Pi History  Pi and the Computer 
The Illustrated History of Pi 



Pi and the Computer 





Following John Von Neumann's use of ENIAC, the first general purpose electronic digital computer, to compute 2037 digits of Pi in 1949, new records involving the computer calculation of thousands, and then millions of additional digits of pi were set  only to be broken again. 



What made this possible was not simply greater computer horsepower, but better, faster, more advanced, and more elegant methods of computing pi  many of them based on ideas developed long ago, as if they were waiting for the advent of the computer. 



As has already been noted, the early 20th century work by Indian mathematician Srinivasa Ramanujan was the source of ideas that proved valuable more than halfacentury later when William Gosper undertook the thenrecord multimillion digit computed value of pi, and again when the Chudnovsky borthers Greg and David broke those records. 



In the 1960's work with fast Fourier transforms (FFT's), algorithms which enable computers to perform rapid arithmetic on extremely large numbers, enabled even greater numbers of the digits of pi to be calculated. 



In 1976 mathematician Eugene Salamin built an even more accurate and less computationally intensive method for computer calculation of pi  building on work and ideas set down centuries earlier by noted German mathematician Carl Friedrich Gauss (1777  1855) and French mathematician AdrienMarie Legendre (1752  1833). 




Some of the milestones in computer calculation of the digits of pi, following the first calculations by ENIAC and NORC: 





1,000,000 digits
(one million digits) 
1973 
computer calculation performed by Jean Guillord and Marine Bouyer (using a CDC7600 computer) 





1,011,196,691 digits
(one billion + digits) 
1989 
computer calculation performed by the brothers David and Gregory Chudnovsky 





1,073,740,000 
1989 
computer calculation performed by Yasumasa Kanada 





2,160,000,000 
1991 
computer calculation performed by the brothers David and Gregory Chudnovsky 





3,221,200,000 
1995 
computer calculation performed by Yasumasa Kanada 







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