Pi charts


Here are some of the records in the calculation of pi over the centuries:

NAME YEAR NUMBER OF DECIMAL PLACES
Al-Kashi 1429 16
Ludolph van Ceulen 1610 35
Sharp 1699 71
Machin 1706 100
Johann Dase 1844 200
Ferguson and Wrench 1948 808
ENIAC 1949 2,037
Guilloud and Bouyer 1973 1,000,000
Chudnovsky brothers 1989 1,011,196,691
Yasumasa Kanada 1989 1,073,740,000
Chudnovsky brothers 1991 2,160,000,000
Yasumasa Kanada 1995 3,221,220,000

Yasumasa Kanada, at the University of Tokyo, found the new record number of digits between 16 and 26 June 1995. He used two methods to check himself: Borwein's quartic convergent algorithm and the Gauss-Legendre algorithm.

Chudnovsky brothers 1996 over 8 billion!!!

Find out more about the Chudnovsky brothers here


Comparison of "Time Per Digit" in certain calculations of pi!

Year Computer Time # of digits Time per digit
1873 Wm. Shanks (by hand) Shanks calculated those decimals by the Machin's formula (1706): pi/4 = 4artg(1/5) - artg(1/239) and used the artg power-serie of Gregory-Leibniz. ca. 22 yrs. 707 (only 527 were correct-(Proceedings of The Royal Society of London, Vol. XXI., p.319) 1 week!
1844 Johann Dase (by hand) < 2 months 200 7 hrs.
1947 D. F. Ferguson, desk calculator ca. 1 yrs. 808 11 hrs.
1949 U.S. Army, ENIAC 70 hrs. 2,037 2 min.
1954 S. C. Nicholson, J. Jeenel, NORC 13 min. 3089 0.25 sec.
1958 F. Genuys, IBM 704 100 min. 10,000 0.6 sec.
1961 D. Shanks, J. W. Wrench, IBM 7090 8.72 hrs. 100,200 1/3 sec.
1973 J. Guilloud, CDC 7600 23.3 hrs. 1,000,000 1/12 sec.
1983 Y. Tamura, Y. Kanada, HITAC M-28OH < 30 hrs. 16,000,000 < 0.0065 sec.
1986 D. H. Bailey, NASA, Cray-2 28 hrs. > 29,360,000 < 0.00035 sec.
1986 Y. Kanada, Hitachi S-810/820 8 hrs. > 33,554,000 < 0.00086 sec.
1988 Y. Kanada, Hitachi S-820 6 hrs. 201,326,000 < 0.00011 sec.


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