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Користувач:Kusluj/Temp

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The table below is a brief chronology of computed numerical values of, or bounds on, the mathematical constant pi (π). See the history of numerical approximations of pi for explanations, comments and details concerning some of the calculations mentioned below.

Дата Персона Значення пі
(world records in bold)
26-е століття до н. е. Єгипетська Піраміда Хеопса і Піраміда в Медумі[1] 3+1/7 = 22/7
20-е століття до н. е. Єгипетський Папірус Рінда і Московський математичний папірус (16/9)2 = 3.160493…
19-е століття до н. е. Вивилонська математика 25/8 = 3.125
9-е століття до н. е. Індійська Шатапатха Брахмана 339/108 = 3.138888…
434 до н.е Анаксагор намагався знайти квадратуру круга за допомогою циркуля і лінійки  
близько 250 до н.е. Архімед 223/71 < π < 22/7
(3.140845… < π < 3.142857…)
20 до н.е. Вітрувій 25/8 = 3.125
5 Liu Xin 3.154
130 Zhang Heng √10 = 3.162277…
150 Птоломей 377/120 = 3.141666…
250 Wang Fan 142/45 = 3.155555…
263 Лю Хуей 3.141024
480 Цу Чунчжи 3.1415926 < π < 3.1415927
499 Аріабхата I 62832/20000 = 3.1416
640 Брамагупта √10 = 3.162277…
800 Аль-Хорезмі 3.1416
1150 Bhāskara II 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 Leibniz formula for pi 11 знаків
13 знаків
1424 Jamshīd al-Kāshī 16 знаків
1573 Valentinus Otho (355/113) 6 знаків
1593 François Viète 9 знаків
1593 Adriaen van Roomen 15 знаків
1596 Ludolph van Ceulen 20 знаків
1615 32 знаків
1621 Willebrord Snell (Snellius), a pupil of Van Ceulen 35 знаків
1665 Isaac Newton 16 знаків
1681 Takakazu Seki[2] 11 знаків
16 знаків
1699 Abraham Sharp 71 знаків
1706 John Machin 100 знаків
1706 William Jones introduced the Greek letter 'π'  
1719 Thomas Fantet de Lagny calculated 127 знаків, but not all were correct 112 знаків
1722 Toshikiyo Kamata 24 знаків
1722 Katahiro Takebe 41 знаків
1739 Yoshisuke Matsunaga 51 знаків
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 знаків, but not all are correct 137 знаків
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 знаків, but not all were correct 152 знаків
1844 Zacharias Dase and Strassnitzky calculated 205 знаків, but not all were correct 200 знаків
1847 Thomas Clausen calculated 250 знаків, but not all were correct 248 знаків
1853 Lehmann 261 знаків
1853 William Rutherford 440 знаків
1855 Richter 500 знаків
1874 William Shanks took 15 years to calculate 707 знаків but not all were correct (the error was found by D. F. Ferguson in 1946) 527 знаків
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.[3]  
1910 Srinivasa Ramanujan finds several rapidly converging infinite series of π, which can compute 8 знаків 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 знаків
1947 Ivan Niven gave a very elementary proof that π is irrational
January 1947 D. F. Ferguson (using a desk calculator) 710 знаків
September 1947 D. F. Ferguson (using a desk calculator) 808 знаків
1949 D. F. Ferguson and John Wrench, using a desk calculator 1,120 знаків
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.) [4] 2,037 знаків
1953 Kurt Mahler showed that π is not a Liouville number  
1954 S. C. Nicholson & J. Jeenel, using the NORC (it took 13 minutes) [5] 3,092 знаків
1957 G. E. Felton, using the Ferranti Pegasus computer (London) [6] 7,480 знаків
January 1958 Francois Genuys, using an IBM 704 (1.7 hours) [7] 10,000 знаків
May 1958 G. E. Felton, using the Pegasus computer (London) (33 hours) 10,020 знаків
1959 Francois Genuys, using the IBM 704 (Paris) (4.3 hours) [8] 16,167 знаків
1961 IBM 7090 (London) (39 minutes) 20,000 знаків
1961 Daniel Shanks and John Wrench, using the IBM 7090 (New York) (8.7 hours) Помилка цитування: Недійсний параметр у тезі <ref> 100,265 знаків
1966 Jean Guilloud and J. Filliatre, using the IBM 7030 (Paris) (taking 28 hours??) 250,000 знаків
1967 Jean Guilloud and M. Dichampt, using the CDC 6600 (Paris) (28 hours) 500,000 знаків
1973 Jean Guilloud and Martin Bouyer, using the CDC 7600 1,001,250 знаків
1981 Yasumasa Kanada and Kazunori Miyoshi, FACOM M-200 2,000,036 знаків
1981 Jean Guilloud, Not known 2,000,050 знаків
1982 Yoshiaki Tamura, MELCOM 900II 2,097,144 знаків
1982 Yasumasa Kanada, Yoshiaki Tamura, HITAC M-280H 4,194,288 знаків
1982 Yasumasa Kanada, Yoshiaki Tamura, HITAC M-280H 8,388,576 знаків
1983 Yasumasa Kanada, Yoshiaki Tamura, S. Yoshino, HITAC M-280H 16,777,206 знаків
October 1983 Yasumasa Kanada and Yasunori Ushiro, HITAC S-810/20 10,013,395 знаків
October 1985 Bill Gosper, Symbolics 3670 17,526,200 знаків
January 1986 David H. Bailey, CRAY-2 29,360,111 знаків
September 1986 Yasumasa Kanada, Yoshiaki Tamura, HITAC S-810/20 33,554,414 знаків
October 1986 Yasumasa Kanada, Yoshiaki Tamura, HITAC S-810/20 67,108,839 знаків
January 1987 Yasumasa Kanada, Yoshiaki Tamura, Yoshinobu Kubo, NEC SX-2 134,214,700 знаків
January 1988 Yasumasa Kanada and Yoshiaki Tamura, HITAC S-820/80 201,326,551 знаків
May 1989 Gregory V. Chudnovsky & David V. Chudnovsky, CRAY-2 & IBM 3090/VF 480,000,000 знаків
June 1989 Gregory V. Chudnovsky & David V. Chudnovsky, IBM 3090 535,339,270 знаків
July 1989 Yasumasa Kanada and Yoshiaki Tamura, HITAC S-820/80 536,870,898 знаків
August 1989 Gregory V. Chudnovsky & David V. Chudnovsky, IBM 3090 1,011,196,691 знаків
19 November 1989 Yasumasa Kanada and Yoshiaki Tamura, HITAC S-820/80 1,073,740,799 знаків
August 1991 Gregory V. Chudnovsky & David V. Chudnovsky, Home made parallel computer (details unknown, not verified) [9] 2,260,000,000 знаків
18 May 1994 Gregory V. Chudnovsky & David V. Chudnovsky, New home made parallel computer (details unknown, not verified) 4,044,000,000 знаків
26 June 1995 Yasumasa Kanada and Daisuke Takahashi (mathematician), HITAC S-3800/480 (dual CPU) [10] 3,221,220,000 знаків
28 August 1995 Yasumasa Kanada and Daisuke Takahashi (mathematician), HITAC S-3800/480 (dual CPU) [11] 4,294,960,000 знаків
11 October 1995 Yasumasa Kanada and Daisuke Takahashi (mathematician), HITAC S-3800/480 (dual CPU) [12] 6,442,450,000 знаків
6 July 1997 Yasumasa Kanada and Daisuke Takahashi (mathematician), HITACHI SR2201 (1024 CPU) [13] 51,539,600,000 знаків
5 April 1999 Yasumasa Kanada and Daisuke Takahashi (mathematician), HITACHI SR8000 (64 of 128 nodes) [14] 68,719,470,000 знаків
20 September 1999 Yasumasa Kanada and Daisuke Takahashi (mathematician), HITACHI SR8000/MPP (128 nodes) [15] 206,158,430,000 знаків
24 November 2002 Professor Yasumasa Kanada & 9 man team, HITACHI SR8000/MPP (64 nodes), 600 hours, Department of Information Science at the University of Tokyo in Tokyo, Japan [16] 1,241,100,000,000 знаків
29 April 2009 Professor Daisuke Takahashi (mathematician) et al., T2K Open Supercomputer (640 nodes), single node speed is 147.2 gigaflops, 29.09 hours, computer memory is 13.5 terabytes, Gauss–Legendre algorithm, Center for Computational Sciences at the University of Tsukuba in Tsukuba, Japan[17] 2,576,980,377,524 знаків
All records from Dec 2009 onwards are calculated on home computers with commercially available parts.
31 December 2009 Fabrice Bellard
  • Core i7 CPU at 2.93 GHz
  • 6 GiB (1) of RAM
  • 7.5 TB of disk storage using five 1.5 TB hard disks (Seagate Barracuda 7200.11 model)
  • 64 bit Red Hat Fedora 10 distribution
  • Computation of the binary digits: 103 days
  • Verification of the binary digits: 13 days
  • Conversion to base 10: 12 days
  • Verification of the conversion: 3 days
  • 131 days in total - The verification of the binary digits used a network of 9 Desktop PCs during 34 hours, Chudnovsky algorithm, see [18] for Bellard's homepage.[19]
 2,699,999,990,000 знаків
2 August 2010 Shigeru Kondo[20]
  • using y-cruncher[21] by Alexander Yee
  • the Chudnovsky formula was used for main computation
  • verification used the Bellard & Plouffe formulas on different computers, both computed 32 hexadecimal digits ending with the 4,152,410,118,610th.
  • with 2 x Intel Xeon X5680 @ 3.33 GHz - (12 physical cores, 24 hyperthreaded)
  • 96 GB DDR3 @ 1066 MHz - (12 x 8 GB - 6 channels) - Samsung (M393B1K70BH1)
  • 1 TB SATA II (Boot drive) - Hitachi (HDS721010CLA332), 3 x 2 TB SATA II (Store Pi Output) - Seagate (ST32000542AS) 16 x 2 TB SATA II (Computation) - Seagate (ST32000641AS)
  • Windows Server 2008 R2 Enterprise x64
  • Computation of binary digits: 80 days
  • Conversion to base 10: 8.2 days
  • Verification of the conversion: 45.6 hours
  • Verification of the binary digits: 64 hours (primary), 66 hours (secondary)
  • Total Time: 90 days - The verification of the binary digits were done simultaneously on two separate computers during the main computation.[22]
 5 trillion знаків
Graph showing how the record precision of numerical approximations to pi measured in decimal places (depicted on a logarithmic scale), evolved in human history. The time before 1400 is compressed.

See also ред.

Є частиною серії статей про
математичну сталу π
 
Застосування
Властивості
Значення
Люди
Історія
В культурі
Пов'язані теми

References ред.

  1. ↑ Petrie, W.M.F. Surveys of the Great Pyramids. Nature Journal: 942—943. 1925
  2. ↑ Yoshio, Mikami; Eugene Smith, David (April 2004) [1914]. A History of Japanese Mathematics (вид. paperback). Dover Publications. ISBN 0486434826. {{cite book}}: Проігноровано невідомий параметр |origmonth= (довідка)
  3. ↑ Lopez-Ortiz, Alex (20 лютого 1998). Indiana Bill sets value of Pi to 3. the news.answers WWW archive. Department of Information and Computing Sciences, Utrecht University. Процитовано 1 лютого 2009.
  4. ↑ G. Reitwiesner, "An ENIAC determination of Pi and e to more than 2000 знаків," MTAC, v. 4, 1950, p. 11-15"
  5. ↑ S. C, Nicholson & J. Jeenel, "Some comments on a NORC computation of x," MTAC, v. 9, 1955, p. 162-164
  6. ↑ G. E. Felton, "Electronic computers and mathematicians," Abbreviated Proceedings of the Oxford Mathematical Conference for Schoolteachers and Industrialists at Trinity College, Oxford, April 8–18, 1957, p. 12-17, footnote p. 12-53. This published result is correct to only 7480D, as was established by Felton in a second calculation, using formula (5), completed in 1958 but apparently unpublished. For a detailed account of calculations of x see J. W. Wrench, Jr., "The evolution of extended decimal approximations to x," The Mathematics Teacher, v. 53, 1960, p. 644-650
  7. ↑ F. Genuys, "Dix milles decimales de x," Chiffres, v. 1, 1958, p. 17-22.
  8. ↑ This unpublished value of x to 16167D was computed on an IBM 704 system at the Commissariat à l'Energie Atomique in Paris, by means of the program of Genuys
  9. ↑ Bigger slices of Pi (determination of the numerical value of pi reaches 2.16 billion decimal digits) Science News 24 August 1991 http://www.encyclopedia.com/doc/1G1-11235156.html
  10. ↑ ftp://pi.super-computing.org/README.our_last_record_3b
  11. ↑ ftp://pi.super-computing.org/README.our_last_record_4b
  12. ↑ ftp://pi.super-computing.org/README.our_last_record_6b
  13. ↑ ftp://pi.super-computing.org/README.our_last_record_51b
  14. ↑ ftp://pi.super-computing.org/README.our_last_record_68b
  15. ↑ ftp://pi.super-computing.org/README.our_latest_record_206b
  16. ↑ http://www.super-computing.org/pi_current.html
  17. ↑ http://www.hpcs.is.tsukuba.ac.jp/~daisuke/pi.html
  18. ↑ http://bellard.org
  19. ↑ http://bellard.org/pi/pi2700e9/pipcrecord.pdf
  20. ↑ Shigeru Kondo
  21. ↑ y-cruncher - A Multi-Threaded Pi-Program
  22. ↑ Kondo's 2010 record, A. Yee's program y-cruncher

External links ред.


Отримано з https://uk.wikipedia.org/w/index.php?title=Користувач:Kusluj/Temp&oldid=14659648