History of Pi
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The mathematical constant π = 3.14159... has been subject to extensive study since ancient history.
History of Pi
The symbol "π" for Archimedes' constant was first introduced in 1706 by William Jones when he published A New Introduction to Mathematics, although the same symbol had been used earlier to indicate the circumference of a circle. The notation became standard after it was adopted by Leonhard Euler. In either case, 'π' is the first letter of περιμετρος (perimetros), meaning 'measure around' in Greek.
Here is a brief chronology of π:
| Date | Who | Value of π (world records in bold) |
|---|---|---|
| 20th century BC | Babylonians | 25/8 = 3.125 |
| 20th century BC | Egyptian Rhind Mathematical Papyrus | (16/9)² = 3.160493... |
| 12th century BC | Chinese | 3 |
| 434 BC | Anaxagoras tried to square the circle with straightedge and compass | |
| c. 250 BC | Archimedes | 223/71 < π < 22/7 (3.140845... < π < 3.142857...) 211875/67441 = 3.14163... |
| 20 BC | Vitruvius | 25/8 = 3.125 |
| 130 | Chang Hong | √10 = 3.162277... |
| 150 | Ptolemy | 377/120 = 3.141666... |
| 250 | Wang Fau | 142/45 = 3.155555... |
| 263 | Liu Hui | 3.14159 |
| 480 | Zu Chongzhi | 3.1415926 < π < 3.1415927 |
| 499 | Aryabhatta | 62832/20000 = 3.1416 |
| 598 | Brahmagupta | √10 = 3.162277... |
| 800 | Al Khwarizmi | 3.1416 |
| 12th Century | Bhaskara | 3.14156 |
| 1220 | Fibonacci | 3.141818 |
| 1400 | Madhava | 3.14159265359 |
| All records from 1424 onwards are given as the number of correct decimal places (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 | De Lagny calculated 127 decimal places, but not all were correct | 112 dps |
| 1723 | Takebe | 41 dps |
| 1734 | Leonhard Euler adopted the Greek letter 'π' and assured its popularity | |
| 1739 | Matsunaga | 50 dps |
| 1761 | Johann Heinrich Lambert proved that π is irrational | |
| 1775 | Euler pointed out the possibility that π might be transcendental | |
| 1789 | 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 | Rutherford calculated 208 decimal places, but not all were correct | 152 dps |
| 1844 | Zacharias Dase and Strassnitzky | 200 dps |
| 1847 | Thomas Clausen | 248 dps |
| 1853 | Lehmann | 261 dps |
| 1853 | Rutherford | 440 dps |
| 1853 | William Shanks | 527 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. | |
| 1946 | D. F. Ferguson (using a desk calculator) | 620 dps |
| 1947 | 710 dps | |
| 1947 | 808 dps | |
| 1949 | Ferguson and John W. Wrench, using a desk calculator | 1120 dps |
| All records from 1949 onwards were calculated with electronic computers. | ||
| 1949 | J. 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 | Mahler showed that π is not a Liouville number | |
| 1954 | Jeenel Nicholson, using the NORC (it took 13 minutes) | 3,089 dps |
| 1957 | Felton, using the Ferranti Pegasus computer (London) | 7,480 dps |
| 1958 | Genuys, using an IBM 704 (1.7 hours) | 10,000 dps |
| 1958 | Felton, using the Pegasus computer (London) (33 hours) | 10,021 dps |
| 1959 | Guilloud, 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) | 100,000 dps |
| 1966 | J. Guilloud and J. Filliatre, using the IBM 7030 (Paris) (taking 28 hours??) | 250,000 dps |
| 1967 | Guilloud and Dichampt, using the CDC 6600 (Paris) (28 hours) | 500,000 dps |
| 1974 | Guilloud and Bouyer, using the CDC 7600 | 1,000,000 dps |
| 1992 | 2,180,000,000 dps | |
| 1995 | Yasumasa Kanada | > 6,000,000,000 dps |
| 1997 | Kanada and Takahashi | > 51,500,000,000 dps |
| 1999 | > 206,000,000,000 dps | |
| 2002 | Kanada and team | > 1,240,000,000,000 dps |
| 2003 | > 1,241,100,000,000 dps | |
References and links
- A History of Pi, by Petr Beckmann
- Records in the calculation of pi (http://www-groups.dcs.st-and.ac.uk/~history/HistTopics/Pi_chronology.html)