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 pi (π). For more detailed explanations for some of these calculations, see Approximations of π.
Date  Who  Value of pi (world records in bold) 

26th century BC  Egyptian Great Pyramid of Giza and Meidum Pyramid^{1}^{unreliable source?}  3+1/7 = 22/7 = 3.142... 
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 
5  Liu Xin  3.1457 
130  Zhang Heng  √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 = 3.1416 
400  He Chengtian  111035/35329 = 3.142885... 
480  Zu Chongzhi  3.1415926 < π < 3.1415927 Zu's ratio 355/113 = 3.1415929 
499  Aryabhata  62832/20000 = 3.1416 
640  Brahmagupta  √10 = 3.162277... 
800  Al Khwarizmi  3.1416 
1150  Bhāskara II  3.14156 
1220  Fibonacci  3.141818 
1320  Zhao Youqin  3.141592+ 
All records from 1400 onwards are given as the number of correct decimal places.  
1400  Madhava of Sangamagrama probably discovered the infinite power series expansion of π, now known as the Leibniz formula for pi^{2}  10 decimal places 
1424  Jamshīd alKāshī^{3}  17 decimal places 
1573  Valentinus Otho (355/113)  6 decimal places 
1579  François Viète^{4}  9 decimal places 
1593  Adriaan van Roomen^{5}  15 decimal places 
1596  Ludolph van Ceulen  20 decimal places 
1615  32 decimal places  
1621  Willebrord Snell (Snellius), a pupil of Van Ceulen  35 decimal places 
1630  Christoph Grienberger^{6}^{7}  38 decimal places 
1665  Isaac Newton  16 decimal places 
1681  Takakazu Seki^{8}  11 decimal places 16 decimal places 
1699  Abraham Sharp calculated pi to 72 digits, but not all were correct  71 decimal places 
1706  John Machin  100 decimal places 
1706  William Jones introduced the Greek letter 'π'  
1719  Thomas Fantet de Lagny calculated 127 decimal places, but not all were correct  112 decimal places 
1722  Toshikiyo Kamata  24 decimal places 
1722  Katahiro Takebe  41 decimal places 
1739  Yoshisuke Matsunaga  51 decimal places 
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 decimal places 
1794  Jurij Vega calculated 140 decimal places, but not all were correct  136 decimal places 
1794  AdrienMarie 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 decimal places 
1841  William Rutherford calculated 208 decimal places, but not all were correct  152 decimal places 
1844  Zacharias Dase and Strassnitzky calculated 205 decimal places, but not all were correct  200 decimal places 
1847  Thomas Clausen calculated 250 decimal places, but not all were correct  248 decimal places 
1853  Lehmann  261 decimal places 
1855  Richter  500 decimal places 
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 decimal places 
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 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.^{9}  
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 (using a desk calculator)  620 decimal places 
1947  Ivan Niven gave a very elementary proof that π is irrational  
January 1947  D. F. Ferguson (using a desk calculator)  710 decimal places 
September 1947  D. F. Ferguson (using a desk calculator)  808 decimal places 
1949  D. F. Ferguson and John Wrench, using a desk calculator  1,120 decimal places 
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 (it took 70 hours) (also attributed to Reitwiesner et al.) ^{10}  2,037 decimal places 
1953  Kurt Mahler showed that π is not a Liouville number  
1954  S. C. Nicholson & J. Jeenel, using the NORC (13 minutes) ^{11}  3,093 decimal places 
1957  George E. Felton, using the Ferranti Pegasus computer (London), calculated 10,021 digits, but not all were correct ^{12}  7,480 decimal places 
January 1958  Francois Genuys, using an IBM 704 (1.7 hours) ^{13}  10,000 decimal places 
May 1958  George E. Felton, using the Pegasus computer (London) (33 hours)  10,021 decimal places 
1959  Francois Genuys, using the IBM 704 (Paris) (4.3 hours) ^{14}  16,167 decimal places 
1961  Daniel Shanks and John Wrench, using the IBM 7090 (New York) (8.7 hours) ^{15}  100,265 decimal places 
1961  J.M. Gerard, using the IBM 7090 (London) (39 minutes)  20,000 decimal places 
1966  Jean Guilloud and J. Filliatre, using the IBM 7030 (Paris) (taking 28 hours??)  250,000 decimal places 
1967  Jean Guilloud and M. Dichampt, using the CDC 6600 (Paris) (28 hours)  500,000 decimal places 
1973  Jean Guilloud and Martin Bouyer, using the CDC 7600 (23.3 hours)  1,001,250 decimal places 
1981  Kazunori Miyoshi and Yasumasa Kanada, FACOM M200  2,000,036 decimal places 
1981  Jean Guilloud, Not known  2,000,050 decimal places 
1982  Yoshiaki Tamura, MELCOM 900II  2,097,144 decimal places 
1982  Yoshiaki Tamura and Yasumasa Kanada, HITAC M280H (2.9 hours)  4,194,288 decimal places 
1982  Yoshiaki Tamura and Yasumasa Kanada, HITAC M280H  8,388,576 decimal places 
1983  Yasumasa Kanada, Sayaka Yoshino and Yoshiaki Tamura, HITAC M280H  16,777,206 decimal places 
October 1983  Yasunori Ushiro and Yasumasa Kanada, HITAC S810/20  10,013,395 decimal places 
October 1985  Bill Gosper, Symbolics 3670  17,526,200 decimal places 
January 1986  David H. Bailey, CRAY2  29,360,111 decimal places 
September 1986  Yasumasa Kanada, Yoshiaki Tamura, HITAC S810/20  33,554,414 decimal places 
October 1986  Yasumasa Kanada, Yoshiaki Tamura, HITAC S810/20  67,108,839 decimal places 
January 1987  Yasumasa Kanada, Yoshiaki Tamura, Yoshinobu Kubo and others, NEC SX2  134,214,700 decimal places 
January 1988  Yasumasa Kanada and Yoshiaki Tamura, HITAC S820/80  201,326,551 decimal places 
May 1989  Gregory V. Chudnovsky & David V. Chudnovsky, CRAY2 & IBM 3090/VF  480,000,000 decimal places 
June 1989  Gregory V. Chudnovsky & David V. Chudnovsky, IBM 3090  535,339,270 decimal places 
July 1989  Yasumasa Kanada and Yoshiaki Tamura, HITAC S820/80  536,870,898 decimal places 
August 1989  Gregory V. Chudnovsky & David V. Chudnovsky, IBM 3090  1,011,196,691 decimal places 
19 November 1989  Yasumasa Kanada and Yoshiaki Tamura, HITAC S820/80  1,073,740,799 decimal places 
August 1991  Gregory V. Chudnovsky & David V. Chudnovsky, Homemade parallel computer (details unknown, not verified) ^{16}  2,260,000,000 decimal places 
18 May 1994  Gregory V. Chudnovsky & David V. Chudnovsky, New homemade parallel computer (details unknown, not verified)  4,044,000,000 decimal places 
26 June 1995  Yasumasa Kanada and Daisuke Takahashi, HITAC S3800/480 (dual CPU) ^{17}  3,221,220,000 decimal places 
1995  Simon Plouffe finds a formula that allows the nth digit of pi to be calculated without calculating the preceding digits.  
28 August 1995  Yasumasa Kanada and Daisuke Takahashi, HITAC S3800/480 (dual CPU) ^{18}  4,294,960,000 decimal places 
11 October 1995  Yasumasa Kanada and Daisuke Takahashi, HITAC S3800/480 (dual CPU) ^{19}  6,442,450,000 decimal places 
6 July 1997  Yasumasa Kanada and Daisuke Takahashi, HITACHI SR2201 (1024 CPU) ^{20}  51,539,600,000 decimal places 
5 April 1999  Yasumasa Kanada and Daisuke Takahashi, HITACHI SR8000 (64 of 128 nodes) ^{21}  68,719,470,000 decimal places 
20 September 1999  Yasumasa Kanada and Daisuke Takahashi, HITACHI SR8000/MPP (128 nodes) ^{22}  206,158,430,000 decimal places 
24 November 2002  Yasumasa Kanada & 9 man team, HITACHI SR8000/MPP (64 nodes), 600 hours, Department of Information Science at the University of Tokyo in Tokyo, Japan ^{23}  1,241,100,000,000 decimal places 
29 April 2009  Daisuke Takahashi 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^{24}  2,576,980,377,524 decimal places 
All records from Dec 2009 onwards are calculated on home computers with commercially available parts.  
31 December 2009  Fabrice Bellard

2,699,999,990,000 decimal places 
2 August 2010  Shigeru Kondo^{27}

5,000,000,000,000 decimal places 
17 October 2011  Shigeru Kondo^{30}

10,000,000,000,050 decimal places 
28 December 2013  Shigeru Kondo^{31}

12,100,000,000,050 decimal places 
8 October 2014  "houkouonchi"^{32}

13,300,000,000,000 decimal places 
See also
Part of a series of articles on the 
mathematical constant π 

Uses 
Properties 
Value 
People 
History 

In culture 
Related topics 
References
 ^ Petrie, W.M.F. Surveys of the Great Pyramids. Nature Journal: 942–943. 1925
 ^ Bag, A. K. (1980). "Indian Literature on Mathematics During 1400–1800 A.D." (PDF). Indian Journal of History of Science 15 (1): 86. — Madhava gave π ≈ 2,827,433,388,233/9×10^{−11} = 3.14159 26535 92222…, good to 10 decimal places.
 ^ approximated 2π to 9 sexagesimal digits. AlKashi, author: Adolf P. Youschkevitch, chief editor: Boris A. Rosenfeld, p. 256 O'Connor, John J.; Robertson, Edmund F., "Ghiyath alDin Jamshid Mas'ud alKashi", MacTutor History of Mathematics archive, University of St Andrews.. Azarian, Mohammad K. (2010), "alRisāla almuhītīyya: A Summary", Missouri Journal of Mathematical Sciences 22 (2): 64–85.
 ^ Viète, François (1579). Canon mathematicus seu ad triangula : cum adpendicibus (in Latin).
 ^ Romanus, Adrianus (1593). Ideae mathematicae pars prima, sive methodus polygonorum (in Latin).
 ^ Grienbergerus, Christophorus (1630). Elementa Trigonometrica (PDF) (in Latin).
 ^ Hobson, Ernest William (1913). "Squaring the Circle": a History of the Problem (PDF). p. 27.
 ^ Yoshio, Mikami; Eugene Smith, David (April 2004) [January 1914]. A History of Japanese Mathematics (paperback ed.). Dover Publications. ISBN 0486434826.
 ^ LopezOrtiz, 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 20090201.
 ^ 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/1G111235156.html
 ^ ftp://pi.supercomputing.org/README.our_last_record_3b
 ^ ftp://pi.supercomputing.org/README.our_last_record_4b
 ^ ftp://pi.supercomputing.org/README.our_last_record_6b
 ^ ftp://pi.supercomputing.org/README.our_last_record_51b
 ^ ftp://pi.supercomputing.org/README.our_last_record_68b
 ^ ftp://pi.supercomputing.org/README.our_latest_record_206b
 ^ http://www.supercomputing.org/pi_current.html
 ^ http://www.hpcs.is.tsukuba.ac.jp/~daisuke/pi.html
 ^ http://bellard.org
 ^ http://bellard.org/pi/pi2700e9/pipcrecord.pdf
 ^ Shigeru Kondo
 ^ ycruncher – A MultiThreaded PiProgram
 ^ Kondo's 2010 record, A. Yee's program ycruncher
 ^ Pi – 10 Trillion Digits
 ^ Pi  12.1 Trillion Digits
 ^ Pi  13.3 Trillion Digits
External links
 Borwein, Jonathan, "The Life of Pi"
 Kanada Laboratory home page
 Stu's Pi page
 Takahashi's page