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.
Part of a series of articles on the 
mathematical constant π 

Uses 
Properties 
Value 
People 
History 

In culture 
Related topics 
Date  Whom  Formulation  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  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+ 
Date  Whom  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  Probably discovered the infinite power series expansion of π, now known as the Leibniz formula for pi^{2} 
10 
1424  Jamshīd alKāshī^{3}  17  
1573  Valentinus Otho  355/113  6 
1579  François Viète^{4}  9  
1593  Adriaan van Roomen^{5}  15  
1596  Ludolph van Ceulen  20  
1615  32  
1621  Willebrord Snell (Snellius)  Pupil of Van Ceulen  35 
1630  Christoph Grienberger^{6}^{7}  38  
1665  Isaac Newton  16  
1681  Takakazu Seki^{8}  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  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 
1841  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  
1855  Richter  500  
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.^{9}  1 
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 
Date  Whom  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.) ^{10}  70 hours  2,037 
1953  Kurt Mahler  Showed that π is not a Liouville number  
1954  S. C. Nicholson & J. Jeenel  Using the NORC ^{11}  13 minutes  3,093 
1957  George E. Felton  Ferranti Pegasus computer (London), calculated 10,021 digits, but not all were correct ^{12}  7,480  
January 1958  Francois Genuys  IBM 704 ^{13}  1.7 hours  10,000 
May 1958  George E. Felton  Pegasus computer (London)  33 hours  10,021 
1959  Francois Genuys  IBM 704 (Paris)^{14}  4.3 hours  16,167 
1961  Daniel Shanks and John Wrench  IBM 7090 (New York)^{15}  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 M200  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 M280H  2.9 hours  4,194,288 
1982  Yoshiaki Tamura and Yasumasa Kanada  HITAC M280H  8,388,576  
1983  Yasumasa Kanada, Sayaka Yoshino and Yoshiaki Tamura  HITAC M280H  16,777,206  
October 1983  Yasunori Ushiro and Yasumasa Kanada  HITAC S810/20  10,013,395  
October 1985  Bill Gosper  Symbolics 3670  17,526,200  
January 1986  David H. Bailey  CRAY2  29,360,111  
September 1986  Yasumasa Kanada, Yoshiaki Tamura  HITAC S810/20  33,554,414  
October 1986  Yasumasa Kanada, Yoshiaki Tamura  HITAC S810/20  67,108,839  
January 1987  Yasumasa Kanada, Yoshiaki Tamura, Yoshinobu Kubo and others  NEC SX2  134,214,700  
January 1988  Yasumasa Kanada and Yoshiaki Tamura  HITAC S820/80  201,326,551  
May 1989  Gregory V. Chudnovsky & David V. Chudnovsky  CRAY2 & 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 S820/80  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 S820/80  1,073,740,799  
August 1991  Gregory V. Chudnovsky & David V. Chudnovsky  Homemade parallel computer (details unknown, not verified) ^{16}  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 S3800/480 (dual CPU) ^{17}  3,221,220,000  
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  
11 October 1995  Yasumasa Kanada and Daisuke Takahashi  HITAC S3800/480 (dual CPU) ^{19}  6,442,450,000  
6 July 1997  Yasumasa Kanada and Daisuke Takahashi  HITACHI SR2201 (1024 CPU) ^{20}  51,539,600,000  
5 April 1999  Yasumasa Kanada and Daisuke Takahashi  HITACHI SR8000 (64 of 128 nodes) ^{21}  68,719,470,000  
20 September 1999  Yasumasa Kanada and Daisuke Takahashi  HITACHI SR8000/MPP (128 nodes) ^{22}  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 ^{23}  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^{24}  29.09 hours  2,576,980,377,524 
Date  Whom  Implementation  Time  Decimal places (world records in bold) 

All records from Dec 2009 onwards are calculated on home computers with commercially available parts.  
31 December 2009  Fabrice Bellard 

131 days  2,699,999,990,000 
2 August 2010  Shigeru Kondo^{27} 

90 days  5,000,000,000,000 
17 October 2011  Shigeru Kondo^{30} 

371 days  10,000,000,000,050 
28 December 2013  Shigeru Kondo^{31} 

94 days  12,100,000,000,050 
8 October 2014  "houkouonchi"^{32} 

208 days  13,300,000,000,000 
See also
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.
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
 ^ "Fabrice Bellard's Home Page". bellard.org. Retrieved 28 August 2015.
 ^ http://bellard.org/pi/pi2700e9/pipcrecord.pdf
 ^ "PIworld". calico.jp. Retrieved 28 August 2015.
 ^ "ycruncher  A MultiThreaded Pi Program". numberworld.org. Retrieved 28 August 2015.
 ^ "Pi  5 Trillion Digits". numberworld.org. Retrieved 28 August 2015.
 ^ "Pi  10 Trillion Digits". numberworld.org. Retrieved 28 August 2015.
 ^ "Pi  12.1 Trillion Digits". numberworld.org. Retrieved 28 August 2015.
 ^ "ycruncher  A MultiThreaded Pi Program". numberworld.org. Retrieved 28 August 2015.
External links
 Borwein, Jonathan, "The Life of Pi"
 Kanada Laboratory home page
 Stu's Pi page
 Takahashi's page