Cronologia do cálculo de pi: diferenças entre revisões
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Revisão das 22h49min de 12 de janeiro de 2017
Cronologia do cálculo de
A tabela abaixo é uma breve cronologia dos valores numéricos computados ou limites da constante matemática pi ().
Antes de 1400
Data | Quem | Formulação | Valor de pi | Dígitos decimais (recordes mundiais em negrito) |
---|---|---|---|---|
2000? a.C. | Matemática do Antigo Egito[1] | 4*(8/9)2 | 3,16045... | 1 |
2000? a.C. | Antigos babilônios[1] | 3+1/8 | 3,125 | 1 |
1200? a.C. | China[1] | 3 | 1 | |
550? a.C. | Bíblia (1 Kings 7:23)[1] | "...a molten sea, ten cubits from the one brim to the other: it was round all about,... a line of thirty cubits did compass it round about" | 3 | 1 |
434 a.C. | Anaxagoras tentou a quadratura do círculo[2] | régua e compasso | Anaxagoras não obteve solução | 0 |
350? a.C. | Shulba Sutras[3][4] | (6/(2+√2))2 | 3,088311 … | 1 |
c. 250 a.C. | Arquimedes[1] | 223/71 < < 22/7 | 3,140845... < < 3,142857... 3,1418 (ave.) |
3 |
15 a.C. | Vitruvius[3] | 25/8 | 3,125 | 1 |
5 | Liu Xin[3] | o método exato édesconhecido | 3,1457 | 2 |
130 | Zhang Heng (Book of the Later Han)[1] | √10 = 3,162277... 730/232 |
3,146551... | 1 |
150 | Ptolemeu[1] | 377/120 | 3,141666... | 3 |
250 | Wang Fan[1] | 142/45 | 3,155555... | 1 |
263 | Liu Hui[1] | 3,141024 < < 3,142074 3927/1250 |
3,14159 | 5 |
400 | He Chengtian[3] | 111035/35329 | 3,142885... | 2 |
480 | Zu Chongzhi[1] | 3,1415926 < < 3,1415927 Zu's ratio 355/113 |
3,1415926 | 7 |
499 | Aryabhata[1] | 62832/20000 | 3,1416 | 4 |
640 | Brahmagupta[1] | √10 | 3,162277... | 1 |
800 | al-Khwārizmī[1] | 3,1416 | 4 | |
1150 | Bhaskara II[3] | 3927/1250 e 754/240 | 3,1416 | 3 |
1220 | Leonardo Fibonacci[1] | 3,141818 | 3 | |
1320 | Zhao Youqin[3] | 3,1415926 | 7 |
A partir de 1400
Data | Quem | Nota | Dígitos decimais (recordes mundiais em negrito) |
---|---|---|---|
All records from 1400 onwards are given as the number of correct decimal places. | |||
1400 | Madhava de Sangamagrama | Descobriu provavelmente a série de potências infinita de , conhecida como Fórmula de Leibniz para π[5] | 10 |
1424 | Jamshīd al-Kāshī[6] | 17 | |
1573 | Valentinus Otho | 355/113 | 6 |
1579 | François Viète[7] | 9 | |
1593 | Adriaan van Roomen[8] | 15 | |
1596 | Ludolph van Ceulen | 20 | |
1615 | 32 | ||
1621 | Willebrord Snel van Royen | Pupil of Van Ceulen | 35 |
1630 | Christoph Grienberger[9][10] | 38 | |
1665 | Isaac Newton[1] | 16 | |
1681 | Seki Takakazu[11] | 11 16 | |
1699 | Abraham Sharp[1] | Calculated pi to 72 digits, but not all were correct | 71 |
1706 | John Machin[1] | 100 | |
1706 | William Jones | Introduziu a letra grega '' | |
1719 | Thomas Fantet de Lagny[1] | Calculated 127 decimal places, but not all were correct | 112 |
1722 | Toshikiyo Kamata | 24 | |
1722 | Katahiro Takebe | 41 | |
1739 | Yoshisuke Matsunaga | 51 | |
1748 | Leonhard Euler | Usou a letra grega '' em seu livro Introductio in Analysin Infinitorum e assegorou sua popularidade. | |
1761 | Johann Heinrich Lambert | Provou que é Número irracional/irracional | |
1775 | Euler | Pointed out the possibility that might be transcendental | |
1789 | Jurij Vega | Calculated 143 decimal places, but not all were correct | 126 |
1794 | Jurij Vega[1] | Calculated 140 decimal places, but not all were correct | 136 |
1794 | Adrien-Marie Legendre | Mostrou que ² (e portanto ) é irracional, e mencionou a possibilidade que pode ser transcendente. | |
Late 18th century | Anonymous manuscript | Turns up at Radcliffe Library, in Oxford, England, discovered by F. X. von Zach, giving the value of pi to 154 digits, 152 of which were correct | 152 |
1841 | William Rutherford[1] | Calculou 208 dígitos decimais, mas nem todos eram corretos | 152 |
1844 | Zacharias Dase e Strassnitzky[1] | Calculou 205 dígitos decimais, mas nem todos eram corretos | 200 |
1847 | Thomas Clausen[1] | Calculou 250 dígitos decimais, mas nem todos eram corretos | 248 |
1853 | Lehmann[1] | 261 | |
1855 | Richter | 500 | |
1874 | William Shanks[1] | Durante 15 anos calculou 707 dígitos decimais, mas nem todos eram corretos (os erros foram identificados por D. F. Ferguson em 1946) | 527 |
1882 | Ferdinand von Lindemann | Provou que é transcendental (teorema de Lindemann–Weierstrass) | |
1897 | The U.S. state of Indiana | Came close to legislating the value 3,2 (among others) for . 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.[12] | 1 |
1910 | Srinivasa Ramanujan | Found several rapidly converging infinite series of , which can compute 8 decimal places of with each term in the series. Since the 1980s, his series have become the basis for the fastest algorithms currently used by Yasumasa Kanada e the Chudnovsky brothers to compute . | |
1946 | D. F. Ferguson | Desk calculator | 620 |
1947 | Ivan Morton Niven | Apresentou uma Gave a very elementary proof that is irrational | |
January 1947 | D. F. Ferguson | Desk calculator | 710 |
September 1947 | D. F. Ferguson | Desk calculator | 808 |
1949 | D. F. Ferguson e John Wrench | Desk calculator | 1,120 |
Idade da computação eletrônica (a partir de 1949)
Data | Quem | Implementação | Tempo | Dígitos decimais (recordes mundiais em negrito) |
---|---|---|---|---|
All records from 1949 onwards were calculated with electronic computers. | ||||
1949 | John Wrench e L. R. Smith | Were the first to use an electronic computer (the ENIAC) to calculate (also attributed to Reitwiesner et al.) [13] | 70 horas | 2,037 |
1953 | Kurt Mahler | Mostrou que não é um número de Liouville | ||
1954 | S. C. Nicholson & J. Jeenel | Using the NORC [14] | 13 minutes | 3,093 |
1957 | George E. Felton | Ferranti Pegasus computer (London), calculated 10,021 digits, but not all were correct [15] | 7.480 | |
January 1958 | Francois Genuys | IBM 704 [16] | 1,7 horas | 10.000 |
May 1958 | George E. Felton | Pegasus computer (London) | 33 horas | 10,021 |
1959 | Francois Genuys | IBM 704 (Paris)[17] | 4,3 horas | 16,167 |
1961 | Daniel Shanks e John Wrench | IBM 7090 (New York)[18] | 8,7 horas | 100.265 |
1961 | J.M. Gerard | IBM 7090 (London) | 39 minutes | 20.000 |
1966 | Jean Guilloud e J. Filliatre | IBM 7030 (Paris) | 28 horas {?) | 250,000 |
1967 | Jean Guilloud e M. Dichampt | CDC 6600 (Paris) | 28 horas | 500,000 |
1973 | Jean Guilloud e Martin Bouyer | CDC 7600 | 23,3 horas | 1.001.250 |
1981 | Kazunori Miyoshi e Yasumasa Kanada | FACOM M-200 | 2.000.036 | |
1981 | Jean Guilloud | Not known | 2.000.050 | |
1982 | Yoshiaki Tamura | MELCOM 900II | 2.097.144 | |
1982 | Yoshiaki Tamura e Yasumasa Kanada | HITAC M-280H | 2,9 horas | 4.194.288 |
1982 | Yoshiaki Tamura e Yasumasa Kanada | HITAC M-280H | 8.388.576 | |
1983 | Yasumasa Kanada, Sayaka Yoshino e Yoshiaki Tamura | HITAC M-280H | 16.777.206 | |
October 1983 | Yasunori Ushiro e Yasumasa Kanada | HITAC S-810/20 | 10.013.395 | |
October 1985 | Bill Gosper | Symbolics 3670 | 17.526.200 | |
January 1986 | David H. Bailey | CRAY-2 | 29.360.111 | |
September 1986 | Yasumasa Kanada, Yoshiaki Tamura | HITAC S-810/20 | 33.554.414 | |
October 1986 | Yasumasa Kanada, Yoshiaki Tamura | HITAC S-810/20 | 67.108.839 | |
January 1987 | Yasumasa Kanada, Yoshiaki Tamura, Yoshinobu Kubo e outros | NEC SX-2 | 134.214.700 | |
January 1988 | Yasumasa Kanada e Yoshiaki Tamura | HITAC S-820/80 | 201.326.551 | |
May 1989 | Gregory V. Chudnovsky & David V. Chudnovsky | CRAY-2 & IBM 3090/VF | 480,000,000 | |
June 1989 | Gregory V. Chudnovsky & David V. Chudnovsky | IBM 3090 | 535.339.270 | |
July 1989 | Yasumasa Kanada e Yoshiaki Tamura | HITAC S-820/80 | 536.870.898 | |
August 1989 | Gregory V. Chudnovsky & David V. Chudnovsky | IBM 3090 | 1.011.196.691 | |
19 de novembro de 1989 | Yasumasa Kanada e Yoshiaki Tamura | HITAC S-820/80 | 1.073.740.799 | |
August 1991 | Gregory V. Chudnovsky & David V. Chudnovsky | Homemade parallel computer (details unknown, not verified) [19] | 2.260.000.000 | |
18 May 1994 | Gregory V. Chudnovsky & David V. Chudnovsky | New homemade parallel computer (details unknown, not verified) | 4.044.000.000 | |
26 June 1995 | Yasumasa Kanada e Daisuke Takahashi | HITAC S-3800/480 (dual CPU) [20] | 3.221.220.000 | |
1995 | Simon Plouffe | Finds a formula that allows the nth hexadecimal digit of pi to be calculated without calculating the preceding digits. | ||
28 August 1995 | Yasumasa Kanada e Daisuke Takahashi | HITAC S-3800/480 (dual CPU) [21] | 4.294.960.000 | |
11 October 1995 | Yasumasa Kanada e Daisuke Takahashi | HITAC S-3800/480 (dual CPU) [22] | 6.442.450.000 | |
6 July 1997 | Yasumasa Kanada e Daisuke Takahashi | HITACHI SR2201 (1024 CPU) [23] | 51.539.600.000 | |
5 April 1999 | Yasumasa Kanada e Daisuke Takahashi | HITACHI SR8000 (64 of 128 nodes) [24] | 68.719.470.000 | |
20 September 1999 | Yasumasa Kanada e Daisuke Takahashi | HITACHI SR8000/MPP (128 nodes) [25] | 206.158.430.000 | |
24 de novembro de 2002 | Yasumasa Kanada & 9 man team | HITACHI SR8000/MPP (64 nodes), Department of Information Science at the University of Tokyo in Tokyo, Japan [26] | 600 horas | 1.241.100.000.000 |
29 April 2009 | Daisuke Takahashi et al. | T2K Open Supercomputer (640 nodes), single node speed is 147,2 gigaflops, computer memory is 13,5 terabytes, Gauss–Legendre algorithm, Center for Computational Sciences at the University of Tsukuba in Tsukuba, Japan[27] | 29,09 horas | 2.576.980.377.524 |
Data | Quem | Implementação | Tempo | Dígitos decimais (recordes mundiais em negrito) |
---|---|---|---|---|
All records from Dec 2009 onwards are calculated on home computers with commercially available parts. | ||||
31 December 2009 | Fabrice Bellard |
|
131 dias | 2.699.999.990.000 |
2 August 2010 | Shigeru Kondo[30] |
|
90 dias | 5.000.000.000.000 |
17 October 2011 | Shigeru Kondo[33] |
|
371 dias | 10.000.000.000.050 |
28 December 2013 | Shigeru Kondo[34] |
|
94 dias | 12.100.000.000.050 |
8 October 2014 | "houkouonchi"[35] |
|
208 dias | 13.300.000.000.000 |
11 de novembro de 2016 | Peter Trueb[36][37] |
|
105 dias | 22.459.157.718.361[39] |
Parte de uma série de artigos sobre: |
a constante matemática π |
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3.1415926535897932384626433... |
Utilização |
Propriedades |
Valor |
Pessoas |
História |
Na cultura |
Tópicos relacionados |
Referências
- ↑ a b c d e f g h i j k l m n o p q r s t u v w x David H. Bailey, Jonathan M. Borwein, Peter B. Borwein & Simon Plouffe (1997). «The quest for pi» (PDF). Mathematical Intelligencer. 19 (1): 50–57
- ↑ https://www.math.rutgers.edu/~cherlin/History/Papers2000/wilson.html
- ↑ a b c d e f Ravi P. Agarwal, Hans Agarwal & Syamal K. Sen (2013). «Birth, growth and computation of pi to ten trillion digits». Advances in Difference Equations. 2013: 100. doi:10.1186/1687-1847-2013-100
- ↑ https://books.google.com/books?id=DHvThPNp9yMC&lpg=PA18&ots=Aoy0T2r3Qz&dq=Shulba%20Sutras%20date%20of%20creation&hl=de&pg=PA18#v=onepage&q=Shulba%20Sutras%20date%20of%20creation&f=false
- ↑ Bag, A. K. (1980). «Indian Literature on Mathematics During 1400–1800 A.D.» (PDF). Indian Journal of History of Science. 15 (1): 86.
≈ 2.827.433.388.233/9×10−11 = 3,14159 26535 92222…, good to 10 decimal places.
- ↑ approximated 2π to 9 sexagesimal digits. Al-Kashi, author: Adolf P. Youschkevitch, chief editor: Boris A. Rosenfeld, p. 256 John J. O’Connor, Edmund F. Robertson: Ghiyath al-Din Jamshid Mas'ud al-Kashi. In: MacTutor History of Mathematics archive.. Azarian, Mohammad K. (2010), "al-Risāla al-muhītīyya: A Summary", Missouri Journal of Mathematical Sciences 22 (2): 64–85.
- ↑ Viète, François (1579). Canon mathematicus seu ad triangula : cum adpendicibus (em Latin). [S.l.: s.n.]
- ↑ Romanus, Adrianus (1593). Ideae mathematicae pars prima, sive methodus polygonorum (em Latin). [S.l.: s.n.]
- ↑ Grienbergerus, Christophorus (1630). Elementa Trigonometrica (PDF) (em Latin). [S.l.: s.n.]
- ↑ Hobson, Ernest William (1913). "Squaring the Circle": a History of the Problem (PDF). [S.l.: s.n.] p. 27
- ↑ Yoshio, Mikami; Eugene Smith, David (April 2004) [January 1914]. A History of Japanese Mathematics paperback ed. [S.l.]: Dover Publications. ISBN 0-486-43482-6 Verifique data em:
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(ajuda) - ↑ 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. Consultado em 1 de fevereiro de 2009 Verifique data em:
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(ajuda) - ↑ G. Reitwiesner, "An ENIAC determination of Pi and e to more than 2000 decimal places," MTAC, v. 4, 1950, pp. 11–15"
- ↑ S. C, Nicholson & J. Jeenel, "Some comments on a NORC computation of x," MTAC, v. 9, 1955, pp. 162–164
- ↑ 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, pp. 12–17, footnote pp. 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, pp. 644–650
- ↑ F. Genuys, "Dix milles decimales de x," Chiffres, v. 1, 1958, pp. 17–22.
- ↑ 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
- ↑ [1] "Calculation of Pi to 100,000 Decimals" in the journal Mathematics of Computation, vol 16 (1962), issue 77, pages 76–99.
- ↑ 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
- ↑ ftp://pi.super-computing.org/README.our_last_record_3b
- ↑ ftp://pi.super-computing.org/README.our_last_record_4b
- ↑ ftp://pi.super-computing.org/README.our_last_record_6b
- ↑ ftp://pi.super-computing.org/README.our_last_record_51b
- ↑ ftp://pi.super-computing.org/README.our_last_record_68b
- ↑ ftp://pi.super-computing.org/README.our_latest_record_206b
- ↑ http://www.super-computing.org/pi_current.html
- ↑ http://www.hpcs.is.tsukuba.ac.jp/~daisuke/pi.html
- ↑ «Fabrice Bellard's Home Page». bellard.org. Consultado em 28 August 2015 Verifique data em:
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(ajuda) - ↑ http://bellard.org/pi/pi2700e9/pipcrecord.pdf
- ↑ «PI-world». calico.jp. Consultado em 28 August 2015 Verifique data em:
|acessodata=
(ajuda) - ↑ «y-cruncher - A Multi-Threaded Pi Program». numberworld.org. Consultado em 28 August 2015 Verifique data em:
|acessodata=
(ajuda) - ↑ «Pi - 5 Trillion Digits». numberworld.org. Consultado em 28 August 2015 Verifique data em:
|acessodata=
(ajuda) - ↑ «Pi - 10 Trillion Digits». numberworld.org. Consultado em 28 August 2015 Verifique data em:
|acessodata=
(ajuda) - ↑ «Pi - 12,1 Trillion Digits». numberworld.org. Consultado em 28 August 2015 Verifique data em:
|acessodata=
(ajuda) - ↑ «y-cruncher - A Multi-Threaded Pi Program». numberworld.org. Consultado em 28 August 2015 Verifique data em:
|acessodata=
(ajuda) - ↑ «pi2e». pi2e.ch. Consultado em 15 de novembro de 2016
- ↑ «y-cruncher - A Multi-Threaded Pi Program». numberworld.org. Consultado em 15 de novembro de 2016
- ↑ «Hexadecimal Digits are Correct! - pi2e trillion digits of pi». pi2e.ch. Consultado em 15 de novembro de 2016
- ↑ 22.459.157.718.361 is e*1012 rounded down.
Ligações externas
- Borwein, Jonathan, "The Life of Pi"
- Kanada Laboratory home page
- Stu's Pi page
- Takahashi's page