Development of the Accuracy of Pi in Different Cultures over Time (original) (raw)

The accuracy of the constant pi, which is the ratio of the perimeter over the diameter, developed in different cultures over time. This constant was investigated in these cultures from 1650 BC to 2000 AD and the early estimations of pi were merely based on its measurement. Mathematical approaches to estimate the value of pi came much later with Egyptians, Europeans, Greeks, Chinese, and Arabs. One of the first mathematicians to provide a scientific method for calculating pi to a certain degree of accuracy was Archimedes of Syracuse. He estimated the value of pi using the areas and the semi-perimeters of two inscribed and the circumscribed regular polygons. The most progress was made fastest in cultures that used the decimal system and in cultures that used the hexadecimal systems such as the Chinese and the Arabs. Not much progress was made in Europe where the Roman numerals were used which delayed the development. In 1665 Isaac Newton from England estimated a value for pi by finding the area under the curve of a semicircle using integral calculus and a broader binomial theorem that he developed during the Great Plague Years. A French mathematician George Louis Leclerc used probability to approximate the value of pi by randomly throwing a needle several times on a flat surface with parallel lines drawn on the surface and counting the number of times that the needle cut the lines. A Swiss mathematician Johann Heinrich Lambert established the irrationality of in 1767, which indicated that the decimals of pi are not periodic. However, the irrationality of pi can also be demonstrated using statistics and goodness-to-fit test. Unnecessary digits of pi were calculated in order to hold the record for the most accurate pi value. With the arrival of computers the accuracy of pi in technologically advanced cultures was boosted to thousands of digits and became a way to test technological capabilities of computers. Consequently, cultures with advance mathematical tools have developed the most in calculating the value of pi.