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It was used in the world record calculations of 2.7 trillion digits of π in December 2009, [3] 10 trillion digits in October 2011, [4] [5] 22.4 trillion digits in November 2016, [6] 31.4 trillion digits in September 2018–January 2019, [7] 50 trillion digits on January 29, 2020, [8] 62.8 trillion digits on August 14, 2021, [9] 100 trillion ...
The Bailey–Borwein–Plouffe formula (BBP formula) is a formula for π. It was discovered in 1995 by Simon Plouffe and is named after the authors of the article in which it was published, David H. Bailey, Peter Borwein, and Plouffe. [1] Before that, it had been published by Plouffe on his own site. [2] The formula is:
The number π (/ p aɪ / ⓘ; spelled out as "pi") is a mathematical constant, approximately equal to 3.14159, that is the ratio of a circle's circumference to its diameter.It appears in many formulae across mathematics and physics, and some of these formulae are commonly used for defining π, to avoid relying on the definition of the length of a curve.
The digits of pi extend into infinity, and pi is itself an irrational number, meaning it can’t be truly represented by an integer fraction (the one we often learn in school, 22/7, is not very ...
The 2002 record for digits of π, 1,241,100,000,000, was obtained by Yasumasa Kanada of Tokyo University. The calculation was performed on a 64-node Hitachi supercomputer with 1 terabyte of main memory, performing 2 trillion operations per second.
Machin's particular formula was used well into the computer era for calculating record numbers of digits of π, [39] but more recently other similar formulae have been used as well. For instance, Shanks and his team used the following Machin-like formula in 1961 to compute the first 100,000 digits of π : [ 39 ]
where C is the circumference of a circle, d is the diameter, and r is the radius.More generally, = where L and w are, respectively, the perimeter and the width of any curve of constant width.
The first belongs to a family of formulas which were rigorously proven by the Chudnovsky brothers in 1989 [11] and later used to calculate 10 trillion digits of π in 2011. [12] The second formula, and the ones for higher levels, was established by H.H. Chan and S. Cooper in 2012. [3]