Chronology of computation of π - wikipedia Chronology of computation of π This article needs additional citations for verification. Please help improve this article by adding citations to reliable sources. Unsourced material may be challenged and removed. ( October 2014 ) The table below is a brief chronology of computed numerical values of, or bounds on, the mathematical constant pi ( π ). For more detailed explanations for some of these calculations, see Approximations of π. 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. Contents 1 Before 1400 2 From 1400 onwards 3 The age of electronic computers ( from 1949 onwards ) 4 See also 5 References 6 External links Before 1400 Date Who Description / Computation method used Value of pi Decimal places ( world records in bold ) 2000 ? BCЕ 4 × ( 8 / 9 ) 3.16045... 2000 ? BCЕ Ancient Babylonians 3 + 1 / 8 3.125 1800 ? BCE or before Ancient Indians ( Bharatiya ) शतपथ ब्राह्मण SB 7.1. 1.18 `` स चतस्रः प्राचीरुपदधाति द्वे पश्चात्तिरश्च्यौ द्वे पुरस्तात्तद्याश्चतस्रः प्राचीरुपदधाति स आत्मा तद्यत्ताश्चतस्रो भवन्ति चतुर्विधो ह्ययमात्माथ ये पश्चात्ते सक्थ्यौ ये पुरस्तात्तौ बाहू यत्र वा आत्मा तदेव शिरः sa catasraḥ prācīrupadadhāti dve paścāttiraścyau dve purastāttadyāścatasraḥ prācīrupadadhāti sa ātmā tadyattāścatasro bhavanti caturvidho hyayamātmātha ye paścātte sakthyau ye purastāttau bāhū yatra vā ātmā tadeva śiraḥ He puts on ( the circular site ) four ( bricks ) running eastwards 1 ; two behind running crosswise ( from south to north ), and two ( such ) in front. Now the four which he puts on running eastwards are the body ; and as to there being four of these, it is because this body ( of ours ) consists, of four parts 2. The two at the back then are the thighs ; and the two in front the arms ; and where the body is that ( includes ) the head. '' 25 / 8 = 3.125 1200 ? BCЕ China 0 800 ? BCЕ Sulbasutras ( 6 / ( 2 + √ 2 ) ) 3.088311... 0 550 ? BCЕ Bible ( 1 Kings 7 : 23 ) ``... 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 '' 0 434 BCE Anaxagoras attempted to square the circle compass and straightedge Anaxagoras did n't offer any solution 0 c. 250 BCE Archimedes 223 / 71 < π < 22 / 7 3.140845... < π < 3.142857... 15 BCE Vitruvius 25 / 8 3.125 5 Liu Xin the exact method is unknown 3.1457 130 Zhang Heng ( Book of the Later Han ) √ 10 = 3.162277... 730 / 232 3.146551... 150 Ptolemy 377 / 120 3.141666... 250 Wang Fan 142 / 45 3.155555... 263 Liu Hui 3.141024 < π < 3.142074 3927 / 1250 3.14159 5 400 He Chengtian 111035 / 35329 3.142885... 480 Zu Chongzhi 3.1415926 < π < 3.1415927 Zu 's ratio 355 / 113 3.1415926 7 499 Aryabhata 62832 / 20000 3.1416 640 Brahmagupta √ 10 3.162277... 800 Al Khwarizmi 3.1416 1150 Bhāskara II 3927 / 1250 and 754 / 240 3.1416 1220 Fibonacci 3.141818 1320 Zhao Youqin 3.1415926 7 From 1400 onwards Date Who Note Decimal places ( world records in bold ) 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 10 1424 Jamshīd al - Kāshī 16 1573 Valentinus Otho 355 / 113 6 1579 François Viète 9 1593 Adriaan van Roomen 15 1596 Ludolph van Ceulen 20 1615 32 1621 Willebrord Snell ( Snellius ) Pupil of Van Ceulen 35 1630 Christoph Grienberger 38 1665 Isaac Newton 16 1681 Takakazu Seki 11 16 1699 Abraham Sharp Calculated pi to 72 digits, but not all were correct 71 1706 John Machin 100 1706 William Jones Introduced the Greek letter ' π ' 1719 Thomas Fantet de Lagny 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 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 1789 Jurij Vega Calculated 143 decimal places, but not all were correct 126 1794 Jurij Vega Calculated 140 decimal places, but not all were correct 136 1794 Adrien - Marie Legendre Showed that π2 ( and hence π ) is irrational, and mentioned the possibility that π might be transcendental. 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 1824 William Rutherford Calculated 208 decimal places, but not all were correct 152 1844 Zacharias Dase and Strassnitzky Calculated 205 decimal places, but not all were correct 200 1847 Thomas Clausen Calculated 250 decimal places, but not all were correct 248 1853 Lehmann 261 1853 Rutherford 440 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 1882 Ferdinand von Lindemann Proved that π is transcendental ( the Lindemann -- Weierstrass theorem ) 1897 The U.S. state of Indiana Came close to legislating the value 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. 1910 Srinivasa Ramanujan Found 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 Desk calculator 620 1947 Ivan Niven Gave a very elementary proof that π is irrational January 1947 D.F. Ferguson Desk calculator 710 September 1947 D.F. Ferguson Desk calculator 808 1949 D.F. Ferguson and John Wrench Desk calculator 1,120 The age of electronic computers ( from 1949 onwards ) Date Who Implementation Time Decimal places ( world records in bold ) All records from 1949 onwards were calculated with electronic computers. 1949 John Wrench, and L.R. Smith Were the first to use an electronic computer ( the ENIAC ) to calculate π ( also attributed to Reitwiesner et al. ) 70 hours 2,037 1953 Kurt Mahler Showed that π is not a Liouville number 1954 S.C. Nicholson & J. Jeenel Using the NORC 13 minutes 3,093 1957 George E. Felton Ferranti Pegasus computer ( London ), calculated 10,021 digits, but not all were correct 7,480 January 1958 Francois Genuys IBM 704 1.7 hours 10,000 May 1958 George E. Felton Pegasus computer ( London ) 33 hours 10,021 1959 Francois Genuys IBM 704 ( Paris ) 4.3 hours 16,167 1961 Daniel Shanks and John Wrench IBM 7090 ( New York ) 8.7 hours 100,265 1961 J.M. Gerard IBM 7090 ( London ) 39 minutes 20,000 1966 Jean Guilloud and J. Filliatre IBM 7030 ( Paris ) 28 hours 250,000 1967 Jean Guilloud and M. Dichampt CDC 6600 ( Paris ) 28 hours 500,000 1973 Jean Guilloud and Martin Bouyer CDC 7600 23.3 hours 1,001,250 1981 Kazunori Miyoshi and 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 and Yasumasa Kanada HITAC M - 280H 2.9 hours 4,194,288 1982 Yoshiaki Tamura and Yasumasa Kanada HITAC M - 280H 8,388,576 Yasumasa Kanada, Sayaka Yoshino and Yoshiaki Tamura HITAC M - 280H 16,777,206 October 1983 Yasunori Ushiro and 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 and others NEC SX - 2 134,214,700 January 1988 Yasumasa Kanada and 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 and Yoshiaki Tamura HITAC S - 820 / 80 536,870,898 August 1989 Gregory V. Chudnovsky & David V. Chudnovsky IBM 3090 1,011,196,691 19 November 1989 Yasumasa Kanada and 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 ) 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 and Daisuke Takahashi HITAC S - 3800 / 480 ( dual CPU ) 3,221,220,000 1995 Simon Plouffe Finds a formula that allows the n th hexadecimal digit of pi to be calculated without calculating the preceding digits. 28 August 1995 Yasumasa Kanada and Daisuke Takahashi HITAC S - 3800 / 480 ( dual CPU ) 4,294,960,000 11 October 1995 Yasumasa Kanada and Daisuke Takahashi HITAC S - 3800 / 480 ( dual CPU ) 6,442,450,000 6 July 1997 Yasumasa Kanada and Daisuke Takahashi HITACHI SR2201 ( 1024 CPU ) 51,539,600,000 5 April 1999 Yasumasa Kanada and Daisuke Takahashi HITACHI SR8000 ( 64 of 128 nodes ) 68,719,470,000 20 September 1999 Yasumasa Kanada and Daisuke Takahashi HITACHI SR8000 / MPP ( 128 nodes ) 206,158,430,000 24 November 2002 Yasumasa Kanada & 9 man team HITACHI SR8000 / MPP ( 64 nodes ), Department of Information Science at the University of Tokyo in Tokyo, Japan 600 hours 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 29.09 hours 2,576,980,377,524 Date Who Implementation Time Decimal places ( world records in bold ) All records from Dec 2009 onwards are calculated and verified on servers and / or 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 Verification of the binary digits used a network of 9 Desktop PCs during 34 hours, Chudnovsky algorithm, see for Bellard 's homepage. 131 days 2,699,999,990,000 2 August 2010 Shigeru Kondo using y - cruncher by Alexander Yee the Chudnovsky algorithm was used for main computation verification used the Bellard & Plouffe formulas on different computers, both computed 32 hexadecimal digits ending with the 4,152,410,118,610 th. with 2 x Intel Xeon X5680 @ 3.33 GHz -- ( 12 physical cores, 24 hyperthreaded ) 96 GB DDR3 @ 1066 MHz -- ( 12 × 8 GB -- 6 channels ) -- Samsung ( M393B1K70BH1 ) 1 TB SATA II ( Boot drive ) -- Hitachi ( HDS721010CLA332 ), 3 × 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 ) Verification of the binary digits were done simultaneously on two separate computers during the main computation. 90 days 5,000,000,000,000 17 October 2011 Shigeru Kondo using y - cruncher by Alexander Yee Verification : 1.86 days and 4.94 days 371 days 10,000,000,000,050 28 December 2013 Shigeru Kondo using y - cruncher by Alexander Yee with 2 x Intel Xeon E5 - 2690 @ 2.9 GHz -- ( 16 physical cores, 32 hyperthreaded ) 128 GB DDR3 @ 1600 MHz -- 8 x 16 GB -- 8 channels Windows Server 2012 x64 Verification : 46 hours 94 days 12,100,000,000,050 8 October 2014 Sandon Nash Van Ness `` houkouonchi '' using y - cruncher by Alexander Yee with 2 x Xeon E5 - 4650L @ 2.6 GHz 192 GB DDR3 @ 1333 MHz 24 x 4 TB + 30 x 3 TB Verification : 182 hours 208 days 13,300,000,000,000 11 November 2016 Peter Trueb using y - cruncher by Alexander Yee with 4 x Xeon E7 - 8890 v3 @ 2.50 GHz ( 72 cores, 144 threads ) 1.25 TB DDR4 20 x 6 TB Verification : 28 hours 105 days 22,459,157,718,361 See also History of pi Part of a series of articles on the mathematical constant π 3.14159 26535 89793 23846 26433... Uses Area of a circle Circumference Use in other formulae Properties Irrationality Transcendence Value Less than 22 / 7 Approximations Memorization People Archimedes Liu Hui Zu Chongzhi Aryabhata Madhava Ludolph van Ceulen Seki Takakazu Takebe Kenko William Jones John Machin William Shanks Srinivasa Ramanujan John Wrench Chudnovsky brothers Yasumasa Kanada History Chronology Book In culture Legislation Pi Day Related topics Squaring the circle Basel problem Six nines in π Other topics related to π References ^ Jump up to : David H. Bailey, Jonathan M. Borwein, Peter B. Borwein & Simon Plouffe ( 1997 ). `` The quest for pi '' ( PDF ). Mathematical Intelligencer. 19 ( 1 ) : 50 -- 57. CS1 maint : Uses authors parameter ( link ) Jump up ^ http://mduchin.math.tufts.edu/UCD/111/readings/kak1.pdf Jump up ^ The Sacred Books of the East : The Satapatha - Brahmana, pt. 3. Clarendon Press. 1894. p. 303. This article incorporates text from this source, which is in the public domain. Jump up ^ http://www-history.mcs.st-and.ac.uk/Projects/Pearce/Chapters/Ch4_2.html ^ Jump up to : 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. CS1 maint : Uses authors parameter ( link ) Jump up ^ 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 Jump up ^ https://www.math.rutgers.edu/~cherlin/History/Papers2000/wilson.html Jump up ^ Bag, A.K. ( 1980 ). `` Indian Literature on Mathematics During 1400 -- 1800 A.D. '' ( PDF ). Indian Journal of History of Science. 15 ( 1 ) : 86. π ≈ 2,827,433,388,233 / 9 × 10 = 3.14159 26535 92222..., good to 10 decimal places. Jump up ^ approximated 2π to 9 sexagesimal digits. Al - Kashi, author : Adolf P. Youschkevitch, chief editor : Boris A. Rosenfeld, p. 256 O'Connor, John J. ; Robertson, Edmund F., `` Ghiyath al - Din Jamshid Mas'ud al - Kashi '', MacTutor History of Mathematics archive, University of St Andrews... Azarian, Mohammad K. ( 2010 ), `` al - Risāla al - muhītīyya : A Summary '', Missouri Journal of Mathematical Sciences 22 ( 2 ) : 64 -- 85. Jump up ^ Viète, François ( 1579 ). Canon mathematicus seu ad triangula : cum adpendicibus ( in Latin ). Jump up ^ Romanus, Adrianus ( 1593 ). Ideae mathematicae pars prima, sive methodus polygonorum ( in Latin ). Jump up ^ Grienbergerus, Christophorus ( 1630 ). Elementa Trigonometrica ( PDF ) ( in Latin ). Archived from the original ( PDF ) on 2014 - 02 - 01. Jump up ^ Hobson, Ernest William ( 1913 ). `` Squaring the Circle '' : a History of the Problem ( PDF ). p. 27. Jump up ^ Yoshio, Mikami ; Eugene Smith, David ( April 2004 ) ( January 1914 ). A History of Japanese Mathematics ( paperback ed. ). Dover Publications. ISBN 0 - 486 - 43482 - 6. Jump up ^ 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. Jump up ^ G. Reitwiesner, `` An ENIAC determination of Pi and e to more than 2000 decimal places, '' MTAC, v. 4, 1950, pp. 11 -- 15 '' Jump up ^ S. C, Nicholson & J. Jeenel, `` Some comments on a NORC computation of x, '' MTAC, v. 9, 1955, pp. 162 -- 164 Jump up ^ 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 Jump up ^ F. Genuys, `` Dix milles decimales de x, '' Chiffres, v. 1, 1958, pp. 17 -- 22. Jump up ^ 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 Jump up ^ ( 1 ) `` Calculation of Pi to 100,000 Decimals '' in the journal Mathematics of Computation, vol 16 ( 1962 ), issue 77, pages 76 -- 99. Jump up ^ 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 Jump up ^ ftp://pi.super-computing.org/README.our_last_record_3b Jump up ^ ftp://pi.super-computing.org/README.our_last_record_4b Jump up ^ ftp://pi.super-computing.org/README.our_last_record_6b Jump up ^ ftp://pi.super-computing.org/README.our_last_record_51b Jump up ^ ftp://pi.super-computing.org/README.our_last_record_68b Jump up ^ ftp://pi.super-computing.org/README.our_latest_record_206b Jump up ^ http://www.super-computing.org/pi_current.html Jump up ^ http://www.hpcs.is.tsukuba.ac.jp/~daisuke/pi.html Jump up ^ `` Fabrice Bellard 's Home Page ''. bellard.org. Retrieved 28 August 2015. Jump up ^ http://bellard.org/pi/pi2700e9/pipcrecord.pdf Jump up ^ `` PI - world ''. calico.jp. Retrieved 28 August 2015. Jump up ^ `` y - cruncher -- A Multi-Threaded Pi Program ''. numberworld.org. Retrieved 28 August 2015. Jump up ^ `` Pi -- 5 Trillion Digits ''. numberworld.org. Retrieved 28 August 2015. Jump up ^ `` Pi -- 10 Trillion Digits ''. numberworld.org. Retrieved 28 August 2015. Jump up ^ `` Pi -- 12.1 Trillion Digits ''. numberworld.org. Retrieved 28 August 2015. Jump up ^ `` y - cruncher -- A Multi-Threaded Pi Program ''. numberworld.org. Retrieved 14 March 2018. Jump up ^ `` pi2e ''. pi2e.ch. Retrieved 15 November 2016. Jump up ^ `` y - cruncher -- A Multi-Threaded Pi Program ''. numberworld.org. Retrieved 15 November 2016. Jump up ^ `` Hexadecimal Digits are Correct ! -- pi2e trillion digits of pi ''. pi2e.ch. Retrieved 15 November 2016. Jump up ^ 22,459,157,718,361 is π × 10 rounded down. External links Borwein, Jonathan, `` The Life of Pi '' Kanada Laboratory home page Stu 's Pi page Takahashi 's page Retrieved from `` https://en.wikipedia.org/w/index.php?title= Chronology_of_computation_of_π&oldid = 830591209 '' Categories : Pi History of mathematics Record progressions Pi algorithms Hidden categories : CS1 maint : Uses authors parameter CS1 Latin - language sources ( la ) Articles containing Latin - language text Articles needing additional references from October 2014 All articles needing additional references All articles with failed verification Articles with failed verification from June 2017 Talk Contents About Wikipedia Català 日本 語 Português 中文 Edit links This page was last edited on 15 March 2018, at 19 : 33. Text is available under the Creative Commons Attribution - ShareAlike License ; additional terms may apply. By using this site, you agree to the Terms of Use and Privacy Policy. 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Question: what is the highest number of decimal places for pi ever found
Answer: 22,459,157,718,361