Pre computer calculations of π

3

088

3

2

2

Circles are to one another as the squares on their diameters.

Computer calculations of π

Mathematician Date Places Type of computer Ferguson Jan 1947 710 Desk calculator Ferguson, Wrench Sept 1947 808 Desk calculator Smith, Wrench 1949 1120 Desk calculator Reitwiesner et al. 1949 2037 ENIAC Nicholson, Jeenel 1954 3092 NORAC Felton 1957 7480 PEGASUS Genuys Jan 1958 10000 IBM 704 Felton May 1958 10021 PEGASUS Guilloud 1959 16167 IBM 704 Shanks, Wrench 1961 100265 IBM 7090 Guilloud, Filliatre 1966 250000 IBM 7030 Guilloud, Dichampt 1967 500000 CDC 6600 Guilloud, Bouyer 1973 1001250 CDC 7600 Miyoshi, Kanada 1981 2000036 FACOM M- 200 Guilloud 1982 2000050 Tamura 1982 2097144 MELCOM 900 II Tamura, Kanada 1982 4194288 HITACHI M- 280 H Tamura, Kanada 1982 8388576 HITACHI M- 280 H Kanada, Yoshino, Tamura 1982 16777206 HITACHI M- 280 H Ushiro, Kanada Oct 1983 10013395 HITACHI S- 810 / 20 Gosper Oct 1985 17526200 SYMBOLICS 3670 Bailey Jan 1986 29360111 CRAY- 2 Kanada, Tamura Sept 1986 33554414 HITACHI S- 810 / 20 Kanada, Tamura Oct 1986 67108839 HITACHI S- 810 / 20 Kanada, Tamura, Kubo Jan 1987 134217700 NEC SX- 2 Kanada, Tamura Jan 1988 201326551 HITACHI S- 820 / 80 Chudnovskys May 1989 480000000 Chudnovskys June 1989 525229270 Kanada, Tamura July 1989 536870898 Chudnovskys Aug 1989 1011196691 Kanada, Tamura Nov 1989 1073741799 Chudnovskys Aug 1991 2260000000 Chudnovskys May 1994 4044000000 Kanada, Tamura June 1995 3221225466 Kanada Aug 1995 4294967286 Kanada Oct 1995 6442450938 Kanada, Takahashi Aug 1997 51539600000 HITACHI SR 2201 Kanada, Takahashi Sept 1999 206158430000 HITACHI SR 8000

1996

n n n

n − 1 n - 1 n − 1

n n n

1997

. In early work it was not known that the ratio of the area of a circle to the square of its radius and the ratio of the circumference to the diameter are the same. Some early texts use different approximations for these two "different" constants. For example, in the Indian text thethe ratio for the area is given aswhile the ratio for the circumference is given as Euclid gives in thePropositionHe makes no attempt to calculate the ratio.. Calculating π to many decimal places was used as a test for new computers in the early days.. There is an algorithm by Bailey, Borwein and Plouffe, published in, which allows theth hexadecimal digit of π to be computed without the preceedingdigits.. Plouffe discovered a new algorithm to compute theth digit of π in any base in