the 20th decimal place is

                      3.14159 26535 89793 23846


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