The History of π (cont.)
While π activity stagnated in Europe, the situation in other parts of the world was quite different. The Mayan civilization, situated on the Yucatan Peninsula in Central America, was quite advanced for its time. The Mayans were top-notch astronomers, developing a very accurate calendar. In order to do this, it would have been necessary for them to have a fairly good value for π. Though no one knows for sure (nearly all Mayan literature was burned during the Spanish conquest of Mexico), most historians agree that the Mayan value was indeed more accurate than that of the Europeans. The Chinese in the 5th century calculated π to an accuracy not surpassed by Europe until the 1500's. The Chinese, as well as the Hindus, arrived at π in roughly the same method as the Europeans until well into the Renaissance, when Europe finally began to pull ahead.
During the Renaissance period, π activity in Europe began to finally get moving again. Two factors fueled this acceleration: the increasing importance of mathematics for use in navigation, and the infiltration of Arabic numerals, including the zero (indirectly introduced from India) and decimal notation (yes, the great mathematicians of antiquity made all of their discoveries without our standard digits of 0-9!). Leonardo Da Vinci and Nicolas Copernicus made minimal contributions to the π endeavor, but François Viète actually made significant improvements to Archimedes' methods. The efforts of Snellius, Gregory, and John Machin eventually culminated in algebraic formulas for π that allowed rapid calculation, leading to ever more accurate values of π during this period.
In the 1700's the invention of calculus by Sir Isaac Newton and Leibniz rapidly accelerated the calculation and theorization of π. Using advanced mathematics, Leonhard Euler found a formula for π that is the fastest to date. In the late 1700's Lambert (Swiss) and Legendre (French) independently proved that π is irrational. Although Legendre predicted that π is also transcendental, this was not proven until 1882 when Lindemann published a thirteen-page paper proving the validity of Legendre's statement. Also in the 18th century, George Louis Leclerc, Comte de Buffon, discovered an experimental method for calculating π. Pierre Simon Laplace, one of the founders of probability theory, followed up on this in the next century. Click here to learn more about Buffon's and Laplace's method.
Starting in 1949 with the ENIAC computer, digital systems have been calculating π to incredible accuracy throughout the second half of the twentieth century. Whereas ENIAC was able to calculate 2,037 digits, the record as of the date of this article is 206,158,430,000 digits, calculated by researchers at the University of Tokyo. It is highly probable that this record will be broken, and there is little chance that the search for ever more accurate values of π will ever come to an end.