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. |