Search results
Results from the WOW.Com Content Network
The Chudnovsky algorithm is a fast method for calculating the digits of π, based on Ramanujan's π formulae. Published by the Chudnovsky brothers in 1988, [ 1 ] it was used to calculate π to a billion decimal places.
The Gauss–Legendre algorithm is an algorithm to compute the digits of π. It is notable for being rapidly convergent, with only 25 iterations producing 45 million correct digits of π . However, it has some drawbacks (for example, it is computer memory -intensive) and therefore all record-breaking calculations for many years have used other ...
This category presents articles pertaining to the calculation of Pi to arbitrary precision. Pages in category "Pi algorithms"
Liu Hui's method of calculating the area of a circle. Liu Hui's π algorithm was invented by Liu Hui (fl. 3rd century), a mathematician of the state of Cao Wei.Before his time, the ratio of the circumference of a circle to its diameter was often taken experimentally as three in China, while Zhang Heng (78–139) rendered it as 3.1724 (from the proportion of the celestial circle to the diameter ...
This algorithm computes π without requiring custom data types having thousands or even millions of digits. The method calculates the nth digit without calculating the first n − 1 digits and can use small, efficient data types. Fabrice Bellard found a variant of BBP, Bellard's formula, which is faster.
The Bailey–Borwein–Plouffe formula (BBP) for calculating π was discovered in 1995 by Simon Plouffe. Using base 16 math, the formula can compute any particular digit of π —returning the hexadecimal value of the digit—without having to compute the intervening digits (digit extraction). [95]
The first recorded algorithm for rigorously calculating the value of π was a geometrical approach using polygons, devised around 250 BC by the Greek mathematician Archimedes, implementing the method of exhaustion. [48] This polygonal algorithm dominated for over 1,000 years, and as a result π is sometimes referred to as Archimedes's constant ...
Since the 1980s, his series have become the basis for the fastest algorithms currently used by Yasumasa Kanada and the Chudnovsky brothers to compute π. 1946 D. F. Ferguson: Made use of a desk calculator [24] 620: 1947 Ivan Niven: Gave a very elementary proof that π is irrational: January 1947 D. F. Ferguson: Made use of a desk calculator [24 ...