In modern times, however, with the advent of computers, the emphasis has shifted to the speed at which the value of Pi can be determined together with increasing the number of decimal places. This paper traces the history of Pi and the efforts made by mathematicians and astronomers to get closer and closer to the “precise” value of π, and then discusses two methods for determining the value of Pi – one ancient method and one modern method.
The very first attempts to determine the value of π date back to around 2000 B.C., when the Babylonians and Egyptians approached the problem in their own ways. While the Babylonians obtained the value of 3+1/8, the Egyptians obtained the value as (4/3) ^4 for π. About the same time, Indians used the value of square root of 10 for Pi. All these values were based, essentially, on measurement of circumferences and diameters of circles of different sizes (Beckmann, 12-15 and 98-106). The first major step towards determining the value of Pi is attributed to the great Greek mathematician and physicist, Archimedes around 250 B.C. The ancient Greeks, with their penchant for precision, were interested in precise mathematical proportions in their architecture, music and other art forms, and hence were curious about better precision in determining the value of Pi. Thus Archimedes developed a method using inscribed and circumscribed polygons for calculating better and better approximations to the value of π and came to the conclusion:
Subsequently, around 150 A.D., the Egyptian mathematician Ptolemy (of Alexandria) gave the value of 377/120, and around 500 A.D., the Chinese Tsu-Ch’ung-Chi gave Pi the value of 355/113. Many others like Ptolemy and Tsu-Ch’ung-Chi continued to use Archimedes’s method to calculate the vale of Pi to better approximations. Ludolph von Ceulen used this method with a 2^62-sided polygon to calculate Pi to 35 decimal