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  1. 2009.06.23 [펌] pi 계산의 역사

원문 링크 : [펌] pi 계산의 역사


Table of computation of Pi from 2000 BC to 1900 AD

Name Year Length Value
Babylonians 2000? BCE 1 3.125 = 3 + 1/8
Egyptians 2000? BCE 1 3.16045
China 1200? BCE 1 3
Bible (1 Kings 7:23)  550? BCE 1 3
Archimedes  250? BCE 3 3.1418 (ave.)
Hon Han Shu  130 AD 1 3.1622 = sqrt(10) ?
Ptolemy  150 3 3.14166
Chung Hing  250? 1 3.16227 = sqrt(10)
Wang Fau  250? 1 3.15555 = 142/45
Liu Hui  263 5 3.14159
Siddhanta  380 3 3.1416
Tsu Ch'ung Chi  480? 7 3.1415926
Aryabhata  499 4 3.14156
Brahmagupta  640? 1 3.162277 = sqrt(10)
Al-Khowarizmi  800 4 3.1416
Fibonacci 1220 3 3.141818
Al-Kashi 1429 14
Otho 1573 6 3.1415929
Viete 1593 9 3.1415926536 (ave.)
Romanus 1593 15
Van Ceulen 1596 20
Van Ceulen 1615 35
Newton 1665 16
Sharp 1699 71
Seki 1700? 10
Kamata 1730? 25
Machin 1706 100
De Lagny 1719 127 (112 correct)
Takebe 1723 41
Matsunaga 1739 50
Vega 1794 140
Rutherford 1824 208 (152 correct)
Strassnitzky and Dase 1844 200
Clausen 1847 248
Lehmann 1853 261
Rutherford 1853 440
Shanks 1874 707 (527 correct)

Brief history of Pi calculation with computers

Name Year Calculated
length
Machine used
G.W. Reitwiesner etc. 1949 2,037 ENIAC
S.C. Nicholson & J. Jeenel 1954 3,092 NORC
G.E. Felton 1957 7,480 Pegasus
F. Genuys 1958 10,000 IBM 704
G.E. Felton 1958 10,020 Pegasus
J. Guilloud 1959 16,167 IBM 704
W. Shanks & T.W. Wrench Jr. 1961 100,265 IBM 7090
J. Guilloud & J. Filliatre 1966 250,000 IBM 7030
J. Guilloud & M. Dichampt 1967 500,000 CDC 6600
J. Guilloud & M. Bouyer 1973 1,001,250 CDC 7600
K. Miyoshi & Y. Kanada 1981 2,000,036 FACOM M-200
J. Guilloud 1981-82 2,000,050 not known
Y. Tamura 1982 2,097,144 MELCOM 900II
Y. Tamura & Kanada 1982 4,194,288 HITAC M-280H
Y. Tamura & Kanada 1982 8,388,576 HITAC M-280H
Y. Kanada, S. Yoshino & Y. Tamura 1983 16,777,206 HITAC M-280H
Y. Ushiro & Y. Kanada 1983/10 (*)10,013,395 HITAC S-810/20
W. Gosper 1985/10 17,526,200 Symbolics 3670
D.H. Bailey 1986/01 29,360,111 CRAY-2
Y. Kanada & Y. Tamura 1986/09 33,554,414 HITAC S-810/20
Y. Kanada & Y. Tamura 1986/10 67,108,839 HITAC S-810/20
Y. Kanada, Y. Tamura, Y. Kubo, etc. 1987/01 134,214,700 NEC SX-2
Y. Kanada & Y. Tamura 1988/01 204,326,551 HITAC S-820/80
G.V. Chudnovsky & D.V. Chudnovsky 1989/05 480,000,000 CRAY-2 & IBM-3090/VF
G.V. Chudnovsky & D.V. Chudnovsky 1989/06 535,339,270 IBM 3090
Y. Kanada & Y. Tamura 1989/07 536,870,898 HITAC S-820/80
G.V. Chudnovsky & D.V. Chudnovsky 1989/08 1,011,196,691 IBM 3090
Y. Kanada & Y. Tamura 1989/11 1,073,740,799 HITAC S-820/80
G.V. Chudnovsky & D.V. Chudnovsky 1991/08 2,260,000,000 Home made parallel computer
(detail unknown. not verified.)
D. Takahashi & Y. Kanada 1995/06 3,221,220,000 HITAC S-3800/480(uses 2 CPU)
G.V. Chudnovsky & D.V. Chudnovsky 1994/05 4,044,000,000 New home made parallel computer
(detail unknown. not verified.)
D. Takahashi & Y. Kanada 1995/08 4,294,960,000 HITAC S-3800/480(uses 2 CPU)
D. Takahashi & Y. Kanada 1995/09 6,442,450,000 HITAC S-3800/480(uses 2 CPU)
D. Takahashi & Y. Kanada 1997/06 51,539,600,000 HITACHI SR2201 Computer Centre,
U. of Tokyo, 1024 Processors
D. Takahashi & Y. Kanada 1999/04 68,719,470,000 HITACHI SR8000 Computer Centre,
U. of Tokyo, 64 of 128 CPUs
D. Takahashi & Y. Kanada 1999/09 206,158,430,000 HITACHI SR8000 Computer Centre,
U. of Tokyo, 128 CPUs
Yasumasa Kanada & 9 man team 2002/09 1.2411 trillion HITACHI supercompute,
Information Technology Center, U. of Tokyo
(*) First pi record calculated with supercomputer. (for the reference.)
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