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It produces about 14 digits of π per term [130] and has been used for several record-setting π calculations, including the first to surpass 1 billion (10 9) digits in 1989 by the Chudnovsky brothers, 10 trillion (10 13) digits in 2011 by Alexander Yee and Shigeru Kondo, [131] and 100 trillion digits by Emma Haruka Iwao in 2022. [132]
As of July 2024, π has been calculated to 202 trillion decimal digits. The last 100 decimal digits of the latest world record computation are: [1] Graph showing how the record precision of numerical approximations to pi measured in decimal places (depicted on a logarithmic scale), evolved in human history.
It can compute one million digits in 40 minutes, two million digits in 90 minutes and four million digits in 220 minutes on a Pentium 90 MHz. Super PI version 1.9 is available from Super PI 1.9 page .
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 ...
Chudnovsky algorithm. 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. [ 2]
Bailey–Borwein–Plouffe formula. 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]
For example, German mathematician Ludolph van Ceulen of the 16th century spent a major part of his life calculating the first 35 digits of pi. [21] Using computers and supercomputers , some of the mathematical constants, including π, e , and the square root of 2, have been computed to more than one hundred billion digits.
In 1995, the Borweins collaborated with Yasumasa Kanada of the University of Tokyo to compute π to more than four billion digits.. Borwein has developed an algorithm that applies Chebyshev polynomials to the Dirichlet eta function to produce a very rapidly convergent series suitable for high precision numerical calculations, which he published on the occasion of the awarding of an honorary ...