Chronology of computation of π
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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) |
|---|---|---|
| 20th century BC | Egyptian Rhind Mathematical Papyrus | (16/9)² = 3.160493... |
| 19th century BC | Babylonians | 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 |
| 130 | Chang 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 (dps). | ||
| 1400 | Madhava of Sangamagrama discovered the infinite power series expansion of π | 11 dps 13 dps |
| 1424 | Jamshid Masud Al Kashi | 16 dps |
| 1573 | Valenthus Otho | 6 dps |
| 1593 | François Viète | 9 dps |
| 1593 | Adriaen van Roomen | 15 dps |
| 1596 | Ludolph van Ceulen | 20 dps |
| 1615 | 32 dps | |
| 1621 | Willebrord Snell (Snellius), a pupil of Van Ceulen | 35 dps |
| 1665 | Isaac Newton | 16 dps |
| 1699 | Abraham Sharp | 71 dps |
| 1700 | Seki Kowa | 10 dps |
| 1706 | John Machin | 100 dps |
| 1706 | William Jones introduced the Greek letter 'π' | |
| 1730 | Kamata | 25 dps |
| 1719 | Thomas Fantet de Lagny calculated 127 decimal places, but not all were correct | 112 dps |
| 1723 | Takebe | 41 dps |
| 1739 | Matsunaga Ryohitsu | 50 dps |
| 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 dps |
| 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 dps |
| 1844 | Zacharias Dase and Strassnitzky calculated 205 decimal places, but not all were correct | 200 dps |
| 1847 | Thomas Clausen calculated 250 decimal places, but not all were correct | 248 dps |
| 1853 | Lehmann | 261 dps |
| 1853 | William Rutherford | 440 dps |
| 1855 | Richter | 500 dps |
| 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 dps |
| 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. More detail can be found at http://www.cs.uu.nl/wais/html/na-dir/sci-math-faq/indianabill.html. | |
| 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 dps |
| 1947 | Ivan Niven gave a very elementary proof that π is irrational | |
| January 1947 | D. F. Ferguson (using a desk calculator) | 710 dps |
| September 1947 | D. F. Ferguson (using a desk calculator) | 808 dps |
| 1949 | D. F. Ferguson and John W. Wrench, using a desk calculator | 1,120 dps |
| 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 dps |
| 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 dps |
| 1957 | G. E. Felton, using the Ferranti Pegasus computer (London) | 7,480 dps |
| January 1958 | Francois Genuys, using an IBM 704 (1.7 hours) | 10,000 dps |
| May 1958 | G. E. Felton, using the Pegasus computer (London) (33 hours) | 10,020 dps |
| 1959 | Francois Genuys, using the IBM 704 (Paris) (4.3 hours) | 16,167 dps |
| 1961 | IBM 7090 (London) (39 minutes) | 20,000 dps |
| 1961 | Daniel Shanks and John W. Wrench, using the IBM 7090 (New York) (8.7 hours) | 100,265 dps |
| 1966 | Jean Guilloud and J. Filliatre, using the IBM 7030 (Paris) (taking 28 hours??) | 250,000 dps |
| 1967 | Jean Guilloud and M. Dichampt, using the CDC 6600 (Paris) (28 hours) | 500,000 dps |
| 1973 | Jean Guilloud and M. Bouyer, using the CDC 7600 | 1,001,250 dps |
| 1981 | Yasumasa Kanada and Kazunori Miyoshi, FACOM M-200 | 2,000,036 dps |
| 1981 | Jean Guilloud, Not known | 2,000,050 dps |
| 1982 | Yoshiaki Tamura, MELCOM 900II | 2,097,144 dps |
| 1982 | Yasumasa Kanada, Yoshiaki Tamura, HITAC M-280H | 4,194,288 dps |
| 1982 | Yasumasa Kanada, Yoshiaki Tamura, HITAC M-280H | 8,388,576 dps |
| 1983 | Yasumasa Kanada, Yoshiaki Tamura, S. Yoshino, HITAC M-280H | 16,777,206 dps |
| October 1983 | Yasumasa Kanada and Yasunori Ushiro, HITAC S-810/20 | 10,013,395 dps |
| October 1985 | William Gosper, Symbolics 3670 | 17,526,200 dps |
| January 1986 | David H. Bailey, CRAY-2 | 29,360,111 dps |
| September 1986 | Yasumasa Kanada, Yoshiaki Tamura, HITAC S-810/20 | 33,554,414 dps |
| October 1986 | Yasumasa Kanada, Yoshiaki Tamura, HITAC S-810/20 | 67,108,839 dps |
| January 1987 | Yasumasa Kanada, Yoshiaki Tamura, Yoshinobu Kubo, NEC SX-2 | 134,214,700 dps |
| January 1988 | Yasumasa Kanada and Yoshiaki Tamura, HITAC S-820/80 | 201,326,551 dps |
| May 1989 | Gregory V. Chudnovsky & David V. Chudnovsky, CRAY-2 & IBM 3090/VF | 480,000,000 dps |
| June 1989 | Gregory V. Chudnovsky & David V. Chudnovsky, IBM 3090 | 535,339,270 dps |
| July 1989 | Yasumasa Kanada and Yoshiaki Tamura, HITAC S-820/80 | 536,870,898 dps |
| August 1989 | Gregory V. Chudnovsky & David V. Chudnovsky, IBM 3090 | 1,011,196,691 dps |
| November 1989 | Yasumasa Kanada and Yoshiaki Tamura, HITAC S-820/80 | 1,073,740,799 dps |
| August 1991 | Gregory V. Chudnovsky & David V. Chudnovsky, Home made parallel computer (details unknown, not verified) | 2,260,000,000 dps |
| May 1994 | Gregory V. Chudnovsky & David V. Chudnovsky, New home made parallel computer (details unknown, not verified) | 4,044,000,000 dps |
| June 1995 | Yasumasa Kanada and Daisuke Takahashi (mathematician), HITAC S-3800/480 (dual CPU) | 3,221,220,000 dps |
| August 1995 | Yasumasa Kanada and Daisuke Takahashi (mathematician), HITAC S-3800/480 (dual CPU) | 4,294,960,000 dps |
| September 1995 | Yasumasa Kanada and Daisuke Takahashi (mathematician), HITAC S-3800/480 (dual CPU) | 6,442,450,000 dps |
| June 1997 | Yasumasa Kanada and Daisuke Takahashi (mathematician), HITACHI SR2201 (1024 CPU) | 51,539,600,000 dps |
| April 1999 | Yasumasa Kanada and Daisuke Takahashi (mathematician), HITACHI SR8000 (64 of 128 nodes) | 68,719,470,000 dps |
| September 1999 | Yasumasa Kanada and Daisuke Takahashi (mathematician), HITACHI SR8000/MPP (128 nodes) | 206,158,430,000 dps |
| September 2002 | Yasumasa Kanada & 9 man team, HITACHI SR8000/MPP (64 nodes), 600 hours | 1,241,100,000,000 dps |
