Chronology of computation of π: Difference between revisions
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|April 2009 |
|April 2009 |
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|[[Daisuke Takahashi (mathematician)]] et al., [[T2K Open Supercomputer]] (640 nodes), |
|[[Daisuke Takahashi (mathematician)]] et al., [[T2K Open Supercomputer]] (640 nodes), 73 hours, 36 minutes<ref>http://gizmodo.com/5339831/pi-calculation-record-destroyed-25-trillion-decimals</ref> |
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|align="right"|'''2,576,980,370,000 decimal places''' |
|align="right"|'''2,576,980,370,000 decimal places''' |
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==See also== |
==See also== |
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* [[History of pi|History of π]] |
* [[History of pi|History of π]] |
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== |
==References== |
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{{Reflist}} |
{{Reflist}} |
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==External links== |
==External links== |
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Revision as of 05:20, 16 October 2009
The table below is a brief chronology of computed numerical values of, or bounds on, the mathematical constant π. See the history of numerical approximations of π for explanations, comments and details concerning some of the calculations mentioned below.
| Date | Who | Value of π (world records in bold) |
|---|---|---|
| 26th century BC | Egyptian Proportions of Giza Great Pyramid Height to Perimeter and Meidum Pyramid | 3 + 1/7 = 3.142857... |
| 20th century BC | Egyptian Rhind Mathematical Papyrus and Moscow Mathematical Papyrus | (16/9)2 = 3.160493... |
| 19th century BC | Babylonian mathematicians | 25/8 = 3.125 |
| 9th century BC | Indian Shatapatha Brahmana | 339/108 = 3.138888... |
| 434 BC | Anaxagoras attempted to square the circle with compass and straightedge | |
| c. 250 BC | Archimedes | 223/71 < π < 22/7 (3.140845... < π < 3.142857...) |
| 20 BC | Vitruvius | 25/8 = 3.125 |
| 5 | Liu Xin | 3.154 |
| 130 | Zhang Heng | √10 = 3.162277... |
| 150 | Ptolemy | 377/120 = 3.141666... |
| 250 | Wang Fan | 142/45 = 3.155555... |
| 263 | Liu Hui | 3.141024 |
| 480 | Zu Chongzhi | 3.1415926 < π < 3.1415927 |
| 499 | Aryabhata | 62832/20000 = 3.1416 |
| 640 | Brahmagupta | √10 = 3.162277... |
| 800 | Al Khwarizmi | 3.1416 |
| 1150 | Bhaskara | 3.14156 |
| 1220 | Fibonacci | 3.141818 |
| All records from 1400 onwards are given as the number of correct decimal places. | ||
| 1400 | Madhava of Sangamagrama discovered the infinite power series expansion of π, now known as the Madhava-Leibniz series | 11 decimal places 13 decimal places |
| 1424 | Jamshīd al-Kāshī | 16 decimal places |
| 1573 | Valentinus Otho (355/113) | 6 decimal places |
| 1593 | François Viète | 9 decimal places |
| 1593 | Adriaen van Roomen | 15 decimal places |
| 1596 | Ludolph van Ceulen | 20 decimal places |
| 1615 | 32 decimal places | |
| 1621 | Willebrord Snell (Snellius), a pupil of Van Ceulen | 35 decimal places |
| 1665 | Isaac Newton | 16 decimal places |
| 1699 | Abraham Sharp | 71 decimal places |
| 1700 | Seki Kowa | 10 decimal places |
| 1706 | John Machin | 100 decimal places |
| 1706 | William Jones introduced the Greek letter 'π' | |
| 1730 | Kamata | 25 decimal places |
| 1719 | Thomas Fantet de Lagny calculated 127 decimal places, but not all were correct | 112 decimal places |
| 1723 | Takebe | 41 decimal places |
| 1739 | Matsunaga Ryohitsu | 50 decimal places |
| 1748 | Leonhard Euler used the Greek letter 'π' in his book Introductio in Analysin Infinitorum and assured its popularity. | |
| 1761 | Johann Heinrich Lambert proved that π is irrational | |
| 1775 | Euler pointed out the possibility that π might be transcendental | |
| 1794 | Jurij Vega calculated 140 decimal places, but not all are correct | 137 decimal places |
| 1794 | Adrien-Marie Legendre showed that π² (and hence π) is irrational, and mentioned the possibility that π might be transcendental. | |
| 1841 | William Rutherford calculated 208 decimal places, but not all were correct | 152 decimal places |
| 1844 | Zacharias Dase and Strassnitzky calculated 205 decimal places, but not all were correct | 200 decimal places |
| 1847 | Thomas Clausen calculated 250 decimal places, but not all were correct | 248 decimal places |
| 1853 | Lehmann | 261 decimal places |
| 1853 | William Rutherford | 440 decimal places |
| 1855 | Richter | 500 decimal places |
| 1874 | William Shanks took 15 years to calculate 707 decimal places but not all were correct (the error was found by D. F. Ferguson in 1946) | 527 decimal places |
| 1882 | Lindemann proved that π is transcendental (the Lindemann-Weierstrass theorem) | |
| 1897 | The U.S. state of Indiana came close to legislating the value of 3.2 (among others) for π. House Bill No. 246 passed unanimously. The bill stalled in the state Senate due to a suggestion of possible commercial motives involving publication of a textbook.[1] | |
| 1910 | Srinivasa Ramanujan finds several rapidly converging infinite series of π, which can compute 8 decimal places of π with each term in the series. Since the 1980s, his series have become the basis for the fastest algorithms currently used by Yasumasa Kanada and the Chudnovsky brothers to compute π. | |
| 1946 | D. F. Ferguson (using a desk calculator) | 620 decimal places |
| 1947 | Ivan Niven gave a very elementary proof that π is irrational | |
| January 1947 | D. F. Ferguson (using a desk calculator) | 710 decimal places |
| September 1947 | D. F. Ferguson (using a desk calculator) | 808 decimal places |
| 1949 | D. F. Ferguson and John Wrench, using a desk calculator | 1,120 decimal places |
| All records from 1949 onwards were calculated with electronic computers. | ||
| 1949 | John W. Wrench, Jr, and L. R. Smith were the first to use an electronic computer (the ENIAC) to calculate π (it took 70 hours) (also attributed to Reitwiesner et al.) | 2,037 decimal places |
| 1953 | Kurt Mahler showed that π is not a Liouville number | |
| 1954 | S. C. Nicholson & J. Jeenel, using the NORC (it took 13 minutes) | 3,092 decimal places |
| 1957 | G. E. Felton, using the Ferranti Pegasus computer (London) | 7,480 decimal places |
| January 1958 | Francois Genuys, using an IBM 704 (1.7 hours) | 10,000 decimal places |
| May 1958 | G. E. Felton, using the Pegasus computer (London) (33 hours) | 10,020 decimal places |
| 1959 | Francois Genuys, using the IBM 704 (Paris) (4.3 hours) | 16,167 decimal places |
| 1961 | IBM 7090 (London) (39 minutes) | 20,000 decimal places |
| 1961 | Daniel Shanks and John Wrench, using the IBM 7090 (New York) (8.7 hours) | 100,265 decimal places |
| 1966 | Jean Guilloud and J. Filliatre, using the IBM 7030 (Paris) (taking 28 hours??) | 250,000 decimal places |
| 1967 | Jean Guilloud and M. Dichampt, using the CDC 6600 (Paris) (28 hours) | 500,000 decimal places |
| 1973 | Jean Guilloud and Martin Bouyer, using the CDC 7600 | 1,001,250 decimal places |
| 1981 | Yasumasa Kanada and Kazunori Miyoshi, FACOM M-200 | 2,000,036 decimal places |
| 1981 | Jean Guilloud, Not known | 2,000,050 decimal places |
| 1982 | Yoshiaki Tamura, MELCOM 900II | 2,097,144 decimal places |
| 1982 | Yasumasa Kanada, Yoshiaki Tamura, HITAC M-280H | 4,194,288 decimal places |
| 1982 | Yasumasa Kanada, Yoshiaki Tamura, HITAC M-280H | 8,388,576 decimal places |
| 1983 | Yasumasa Kanada, Yoshiaki Tamura, S. Yoshino, HITAC M-280H | 16,777,206 decimal places |
| October 1983 | Yasumasa Kanada and Yasunori Ushiro, HITAC S-810/20 | 10,013,395 decimal places |
| October 1985 | William Gosper, Symbolics 3670 | 17,526,200 decimal places |
| January 1986 | David H. Bailey, CRAY-2 | 29,360,111 decimal places |
| September 1986 | Yasumasa Kanada, Yoshiaki Tamura, HITAC S-810/20 | 33,554,414 decimal places |
| October 1986 | Yasumasa Kanada, Yoshiaki Tamura, HITAC S-810/20 | 67,108,839 decimal places |
| January 1987 | Yasumasa Kanada, Yoshiaki Tamura, Yoshinobu Kubo, NEC SX-2 | 134,214,700 decimal places |
| January 1988 | Yasumasa Kanada and Yoshiaki Tamura, HITAC S-820/80 | 201,326,551 decimal places |
| May 1989 | Gregory V. Chudnovsky & David V. Chudnovsky, CRAY-2 & IBM 3090/VF | 480,000,000 decimal places |
| June 1989 | Gregory V. Chudnovsky & David V. Chudnovsky, IBM 3090 | 535,339,270 decimal places |
| July 1989 | Yasumasa Kanada and Yoshiaki Tamura, HITAC S-820/80 | 536,870,898 decimal places |
| August 1989 | Gregory V. Chudnovsky & David V. Chudnovsky, IBM 3090 | 1,011,196,691 decimal places |
| November 1989 | Yasumasa Kanada and Yoshiaki Tamura, HITAC S-820/80 | 1,073,740,799 decimal places |
| August 1991 | Gregory V. Chudnovsky & David V. Chudnovsky, Home made parallel computer (details unknown, not verified) | 2,260,000,000 decimal places |
| May 1994 | Gregory V. Chudnovsky & David V. Chudnovsky, New home made parallel computer (details unknown, not verified) | 4,044,000,000 decimal places |
| June 1995 | Yasumasa Kanada and Daisuke Takahashi (mathematician), HITAC S-3800/480 (dual CPU) | 3,221,220,000 decimal places |
| August 1995 | Yasumasa Kanada and Daisuke Takahashi (mathematician), HITAC S-3800/480 (dual CPU) | 4,294,960,000 decimal places |
| September 1995 | Yasumasa Kanada and Daisuke Takahashi (mathematician), HITAC S-3800/480 (dual CPU) | 6,442,450,000 decimal places |
| June 1997 | Yasumasa Kanada and Daisuke Takahashi (mathematician), HITACHI SR2201 (1024 CPU) | 51,539,600,000 decimal places |
| April 1999 | Yasumasa Kanada and Daisuke Takahashi (mathematician), HITACHI SR8000 (64 of 128 nodes) | 68,719,470,000 decimal places |
| September 1999 | Yasumasa Kanada and Daisuke Takahashi (mathematician), HITACHI SR8000/MPP (128 nodes) | 206,158,430,000 decimal places |
| December 2002 | Yasumasa Kanada & 9 man team, HITACHI SR8000/MPP (64 nodes), 600 hours | 1,241,100,000,000 decimal places |
| April 2009 | Daisuke Takahashi (mathematician) et al., T2K Open Supercomputer (640 nodes), 73 hours, 36 minutes[2] | 2,576,980,370,000 decimal places |
See also
References
- ^ Lopez-Ortiz, Alex (February 20, 1998). "Indiana Bill sets value of Pi to 3". the news.answers WWW archive. Department of Information and Computing Sciences, Utrecht University. Retrieved 2009-02-01.
- ^ http://gizmodo.com/5339831/pi-calculation-record-destroyed-25-trillion-decimals