Chronology of computation of π: Difference between revisions
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The table below is a brief chronology of computed numerical values of, or bounds on, the mathematical constant [[pi|π]]. |
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See the [[history of numerical approximations of π]] for explanations, comments and details concerning some of the calculations mentioned below. |
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{{more citations needed|date=October 2014}} |
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{{DISPLAYTITLE:Chronology of computation of {{pi}}}} |
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{{Pi box}} |
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The table below is a brief chronology of computed numerical values of, or bounds on, the mathematical constant [[pi]] ({{pi}}). For more detailed explanations for some of these calculations, see [[Approximations of π|Approximations of {{pi}}]]. |
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As of July 2024, {{pi}} has been calculated to 202,112,290,000,000 (approximately 202 trillion) decimal digits. The last 100 decimal digits of the latest world record computation are:<ref>{{Cite web |title=y-cruncher validation file |url=http://www.numberworld.org/y-cruncher/records/2024_5_20_pi.txt}}</ref> |
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7034341087 5351110672 0525610978 1945263024 9604509887 5683914937 4658179610 2004394122 9823988073 3622511852 |
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{{toc left}} |
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[[File:PiComputationHistory.svg|thumb|center|600px|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.]] |
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{{clear}} |
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== Before 1400 == |
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{| class="wikitable" |
{| class="wikitable" |
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!align="left"|Date</th> |
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!align="left"|Who</th> |
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!align="right"|Value of π<br />([[world record]]s in '''bold''') |
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!align="left"| Date |
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|26th century BC||[[Egyptian mathematics|Egyptian]] ''Proportions of Giza [[Great Pyramid]] Height to Perimeter'' and ''[[Meidum Pyramid]]''||align="right"|'''3 + 1/7 = 3.142857...''' |
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!align="left"| Who |
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!align="left"| Description/Computation method used |
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!align="right"| Value |
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!align="right"| Decimal places<br />([[world record]]s<br /> in '''bold''') |
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|2000? BC||[[Ancient Egyptian mathematics|Ancient Egyptians]]<ref name="Bailey">{{cite journal|author1=David H. Bailey |author2=Jonathan M. Borwein |author3=Peter B. Borwein |author4=Simon Plouffe |year=1997|title=The quest for pi|url=http://crd-legacy.lbl.gov/~dhbailey/dhbpapers/pi-quest.pdf|journal=[[Mathematical Intelligencer]]|volume=19|issue=1|pages=50–57|doi=10.1007/BF03024340|s2cid=14318695}}</ref> |
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|20th century BC||[[Egyptian mathematics|Egyptian]] ''[[Rhind Mathematical Papyrus]]'' and ''[[Moscow Mathematical Papyrus]]''||align="right"|(16/9)<sup>2</sup> = 3.160493... |
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|4 × ({{frac|8|9}})<sup>2</sup> |
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|align="right"|3.1605...||1 |
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|2000? BC||[[Babylonian mathematics|Ancient Babylonians]]<ref name="Bailey"/> |
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|3 + {{frac|1|8|}} |
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|align="right"|3.125||1 |
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|2000? BC |
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|9th century BC||[[Indian mathematics|Indian]] ''[[Shatapatha Brahmana]]''||align="right"|339/108 = 3.138888... |
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|[[Sumerians|Ancient Sumerians]]<ref>{{cite web |date=2022-03-14 |title=Origins: 3.14159265... |url=https://www.biblicalarchaeology.org/daily/ancient-cultures/origins-pi/ |access-date=2022-06-08 |website=Biblical Archaeology Society |language=en}}</ref> |
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|3 + 23/216 |
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|align="right"|3.1065 |
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|1 |
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|1200? BC||[[Chinese mathematics|Ancient Chinese]]<ref name="Bailey"/> |
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|434 BC||[[Anaxagoras]] attempted to [[squaring the circle|square the circle]] with [[compass and straightedge]]|| |
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|3 |
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|align="right"|3||0 |
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|800–600 BC || [[Shatapatha Brahmana]] – 7.1.1.18 <ref>{{Cite book|last=Eggeling|first=Julius|url=https://archive.org/details/satapathabrahman03egge|title=The Satapatha-brahmana, according to the text of the Madhyandina school|date=1882–1900|publisher=Oxford, The Clarendon Press|others=Princeton Theological Seminary Library|year=1882|pages=302–303}}</ref> |
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|c. 250 BC||[[Archimedes]]||align="right"|223/71 < π < 22/7<br />('''3.140845... < π < 3.142857...''') |
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||Instructions on how to construct a circular altar from oblong bricks: |
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''"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."<ref>{{cite book|title=The Sacred Books of the East: The Satapatha-Brahmana, pt. 3|year=1894|publisher=Clarendon Press|page=303}} {{PD-notice}}</ref>'' |
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|align="right"|{{frac|25|8}} = 3.125||1 |
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|800? BC||[[Shulba Sutras]]<ref>{{cite web|url=http://www-history.mcs.st-and.ac.uk/Projects/Pearce/Chapters/Ch4_2.html|title=4 II. Sulba Sutras|website=www-history.mcs.st-and.ac.uk}}</ref> |
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|20 BC||[[Vitruvius]]||align="right"|25/8 = 3.125 |
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<ref name="Agarwal">{{cite journal |author1=Ravi P. Agarwal |author2=Hans Agarwal |author3=Syamal K. Sen |year=2013 |title=Birth, growth and computation of pi to ten trillion digits |journal=[[Advances in Difference Equations]] |volume=2013 |page=100 |doi=10.1186/1687-1847-2013-100 |doi-access=free }}</ref><ref>{{cite book|page=[https://books.google.com/books?id=DHvThPNp9yMC&pg=PA18 18]|title=Mathematics in India|title-link=Mathematics in India (book)|first=Kim|last=Plofker|date= 2009|publisher=Princeton University Press|isbn=978-0691120676}}</ref> |
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|({{frac|6|(2 + {{radic|2}})}})<sup>2</sup> |
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|align="right"|3.088311 ...||0 |
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|550? BC||[[Bible]] (1 Kings 7:23)<ref name="Bailey"/> |
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|5||[[Liu Xin]]||align="right"|3.154 |
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||"...a [[molten sea]], ten [[Cubit|cubits]] from the one brim to the other: it was round all about,... a line of thirty cubits did compass it round about"||align="right"|3||0 |
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|434 BC||[[Anaxagoras]] attempted to [[squaring the circle|square the circle]]<ref>{{cite web |last1=Wilson |first1=David |title=The History of Pi |url=https://sites.math.rutgers.edu/~cherlin/History/Papers2000/wilson.html |website=sites.math.rutgers.edu |publisher=University Of Rutgers |archive-url=https://web.archive.org/web/20230507165826/https://sites.math.rutgers.edu/~cherlin/History/Papers2000/wilson.html |archive-date=7 May 2023 |language=en |date=2000 |url-status=live}}</ref> |
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|130||[[Zhang Heng]]||align="right"|√10 = 3.162277... |
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|[[compass and straightedge]]||Anaxagoras did not offer a solution||0 |
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| 400 BC to AD 400 || [[Vyasa]]<ref>{{Cite journal|last=Jadhav|first=Dipak|date=2018-01-01|title=On The Value Implied In The Data Referred To In The Mahābhārata for π|url=https://www.academia.edu/37922665|journal=Vidyottama Sanatana: International Journal of Hindu Science and Religious Studies|volume=2|issue=1|page=18|doi=10.25078/ijhsrs.v2i1.511|s2cid=146074061|issn=2550-0651|doi-access=free}}</ref> || |
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|150||[[Ptolemy]]||align="right"|'''377/120 = 3.141666...''' |
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verses: 6.12.40-45 of the [[Bhishma Parva]] of the [[Mahabharata]] offer:<br />"''...''<br /> |
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''The Moon is handed down by memory to be eleven thousand [[Yojana|yojanas]] in diameter. Its peripheral circle happens to be thirty three thousand yojanas when calculated.''<br /> |
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''...''<br /> |
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''The Sun is eight thousand yojanas and another two thousand yojanas in diameter. From that its peripheral circle comes to be equal to thirty thousand yojanas.''<br /> |
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''...''" |
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|align="right"|3||0 |
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|250||[[ |
|c. 250 BC||[[Archimedes]]<ref name="Bailey"/> |
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|{{frac|223|71}} < {{pi}} < {{frac|22|7}} |
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|align="right"|3.140845... < {{pi}} < 3.142857...||'''2''' |
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|15 BC||[[Vitruvius]]<ref name="Agarwal"/> |
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|{{frac|25|8}} |
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|align="right"|3.125||1 |
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|Between 1 BC and AD 5||[[Liu Xin (scholar)|Liu Xin]]<ref name="Agarwal"/><ref>{{cite book|url=https://books.google.com/books?id=_1AsFyM0d84C|title=中西數學史的比較|last=趙良五|date=1991|publisher=臺灣商務印書館|isbn=978-9570502688|via=Google Books}}</ref><ref name="needham volume 3 100">Needham, Joseph (1986). ''Science and Civilization in China: Volume 3, Mathematics and the Sciences of the Heavens and the Earth''. Taipei: Caves Books, Ltd. Volume 3, 100.</ref> |
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|480||[[Zu Chongzhi]]||align="right"|'''3.1415926 < π < 3.1415927''' |
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|Unknown method giving a figure for a [[jialiang]] which [[Liu Xin (scholar)#Calculation of pi (π)|implies a value for {{pi}}]] ≈ {{frac|162|({{radic|50}}+0.095)<sup>2</sup>}}. |
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|align="right"|3.1547...||1 |
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|AD 130||[[Zhang Heng]] ([[Book of the Later Han]])<ref name="Bailey"/> |
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|499||[[Aryabhata]]||align="right"|62832/20000 = 3.1416 |
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|{{radic|10}} = 3.162277...<br />{{frac|736|232}} |
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|align="right"|3.1622...||1 |
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|150||[[Ptolemy]]<ref name="Bailey"/> |
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|640||[[Brahmagupta]]||align="right"|√10 = 3.162277... |
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|{{frac|377|120}} |
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|align="right"|3.141666...||'''3''' |
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|250||[[Wang Fan]]<ref name="Bailey"/> |
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|{{frac|142|45}} |
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|align="right"|3.155555...||1 |
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|263||[[Liu Hui's π algorithm|Liu Hui]]<ref name="Bailey"/> |
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|1150||[[Bhaskara]]||align="right"|3.14156 |
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|3.141024 < {{pi}} < 3.142074<br />{{frac|3927|1250}} |
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|align="right"|3.1416||'''3''' |
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|400||[[:zh:何承天 (南朝)|He Chengtian]]<ref name="Agarwal"/> |
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|1220||[[Leonardo of Pisa|Fibonacci]]||align="right"|3.141818 |
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|{{frac|111035|35329}} |
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|align="right"|3.142885...||2 |
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|480||[[Zu Chongzhi]]<ref name="Bailey"/> |
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|colspan="3" align="center"|''All records from 1400 onwards are given as the number of correct decimal places''. |
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|3.1415926 < {{pi}} < 3.1415927 <br />[[Milü|{{frac|355|113}}]] |
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|align="right"|3.1415926||'''7''' |
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|499||[[Aryabhata]]<ref name="Bailey"/> |
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|1400||[[Madhava of Sangamagrama]] discovered the infinite [[power series|power]] [[Series (mathematics)|series]] expansion of π, now known as the [[Leibniz formula for pi|Madhava-Leibniz series]]||align="right"|'''11 decimal places'''<br />'''13 decimal places''' |
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|{{frac|62832|20000}} |
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|align="right"|3.1416||3 |
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|640||[[Brahmagupta]]<ref name="Bailey"/> |
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|1424||[[Jamshīd al-Kāshī]] |
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|{{radic|10}} |
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|align="right"|'''16 decimal places''' |
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|align="right"|3.162277...||1 |
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|800||[[Al Khwarizmi]]<ref name="Bailey"/> |
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|1573||[[Valentinus Otho]] (355/113) |
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|align="right"|6 decimal places |
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|align="right"|3.1416||3 |
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|1150||[[Bhāskara II]]<ref name="Agarwal"/> |
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|1593||[[François Viète]] |
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| {{frac|3927|1250}} and {{frac|754|240}} |
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|align="right"|9 decimal places |
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|align="right"|3.1416||3 |
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|1220||[[Fibonacci]]<ref name="Bailey"/> |
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|1593||[[Adriaen van Roomen]] |
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|align="right"|15 decimal places |
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|align="right"|3.141818||3 |
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|1320|| [[Zhao Youqin's π algorithm|Zhao Youqin]]<ref name="Agarwal"/> |
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|align="right"|3.141592||6 |
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== 1400–1949 == |
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{| class="wikitable" |
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|- |
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!align="left"| Date |
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!align="left"| Who |
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!align="left"| Note |
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!align="right"| Decimal places<br />{{nowrap| ([[world record]]s in '''bold''') }} |
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| colspan="4" style="text-align:center;background:lightblue;"|''All records from 1400 onwards are given as the number of correct decimal places''. |
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|1400||[[Madhava of Sangamagrama]] |
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|Discovered the infinite [[power series]] expansion of {{pi}} now known as the [[Madhava-Leibniz series|Leibniz formula for pi]]<ref>{{cite journal| first=A. K.| last=Bag| year=1980| title=Indian Literature on Mathematics During 1400–1800 A.D.| journal=Indian Journal of History of Science| volume=15| issue=1| page=86| url=http://www.insa.nic.in/writereaddata/UpLoadedFiles/IJHS/Vol15_1_10_AKBag.pdf|quote={{pi}} ≈ 2,827,433,388,233/9×10<sup>−11</sup> = 3.14159 26535 92222..., good to 10 decimal places.}}</ref> |
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|align="right"|'''10''' |
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|1424||[[Jamshīd al-Kāshī]]<ref>approximated 2π to 9 sexagesimal digits. ''Al-Kashi'', author: Adolf P. Youschkevitch, chief editor: Boris A. Rosenfeld, p. 256 {{MacTutor|id=Al-Kashi|title=Ghiyath al-Din Jamshid Mas'ud al-Kashi}} {{cite journal |last1=Azarian |first1=Mohammad K. |title=Al-Risāla Al-Muhītīyya: A Summary |journal=Missouri Journal of Mathematical Sciences |date=2010 |volume=22 |issue=2 |pages=64–85 |doi=10.35834/mjms/1312233136|doi-access=free}}</ref> |
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|align="right"|'''16''' |
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|1573||[[Valentinus Otho]] |
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|{{frac|355|113}} |
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|align="right"|6 |
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|1579||[[François Viète]]<ref>{{cite book | first=François | last=Viète | author-link=François Viète | title=Canon mathematicus seu ad triangula : cum adpendicibus | year=1579 | language=la | url=http://gallica.bnf.fr/ark:/12148/bpt6k52673b/f171.image}}</ref> |
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|align="right"|9 |
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|1593||[[Adriaan van Roomen]]<ref>{{cite book | first={{lang|la|Adrianus}} | last={{lang|la|Romanus}} | title=Ideae mathematicae pars prima, sive methodus polygonorum | year=1593 | publisher=apud Ioannem Keerbergium | hdl=2027/ucm.5320258006 | language=la }}</ref> |
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|align="right"|15 |
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|1596||rowspan="2"|[[Ludolph van Ceulen]] |
|1596||rowspan="2"|[[Ludolph van Ceulen]] |
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|rowspan="2"| |
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|align="right"|'''20 decimal places''' |
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|align="right"|'''20''' |
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|1615 |
|1615 |
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|align="right"|'''32 |
|align="right"|'''32''' |
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|1621||[[Willebrord Snell]] (Snellius) |
|1621||[[Willebrord Snell]] (Snellius) |
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|Pupil of Van Ceulen |
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|align="right"|'''35 |
|align="right"|'''35''' |
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|1630||[[Christoph Grienberger]]<ref>{{cite book | first=Christophorus | last=Grienbergerus | author-link=Christoph Grienberger | language=la | year=1630 | title=Elementa Trigonometrica | url=http://librarsi.comune.palermo.it/gesuiti2/06.04.01.pdf | url-status=dead | archive-url=https://web.archive.org/web/20140201234124/http://librarsi.comune.palermo.it/gesuiti2/06.04.01.pdf | archive-date=2014-02-01 }}</ref><ref>{{cite book | first1=Ernest William | last1=Hobson | author-link=E. W. Hobson | year=1913 | title='Squaring the Circle': a History of the Problem | page=27 | publisher=Cambridge University Press | url=https://archive.org/stream/squaringcirclehi00hobsuoft#page/27/mode/1up | format=PDF}}</ref> |
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|1665||[[Isaac Newton]] |
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|align="right"|16 decimal places |
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|align="right"|'''38''' <!-- calculated=39; determined=38 --> |
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|1654 |
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|1699||[[Abraham Sharp]] |
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|[[Christiaan Huygens]] |
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|align="right"|'''71 decimal places''' |
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|Used a geometrical method equivalent to [[Richardson extrapolation]] |
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|align="right"|10 |
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|1665||[[Isaac Newton]]<ref name="Bailey"/> |
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|1700||[[Seki Kowa]] |
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|align="right"|10 decimal places |
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|align="right"|16 |
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|1681||[[Seki Kowa|Takakazu Seki]]<ref>{{Cite book|last1=Yoshio|author-link=Yoshio Mikami|first1=Mikami|last2=Eugene Smith|first2=David |orig-year=1914|date=2004|title=A History of Japanese Mathematics|edition=paperback|publisher=Dover Publications|isbn=0-486-43482-6|url=https://archive.org/details/historyofjapanes00smitiala}}</ref> |
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|1706||[[John Machin]] |
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|align="right"|'''100 decimal places''' |
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|align="right"|11 <br />16 |
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|1699||[[Abraham Sharp]]<ref name="Bailey"/> |
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|1706||[[William Jones (mathematician)|William Jones]] introduced the Greek letter '[[Pi (letter)|π]]'|| |
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|Calculated pi to 72 digits, but not all were correct |
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|align="right"|'''71''' |
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|1706||[[John Machin]]<ref name="Bailey"/> |
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|1730||[[Kamata]] |
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|align="right"|25 decimal places |
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|align="right"|'''100''' |
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|1706||[[William Jones (mathematician)|William Jones]] |
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|1719||[[Thomas Fantet de Lagny]] calculated 127 decimal places, but not all were correct |
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|Introduced the Greek letter '[[Pi (letter)|{{pi}}]]' |
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|align="right"|'''112 decimal places''' |
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|1719||[[Thomas Fantet de Lagny]]<ref name="Bailey"/> |
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|1723||[[Takebe]] |
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|Calculated 127 decimal places, but not all were correct |
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|align="right"|'''112''' |
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|1721||Anonymous |
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|1739||[[Matsunaga Ryohitsu]] |
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|Calculation made in [[Philadelphia|Philadelphia, Pennsylvania]], giving the value of pi to 154 digits, 152 of which were correct. First discovered by [[Franz Xaver von Baader|F. X. von Zach]] in a library in Oxford, England in the 1780s, and reported to [[Jean-Étienne Montucla]], who published an account of it.<ref>Benjamin Wardhaugh, "Filling a Gap in the History of {{pi}}: An Exciting Discovery", ''Mathematical Intelligencer'' '''38'''(1) (2016), 6-7</ref> |
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|align="right"|50 decimal places |
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|align="right"|'''152''' |
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|1722||[[Toshikiyo Kamata]] |
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|1748||[[Leonhard Euler]] used the Greek letter 'π' in his book ''Introductio in Analysin Infinitorum'' and assured its popularity.|| |
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|align="right"|24 |
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|1722||[[Takebe Kenko|Katahiro Takebe]] |
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|1761||[[Johann Heinrich Lambert]] proved that π is [[irrational number|irrational]]|| |
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|align="right"|41 |
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|1739||[[Yoshisuke Matsunaga]] |
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|1775||Euler pointed out the possibility that π might be [[transcendental number|transcendental]]|| |
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|align="right"|51 |
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|1748||[[Leonhard Euler]] |
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|1794||[[Jurij Vega]] calculated 140 decimal places, but not all are correct |
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|Used the Greek letter '{{pi}}' in his book ''Introductio in Analysin Infinitorum'' and assured its popularity. |
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|align="right"|'''137 decimal places''' |
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|1761||[[Johann Heinrich Lambert]] |
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|1794||[[Adrien-Marie Legendre]] showed that π² (and hence π) is irrational, and mentioned the possibility that π might be transcendental.|| |
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|Proved that {{pi}} is [[irrational number|irrational]] |
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|1775||Euler |
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|1841||[[William Rutherford (mathematician)|William Rutherford]] calculated 208 decimal places, but not all were correct |
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|Pointed out the possibility that {{pi}} might be [[transcendental number|transcendental]] |
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|align="right"|'''152 decimal places''' |
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|1789||[[Jurij Vega]]<ref>{{cite journal |last=Vega |first=Géorge |year=1795 |orig-year=1789 |title=Detérmination de la demi-circonférence d'un cercle dont le diameter est {{math|{{=}} 1}}, exprimée en {{math|140}} figures decimals |journal=Nova Acta Academiae Scientiarum Petropolitanae |volume=11 |department=Supplement |pages=41–44 |url=https://archive.org/details/novaactaacademia09impe/page/n52/mode/2up}} |
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|1844||Zacharias Dase and Strassnitzky calculated 205 decimal places, but not all were correct |
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<p>{{cite web |last=Sandifer |first=Ed |year=2006 |title=Why 140 Digits of Pi Matter |website=Southern Connecticut State University |url=http://www.southernct.edu/~sandifer/Ed/History/Preprints/Talks/Jurij%20Vega/Vega%20math%20script.pdf |url-status=dead |archive-date=2012-02-04 |archive-url=https://web.archive.org/web/20120204040635/http://www.southernct.edu/~sandifer/Ed/History/Preprints/Talks/Jurij%20Vega/Vega%20math%20script.pdf }}</p></ref> |
|||
|align="right"|'''200 decimal places''' |
|||
|Calculated 140 decimal places, but not all were correct |
|||
|align="right"|126 |
|||
|- |
|- |
||
|1794||[[Adrien-Marie Legendre]] |
|||
|1847||Thomas Clausen calculated 250 decimal places, but not all were correct |
|||
|Showed that {{pi}}<sup>2</sup> (and hence {{pi}}) is irrational, and mentioned the possibility that {{pi}} might be transcendental. |
|||
|align="right"|'''248 decimal places''' |
|||
| |
|||
|- |
|- |
||
|1824||[[William Rutherford (mathematician)|William Rutherford]]<ref name="Bailey"/> |
|||
|1853||Lehmann |
|||
| |
|Calculated 208 decimal places, but not all were correct |
||
|align="right"|152 |
|||
|- |
|- |
||
|1844||[[Zacharias Dase]] and Strassnitzky<ref name="Bailey"/> |
|||
|1853||[[William Rutherford (mathematician)|William Rutherford]] |
|||
| |
|Calculated 205 decimal places, but not all were correct |
||
|align="right"|'''200''' |
|||
|- |
|- |
||
|1847||[[Thomas Clausen (mathematician)|Thomas Clausen]]<ref name="Bailey"/> |
|||
|1855||Richter |
|||
| |
|Calculated 250 decimal places, but not all were correct |
||
|align="right"|'''248''' |
|||
|- |
|- |
||
|1853||Lehmann<ref name="Bailey"/> |
|||
|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) |
|||
| |
|||
|align="right"|'''527 decimal places''' |
|||
|align="right"|'''261''' |
|||
|- |
|- |
||
|1853||Rutherford<ref name="Bailey"/> |
|||
|1882||[[Ferdinand von Lindemann|Lindemann]] proved that π is [[Transcendental numbers|transcendental]] (the [[Lindemann-Weierstrass theorem]])|| |
|||
| |
|||
|align="right"|'''440''' |
|||
|- |
|- |
||
|1853||[[William Shanks]]<ref>{{cite magazine |last=Hayes |first=Brian |url=https://www.americanscientist.org/article/pencil-paper-and-pi |title=Pencil, Paper, and Pi |volume=102 |issue=5 |page=342 |magazine=[[American Scientist]] |date=September 2014 |access-date=13 February 2022 |doi=10.1511/2014.110.342}}</ref> |
|||
|1897||The U.S. state of [[Indiana]] came close to legislating the value of 3.2 (among others) for π. [[Indiana Pi Bill|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.<ref>{{cite web|url=http://www.cs.uu.nl/wais/html/na-dir/sci-math-faq/indianabill.html|title=Indiana Bill sets value of Pi to 3|last=Lopez-Ortiz |first=Alex|date=February 20, 1998 |work=the news.answers WWW archive|publisher=Department of Information and Computing Sciences, Utrecht University|accessdate=2009-02-01}}</ref>|| |
|||
|Expanded his calculation to 707 decimal places in 1873, but an error introduced at the beginning of his new calculation rendered all of the subsequent digits invalid (the error was found by D. F. Ferguson in 1946). |
|||
|align="right"|'''527''' |
|||
|- |
|- |
||
|1882||[[Ferdinand von Lindemann]] |
|||
|1910||[[Srinivasa Ramanujan]] finds 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. |
|||
|Proved that {{pi}} is [[Transcendental numbers|transcendental]] (the [[Lindemann–Weierstrass theorem]]) |
|||
| |
|||
|- |
|||
|1897||The U.S. state of [[Indiana]] |
|||
|Came close to legislating the value 3.2 (among others) for {{pi}}. [[Indiana Pi Bill|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.<ref>{{cite web|url=http://www.cs.uu.nl/wais/html/na-dir/sci-math-faq/indianabill.html|title=Indiana Bill sets value of Pi to 3|last=Lopez-Ortiz|first=Alex|date=February 20, 1998|work=the news.answers WWW archive|publisher=Department of Information and Computing Sciences, Utrecht University|access-date=2009-02-01|archive-date=2005-01-09|archive-url=https://web.archive.org/web/20050109144036/http://www.cs.uu.nl/wais/html/na-dir/sci-math-faq/indianabill.html|url-status=dead}}</ref> |
|||
|align="right"|{{color|red|0}} |
|||
|- |
|||
|1910||[[Srinivasa Ramanujan]] |
|||
|Found several rapidly converging infinite series of {{pi}}, which can compute 8 decimal places of {{pi}} 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 {{pi}}. |
|||
| |
|||
|- |
|- |
||
|1946 |
|1946 |
||
|[[D. F. Ferguson]] |
|[[D. F. Ferguson]] |
||
|Made use of a desk calculator<ref name=":3">{{Cite book |last=Wells |first=D. G. |title=The Penguin Dictionary of Curious and Interesting Numbers |date=May 1, 1998 |publisher=Penguin Books |isbn=978-0140261493 |edition=Revised |pages=33}}</ref> |
|||
|align="right"|'''620 decimal places''' |
|||
|align="right"|'''620''' |
|||
|- |
|- |
||
|1947 |
|1947 |
||
|[[Ivan Niven]] |
|[[Ivan Niven]] |
||
|Gave a very [[Proof that π is irrational#Niven's proof|elementary proof that {{pi}} is irrational]] |
|||
| |
|||
|- |
|- |
||
|January 1947 |
|January 1947 |
||
|[[D. F. Ferguson]] |
|[[D. F. Ferguson]] |
||
|Made use of a desk calculator<ref name=":3" /> |
|||
|align="right"|'''710 decimal places''' |
|||
|align="right"|'''710''' |
|||
|- |
|- |
||
|September 1947 |
|September 1947 |
||
|[[D. F. Ferguson]] |
|[[D. F. Ferguson]] |
||
|Made use of a desk calculator<ref name=":3" /> |
|||
|align="right"|'''808 decimal places''' |
|||
|align="right"|'''808''' |
|||
|- |
|- |
||
|1949 |
|1949 |
||
|[[ |
|[[Levi B. Smith]] and [[John Wrench]] |
||
|Made use of a desk calculator |
|||
|align="right"|'''1,120 |
|align="right"|'''1,120''' |
||
|} |
|||
== 1949–2009 == |
|||
{| class="wikitable" |
|||
|- |
|- |
||
!align="left"| Date |
|||
|colspan="3" align="center"|''All records from 1949 onwards were calculated with electronic computers.'' |
|||
!align="left"| Who |
|||
!align="left"| Implementation |
|||
!align="left"| Time |
|||
!align="right"| Decimal places<br />{{nowrap| ([[world record]]s in '''bold''') }} |
|||
|- |
|- |
||
| colspan="5" style="text-align:center;background:lightblue;"|''All records from 1949 onwards were calculated with electronic computers.'' |
|||
|1949 |
|||
|[[John Wrench|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.) |
|||
|align="right"|'''2,037 decimal places''' |
|||
|- |
|- |
||
|September 1949 |
|||
|1953||[[Kurt Mahler]] showed that π is not a [[Liouville number]]|| |
|||
|G. W. Reitwiesner et al. |
|||
|The first to use an electronic computer (the [[ENIAC]]) to calculate {{pi}} <ref>{{cite journal |first=G. |last=Reitwiesner |title= An ENIAC determination of 𝜋 and 𝑒 to more than 2000 decimal places|journal= Mathematics of Computation|volume=4 |year=1950 |issue=29 |pages=11–15 |doi=10.1090/S0025-5718-1950-0037597-6 |doi-access=free }}</ref> |
|||
|70 hours |
|||
|align="right"|'''2,037''' |
|||
|- |
|||
|1953||[[Kurt Mahler]] |
|||
|Showed that {{pi}} is not a [[Liouville number]] |
|||
| |
|||
|align="right"| |
|||
|- |
|- |
||
|1954 |
|1954 |
||
|S. C. Nicholson & J. Jeenel |
|S. C. Nicholson & J. Jeenel |
||
|Using the [[IBM NORC|NORC]]<ref>{{cite journal |first1=S. C. |last1=Nicholson |first2=J. |last2=Jeenel |title= Some comments on a NORC computation of 𝜋|journal= Mathematics of Computation|volume=9 |year=1955 |issue=52 |pages=162–164 |doi=10.1090/S0025-5718-1955-0075672-5 |doi-access=free }}</ref> |
|||
|align="right"|'''3,092 decimal places''' |
|||
|13 minutes |
|||
|align="right"|'''3,093''' |
|||
|- |
|- |
||
|1957 |
|1957 |
||
|[[George E. Felton]] |
|||
|G. E. Felton, using the [[Ferranti]] [[PEGASUS (computer)|Pegasus computer]] (London) |
|||
|[[Ferranti]] [[PEGASUS (computer)|Pegasus computer]] (London), calculated 10,021 digits, but not all were correct<ref>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 <var>π</var> see {{cite journal |first=J. W. Jr. |last=Wrench |title=The evolution of extended decimal approximations to <var>π</var> |journal=The Mathematics Teacher |volume=53 |year=1960 |pages=644–650 |issue=8|doi=10.5951/MT.53.8.0644 |jstor=27956272 }}</ref><ref name=":2">{{Cite book |last1=Arndt |first1=Jörg |last2=Haenel |first2=Christoph |title=Pi - Unleashed |year=2001 |publisher=Springer |isbn=978-3-642-56735-3 |language=en}}</ref> |
|||
|align="right"|'''7,480 decimal places''' |
|||
|33 hours |
|||
|align="right"|'''7,480''' |
|||
|- |
|- |
||
|January 1958 |
|January 1958 |
||
|Francois Genuys |
|Francois Genuys |
||
|[[IBM 704]]<ref>{{cite journal |first=F. |last=Genuys |title=Dix milles decimales de <var>π</var> |journal=Chiffres |volume=1 |year=1958 |pages=17–22 }}</ref> |
|||
|align="right"|'''10,000 decimal places''' |
|||
|1.7 hours |
|||
|align="right"|'''10,000''' |
|||
|- |
|- |
||
|May 1958 |
|May 1958 |
||
| |
|[[George E. Felton]] |
||
|Pegasus computer (London) |
|||
|33 hours |
|||
|align="right"|'''10, |
|align="right"|'''10,021''' |
||
|- |
|- |
||
|1959 |
|1959 |
||
|Francois Genuys |
|Francois Genuys |
||
|IBM 704 (Paris)<ref>This unpublished value of ''x'' to 16167D was computed on an IBM 704 system at the [[French Alternative Energies and Atomic Energy Commission]] in Paris, by means of the program of Genuys</ref> |
|||
|align="right"|'''16,167 decimal places''' |
|||
|4.3 hours |
|||
|align="right"|'''16,167''' |
|||
|- |
|- |
||
|1961 |
|1961 |
||
|[[ |
|[[Daniel Shanks]] and [[John Wrench]] |
||
|[[IBM 7090]] (New York)<ref name="Calculation of Pi to 100,000 Decimals in the journal Mathematics of Computation, vol 16 (1962), issue 77, pages 76–99.">{{cite journal |first1=Daniel |last1=Shanks |first2=John W. J.r |last2=Wrench |title=Calculation of <var>π</var> to 100,000 decimals |journal=[[Mathematics of Computation]] |volume=16 |year=1962 |issue=77 |pages=76–99 |doi=10.1090/S0025-5718-1962-0136051-9 |doi-access=free }}</ref> |
|||
|align="right"|'''20,000 decimal places''' |
|||
|8.7 hours |
|||
|align="right"|'''100,265''' |
|||
|- |
|- |
||
|1961 |
|1961 |
||
|J.M. Gerard |
|||
|[[Daniel Shanks]] and [[John Wrench]], using the [[IBM 7090]] (New York) (8.7 hours) |
|||
|[[IBM 7090]] (London) |
|||
|align="right"|'''100,265 decimal places''' |
|||
|39 minutes |
|||
|align="right"|20,000 |
|||
|- |
|- |
||
|1966 |
|February 1966 |
||
|Jean Guilloud and J. Filliatre |
|Jean Guilloud and J. Filliatre |
||
|[[IBM 7030]] (Paris)<ref name=":2" /> |
|||
|41.92 hours |
|||
|align="right"|'''250,000 |
|align="right"|'''250,000''' |
||
|- |
|- |
||
|1967 |
|1967 |
||
|Jean Guilloud and M. Dichampt |
|Jean Guilloud and M. Dichampt |
||
|[[CDC 6600]] (Paris) |
|||
|28 hours |
|||
|align="right"|'''500,000 |
|align="right"|'''500,000''' |
||
|- |
|- |
||
|1973 |
|1973 |
||
|Jean Guilloud and |
|Jean Guilloud and Martine Bouyer |
||
|[[CDC 7600]] |
|||
|23.3 hours |
|||
|align="right"|'''1,001,250 decimal places''' |
|||
|align="right"|'''1,001,250''' |
|||
|- |
|- |
||
|1981 |
|1981 |
||
|[[ |
|[[Kazunori Miyoshi]] and [[Yasumasa Kanada]] |
||
|[[FACOM M-200]]<ref name=":2" /> |
|||
|align="right"|'''2,000,036 decimal places''' |
|||
|137.3 hours |
|||
|align="right"|'''2,000,036''' |
|||
|- |
|- |
||
|1981 |
|1981 |
||
|Jean Guilloud |
|Jean Guilloud |
||
|Not known |
|||
| |
|||
|align="right"|'''2,000,050 decimal places''' |
|||
|align="right"|'''2,000,050''' |
|||
|- |
|- |
||
|1982 |
|1982 |
||
|[[Yoshiaki Tamura]] |
|[[Yoshiaki Tamura]] |
||
|[[MELCOM 900II]]<ref name=":2" /> |
|||
|7.23 hours |
|||
|align="right"|'''2,097,144 decimal places''' |
|||
|align="right"|'''2,097,144''' |
|||
|- |
|- |
||
|1982 |
|1982 |
||
| |
|[[Yoshiaki Tamura]] and [[Yasumasa Kanada]] |
||
|[[HITAC M-280H]]<ref name=":2" /> |
|||
|align="right"|'''4,194,288 decimal places''' |
|||
|2.9 hours |
|||
|align="right"|'''4,194,288''' |
|||
|- |
|- |
||
|1982 |
|1982 |
||
| |
|[[Yoshiaki Tamura]] and [[Yasumasa Kanada]] |
||
|[[HITAC M-280H]]<ref name=":2" /> |
|||
|align="right"|'''8,388,576 decimal places''' |
|||
|6.86 hours |
|||
|align="right"|'''8,388,576''' |
|||
|- |
|- |
||
|1983 |
|1983 |
||
|[[Yasumasa Kanada]], |
|[[Yasumasa Kanada]], Sayaka Yoshino and [[Yoshiaki Tamura]] |
||
|[[HITAC M-280H]]<ref name=":2" /> |
|||
|align="right"|'''16,777,206 decimal places''' |
|||
|<30 hours |
|||
|align="right"|'''16,777,206''' |
|||
|- |
|- |
||
|October 1983 |
|October 1983 |
||
|[[ |
|[[Yasunori Ushiro]] and [[Yasumasa Kanada]] |
||
|[[HITAC S-810|HITAC S-810/20]] |
|||
|align="right"|10,013,395 decimal places |
|||
| |
|||
|align="right"|10,013,395 |
|||
|- |
|- |
||
|October 1985 |
|October 1985 |
||
| |
|[[Bill Gosper]] |
||
|[[Symbolics 3670]] |
|||
| |
|||
|align="right"|'''17,526,200 decimal places''' |
|||
|align="right"|'''17,526,200''' |
|||
|- |
|- |
||
|January 1986 |
|January 1986 |
||
|David H. Bailey |
|[[David H. Bailey (mathematician)|David H. Bailey]] |
||
|[[CRAY-2]]<ref name=":2" /> |
|||
|align="right"|'''29,360,111 decimal places''' |
|||
|28 hours |
|||
|align="right"|'''29,360,111''' |
|||
|- |
|- |
||
|September 1986 |
|September 1986 |
||
|[[Yasumasa Kanada]], [[Yoshiaki Tamura |
|[[Yasumasa Kanada]], [[Yoshiaki Tamura]] |
||
|[[HITAC S-810|HITAC S-810/20]]<ref name=":2" /> |
|||
|align="right"|'''33,554,414 decimal places''' |
|||
|6.6 hours |
|||
|align="right"|'''33,554,414''' |
|||
|- |
|- |
||
|October 1986 |
|October 1986 |
||
|[[Yasumasa Kanada]], [[Yoshiaki Tamura |
|[[Yasumasa Kanada]], [[Yoshiaki Tamura]] |
||
|[[HITAC S-810|HITAC S-810/20]]<ref name=":2" /> |
|||
|align="right"|'''67,108,839 decimal places''' |
|||
|23 hours |
|||
|align="right"|'''67,108,839''' |
|||
|- |
|- |
||
|January 1987 |
|January 1987 |
||
|[[Yasumasa Kanada]], [[Yoshiaki Tamura]], [[Yoshinobu Kubo]] |
|[[Yasumasa Kanada]], [[Yoshiaki Tamura]], [[Yoshinobu Kubo]] and others |
||
|[[NEC SX-2]]<ref name=":2" /> |
|||
|align="right"|'''134,214,700 decimal places''' |
|||
|35.25 hours |
|||
|align="right"|'''134,214,700''' |
|||
|- |
|- |
||
|January 1988 |
|January 1988 |
||
|[[Yasumasa Kanada]] and [[Yoshiaki Tamura |
|[[Yasumasa Kanada]] and [[Yoshiaki Tamura]] |
||
|[[HITAC S-820|HITAC S-820/80]]<ref>{{Cite book |last=Kanada |first=Y. |title=Proceedings Supercomputing Vol.II: Science and Applications |chapter=Vectorization of multiple-precision arithmetic program and 201,326,000 decimal digits of pi calculation |date=November 1988 |chapter-url=https://ieeexplore.ieee.org/document/74139 |pages=117–128 vol.2 |doi=10.1109/SUPERC.1988.74139|isbn=0-8186-8923-4 |s2cid=122820709 }}</ref> |
|||
|align="right"|'''201,326,551 decimal places''' |
|||
|5.95 hours |
|||
|align="right"|'''201,326,551''' |
|||
|- |
|- |
||
|May 1989 |
|May 1989 |
||
|[[Chudnovsky brothers|Gregory V. Chudnovsky & David V. Chudnovsky]] |
|[[Chudnovsky brothers|Gregory V. Chudnovsky & David V. Chudnovsky]] |
||
|[[CRAY-2]] & [[IBM 3090/VF]] |
|||
| |
|||
|align="right"|'''480,000,000 decimal places''' |
|||
|align="right"|'''480,000,000''' |
|||
|- |
|- |
||
|June 1989 |
|June 1989 |
||
|[[Chudnovsky brothers|Gregory V. Chudnovsky & David V. Chudnovsky]] |
|[[Chudnovsky brothers|Gregory V. Chudnovsky & David V. Chudnovsky]] |
||
|[[IBM 3090]] |
|||
| |
|||
|align="right"|'''535,339,270 decimal places''' |
|||
|align="right"|'''535,339,270''' |
|||
|- |
|- |
||
|July 1989 |
|July 1989 |
||
|[[Yasumasa Kanada]] and [[Yoshiaki Tamura]] |
|[[Yasumasa Kanada]] and [[Yoshiaki Tamura]] |
||
|[[HITAC S-820|HITAC S-820/80]] |
|||
| |
|||
|align="right"|'''536,870,898 decimal places''' |
|||
|align="right"|'''536,870,898''' |
|||
|- |
|- |
||
|August 1989 |
|August 1989 |
||
|[[Chudnovsky brothers|Gregory V. Chudnovsky & David V. Chudnovsky]] |
|[[Chudnovsky brothers|Gregory V. Chudnovsky & David V. Chudnovsky]] |
||
|[[IBM 3090]] |
|||
| |
|||
|align="right"|'''1,011,196,691 decimal places''' |
|||
|align="right"|'''1,011,196,691''' |
|||
|- |
|- |
||
|November 1989 |
|19 November 1989 |
||
|[[Yasumasa Kanada]] and [[Yoshiaki Tamura |
|[[Yasumasa Kanada]] and [[Yoshiaki Tamura]] |
||
|[[HITAC S-820|HITAC S-820/80]]<ref name=":1">{{cite web |title=Computers |url=https://www.sciencenews.org/archive/computers-25 |access-date=2022-08-04 |website=Science News |date=24 August 1991 |language=en-US}}</ref> |
|||
|align="right"|'''1,073,740,799 decimal places''' |
|||
| |
|||
|align="right"|'''1,073,740,799''' |
|||
|- |
|- |
||
|August 1991 |
|August 1991 |
||
|[[Chudnovsky brothers|Gregory V. Chudnovsky & David V. Chudnovsky]] |
|[[Chudnovsky brothers|Gregory V. Chudnovsky & David V. Chudnovsky]] |
||
|Homemade parallel computer (details unknown, not verified) <ref>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</ref><ref name=":1" /> |
|||
|align="right"|2,260,000,000 decimal places |
|||
| |
|||
|align="right"|'''2,260,000,000''' |
|||
|- |
|- |
||
|May 1994 |
|18 May 1994 |
||
|[[Chudnovsky brothers|Gregory V. Chudnovsky & David V. Chudnovsky]] |
|[[Chudnovsky brothers|Gregory V. Chudnovsky & David V. Chudnovsky]] |
||
|New homemade parallel computer (details unknown, not verified) |
|||
| |
|||
|align="right"|4,044,000,000 decimal places |
|||
|align="right"|'''4,044,000,000''' |
|||
|- |
|- |
||
|June 1995 |
|26 June 1995 |
||
|[[Yasumasa Kanada]] and [[Daisuke Takahashi (mathematician) |
|[[Yasumasa Kanada]] and [[Daisuke Takahashi (mathematician)|Daisuke Takahashi]] |
||
|[[HITAC S-3000|HITAC S-3800/480]] (dual CPU) <ref>ftp://pi.super-computing.org/README.our_last_record_3b{{Dead link|date=March 2022 |bot=InternetArchiveBot |fix-attempted=yes }}</ref> |
|||
|align="right"|'''3,221,220,000 decimal places''' |
|||
| |
|||
|align="right"|3,221,220,000 |
|||
|- |
|- |
||
| |
|1995 |
||
|[[Simon Plouffe]] |
|||
|[[Yasumasa Kanada]] and [[Daisuke Takahashi (mathematician)]], [[HITAC S-3800/480]] (dual CPU) |
|||
|Finds a [[Bailey–Borwein–Plouffe formula|formula]] that allows the {{var|n}}th hexadecimal digit of pi to be calculated without calculating the preceding digits. |
|||
|align="right"|'''4,294,960,000 decimal places''' |
|||
| |
|||
| |
|||
|- |
|- |
||
| |
|28 August 1995 |
||
|[[Yasumasa Kanada]] and [[Daisuke Takahashi (mathematician) |
|[[Yasumasa Kanada]] and [[Daisuke Takahashi (mathematician)|Daisuke Takahashi]] |
||
|[[HITAC S-3000|HITAC S-3800/480]] (dual CPU) <ref>ftp://pi.super-computing.org/README.our_last_record_4b{{Dead link|date=March 2022 |bot=InternetArchiveBot |fix-attempted=yes }}</ref><ref name=":0">{{cite web |title=GENERAL COMPUTATIONAL UPDATE |url=http://www.cecm.sfu.ca/organics/papers/borwein/paper/html/local/general/html/node1.html |access-date=2022-08-04 |website=www.cecm.sfu.ca}}</ref> |
|||
|align="right"|'''6,442,450,000 decimal places''' |
|||
|56.74 hours? |
|||
|align="right"|'''4,294,960,000''' |
|||
|- |
|- |
||
|11 October 1995 |
|||
|June 1997 |
|||
|[[Yasumasa Kanada]] and [[Daisuke Takahashi (mathematician) |
|[[Yasumasa Kanada]] and [[Daisuke Takahashi (mathematician)|Daisuke Takahashi]] |
||
|[[HITAC S-3000|HITAC S-3800/480]] (dual CPU) <ref>ftp://pi.super-computing.org/README.our_last_record_6b{{Dead link|date=December 2023 |bot=InternetArchiveBot |fix-attempted=yes }}</ref><ref name=":0" /> |
|||
|align="right"|'''51,539,600,000 decimal places''' |
|||
|116.63 hours |
|||
|align="right"|'''6,442,450,000''' |
|||
|- |
|- |
||
|6 July 1997 |
|||
|April 1999 |
|||
|[[Yasumasa Kanada]] and [[Daisuke Takahashi (mathematician) |
|[[Yasumasa Kanada]] and [[Daisuke Takahashi (mathematician)|Daisuke Takahashi]] |
||
|[[HITACHI SR2201]] (1024 CPU) <ref>ftp://pi.super-computing.org/README.our_last_record_51b{{Dead link|date=March 2022 |bot=InternetArchiveBot |fix-attempted=yes }}</ref><ref>{{cite web |date=2005-12-24 |title=Record for pi : 51.5 billion decimal digits |url=http://oldweb.cecm.sfu.ca/personal/jborwein/Kanada_50b.html |access-date=2022-08-04 |archive-url=https://web.archive.org/web/20051224015531/http://oldweb.cecm.sfu.ca/personal/jborwein/Kanada_50b.html |archive-date=2005-12-24 }}</ref> |
|||
|align="right"|'''68,719,470,000 decimal places''' |
|||
|29.05 hours |
|||
|align="right"|'''51,539,600,000''' |
|||
|- |
|- |
||
| |
|5 April 1999 |
||
|[[Yasumasa Kanada]] and [[Daisuke Takahashi (mathematician) |
|[[Yasumasa Kanada]] and [[Daisuke Takahashi (mathematician)|Daisuke Takahashi]] |
||
|[[HITACHI SR8000]] (64 of 128 nodes) <ref>ftp://pi.super-computing.org/README.our_last_record_68b{{Dead link|date=March 2022 |bot=InternetArchiveBot |fix-attempted=yes }}</ref><ref>{{cite web |last1=Kanada |first1=Yasumasa |title=plouffe.fr/simon/constants/Pi68billion.txt |url=https://www.plouffe.fr/simon/constants/Pi68billion.txt |website=www.plouffe.fr |archive-url=https://web.archive.org/web/20220805103137/https://www.plouffe.fr/simon/constants/Pi68billion.txt |archive-date=5 August 2022 |language=en |url-status=live}}</ref> |
|||
|align="right"|'''206,158,430,000 decimal places''' |
|||
|32.9 hours |
|||
|align="right"|'''68,719,470,000''' |
|||
|- |
|- |
||
|20 September 1999 |
|||
|December 2002 |
|||
|[[Yasumasa Kanada]] |
|[[Yasumasa Kanada]] and [[Daisuke Takahashi (mathematician)|Daisuke Takahashi]] |
||
|[[HITACHI SR8000/MPP]] (128 nodes) <ref>ftp://pi.super-computing.org/README.our_latest_record_206b{{Dead link|date=March 2022 |bot=InternetArchiveBot |fix-attempted=yes }}</ref><ref>{{cite web |title=Record for pi : 206 billion decimal digits |url=http://www.cecm.sfu.ca/~jborwein/Kanada_200b.html |access-date=2022-08-04 |website=www.cecm.sfu.ca}}</ref> |
|||
|align="right"|'''1,241,100,000,000 decimal places''' |
|||
|37.35 hours |
|||
|align="right"|'''206,158,430,000''' |
|||
|- |
|- |
||
|24 November 2002 |
|||
|April 2009 |
|||
|[[Yasumasa Kanada]] & 9 man team |
|||
|[[Daisuke Takahashi (mathematician)]] et al., [[T2K Open Supercomputer]] (640 nodes), 73 hours, 36 minutes<ref>http://gizmodo.com/5339831/pi-calculation-record-destroyed-25-trillion-decimals</ref> |
|||
|[[HITACHI SR8000/MPP]] (64 nodes), Department of Information Science at the [[University of Tokyo]] in [[Tokyo]], [[Japan]]<ref>{{cite web |url=http://www.super-computing.org/pi_current.html |title=Archived copy |access-date=2010-07-08 |archive-url=https://web.archive.org/web/20110312035524/http://www.super-computing.org/pi_current.html |archive-date=2011-03-12 |url-status=dead }}</ref> |
|||
|align="right"|'''2,576,980,377,524 decimal places''' |
|||
|600 hours |
|||
|align="right"|'''1,241,100,000,000''' |
|||
|- |
|||
|29 April 2009 |
|||
|[[Daisuke Takahashi (mathematician)|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]]<ref>{{cite web |url=http://www.hpcs.is.tsukuba.ac.jp/~daisuke/pi.html |title=Archived copy |access-date=2009-08-18 |archive-url=https://web.archive.org/web/20090823020534/http://www.hpcs.is.tsukuba.ac.jp/~daisuke/pi.html |archive-date=2009-08-23 |url-status=dead }}</ref> |
|||
|29.09 hours |
|||
|align="right"|'''2,576,980,377,524''' |
|||
|} |
|||
==2009–present== |
|||
{| class="wikitable" |
|||
|- |
|||
!align="left"| Date |
|||
!align="left"| Who |
|||
!align="left"| Implementation |
|||
!align="left"| Time |
|||
!align="right"| Decimal places<br />{{nowrap| ([[world record]]s in '''bold''') }} |
|||
|- |
|||
| colspan="5" style="text-align:center;background:lightblue;"|''All records from Dec 2009 onwards are calculated and verified on commodity [[x86]] computers with commercially available parts. All use the [[Chudnovsky algorithm]] for the main computation, and [[Bellard's formula]], the [[Bailey–Borwein–Plouffe formula]], or both for verification.'' |
|||
|- |
|||
|31 December 2009 |
|||
|[[Fabrice Bellard]]<ref>{{cite web |last=Bellard |first=Fabrice |authorlink=Fabrice Bellard |title=Computation of 2700 billion decimal digits of Pi using a Desktop Computer |date=11 Feb 2010 |version=4th revision |url=https://bellard.org/pi/pi2700e9/pipcrecord.pdf |language=en |s2cid=12242318}}</ref><ref>{{Cite web |title=TachusPI |url=https://bellard.org/pi/pi2700e9/tpi.html |access-date=2024-10-10 |website=bellard.org}}</ref> |
|||
| |
|||
* Computation: Intel Core i7 @ 2.93 GHz (4 cores, 6 GiB DDR3-1066 RAM) |
|||
* Storage: 7.5 TB (5x 1.5 TB) |
|||
* Red Hat Fedora 10 (x64) |
|||
* Computation of the binary digits (Chudnovsky algorithm): 103 days |
|||
* Verification of the binary digits (Bellard's formula): 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. |
|||
|131 days |
|||
|align="right"|'''2,699,999,990,000'''<br /> = {{val|2.7|e=12}} − {{val|e=4}} |
|||
|- |
|||
|2 August 2010 |
|||
|Shigeru Kondo<ref>{{cite web|url=http://piworld.calico.jp/estart.html|title=PI-world|work=calico.jp|access-date=28 August 2015|archive-url=https://web.archive.org/web/20150831180053/http://piworld.calico.jp/estart.html|archive-date=31 August 2015|url-status=dead}}</ref> |
|||
| |
|||
* using [[y-cruncher]]<ref>{{cite web|url=http://www.numberworld.org/y-cruncher/|title=y-cruncher – A Multi-Threaded Pi Program|work=numberworld.org|access-date=28 August 2015}}</ref> 0.5.4 by Alexander Yee |
|||
* with 2× Intel Xeon X5680 @ 3.33 GHz – (12 physical cores, 24 hyperthreaded) |
|||
* 96 GiB DDR3 @ 1066 MHz – (12× 8 GiB – 6 channels) – Samsung (M393B1K70BH1) |
|||
* 1 TB SATA II (Boot drive) – Hitachi (HDS721010CLA332), 3× 2 TB SATA II (Store Pi Output) – Seagate (ST32000542AS) 16× 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 (Bellard formula), 66 hours (BBP formula) |
|||
* Verification of the binary digits were done simultaneously on two separate computers during the main computation. Both computed 32 hexadecimal digits ending with the 4,152,410,118,610th.<ref>{{cite web|url=http://www.numberworld.org/misc_runs/pi-5t/announce_en.html|title=Pi – 5 Trillion Digits|work=numberworld.org|access-date=28 August 2015}}</ref> |
|||
|90 days |
|||
|align="right"|'''5,000,000,000,000'''<br /> = {{val|5|e=12}} |
|||
|- |
|||
|17 October 2011 |
|||
|Shigeru Kondo<ref>{{cite web|url=http://www.numberworld.org/misc_runs/pi-10t/details.html|title=Pi – 10 Trillion Digits|work=numberworld.org|access-date=28 August 2015}}</ref> |
|||
| |
|||
* using [[y-cruncher]] 0.5.5 |
|||
* with 2× Intel Xeon X5680 @ 3.33 GHz – (12 physical cores, 24 hyperthreaded) |
|||
* 96 GiB DDR3 @ 1066 MHz – (12× 8 GiB – 6 channels) – Samsung (M393B1K70BH1) |
|||
* 1 TB SATA II (Boot drive) – Hitachi (HDS721010CLA332), 5× 2 TB SATA II (Store Pi Output), 24× 2 TB SATA II (Computation) |
|||
* Windows Server 2008 R2 Enterprise (x64) |
|||
* Verification: 1.86 days (Bellard formula) and 4.94 days (BBP formula) |
|||
|371 days |
|||
|align="right"|'''10,000,000,000,050'''<br /> = {{val|e=13}} + 50 |
|||
|- |
|||
|28 December 2013 |
|||
|Shigeru Kondo<ref>{{cite web|url=http://www.numberworld.org/misc_runs/pi-12t/|title=Pi – 12.1 Trillion Digits|work=numberworld.org|access-date=28 August 2015}}</ref> |
|||
| |
|||
* using [[y-cruncher]] 0.6.3 |
|||
* Computation: 2× Intel Xeon E5-2690 @ 2.9 GHz – (32 cores, 128 GiB DDR3-1600 RAM) |
|||
* Storage: 97 TB (32x 3 TB, 1x 1 TB) |
|||
* Windows Server 2012 (x64) |
|||
* Verification using Bellard's formula: 46 hours |
|||
|94 days |
|||
|align="right"|'''12,100,000,000,050'''<br /> = {{val|1.21|e=13}} + 50 |
|||
|- |
|||
|8 October 2014 |
|||
|Sandon Nash Van Ness "houkouonchi"<ref>{{cite web |url=http://www.numberworld.org/digits/Pi/ |title=Pi: Notable large computations |work=numberworld.org |access-date=16 March 2024}}</ref> |
|||
| |
|||
* using [[y-cruncher]] 0.6.3 |
|||
* Computation: 2× Xeon E5-4650L @ 2.6 GHz (16 cores, 192 GiB DDR3-1333 RAM) |
|||
* Storage: 186 TB (24× 4 TB + 30× 3 TB) |
|||
* Verification using Bellard's formula: 182 hours |
|||
|208 days |
|||
|align="right"|'''13,300,000,000,000'''<br /> = {{val|1.33|e=13}} |
|||
|- |
|||
|11 November 2016 |
|||
|Peter Trueb<ref>{{cite web|url=http://pi2e.ch/|title=pi2e|work=pi2e.ch|access-date=15 November 2016}}</ref><ref>{{cite web |url=http://www.numberworld.org/digits/Pi/ |title=Pi: Notable large computations |work=numberworld.org |access-date=16 March 2024}}</ref> |
|||
| |
|||
* using [[y-cruncher]] 0.7.1 |
|||
* Computation: 4× Xeon E7-8890 v3 @ 2.50 GHz (72 cores, 1.25 TiB DDR4 RAM) |
|||
* Storage: 120 TB (20× 6 TB) |
|||
* Linux (x64) |
|||
* Verification using Bellard's formula: 28 hours<ref>{{cite web|url=http://pi2e.ch/blog/2016/10/31/hexadecimal-digits-are-correct/|title=Hexadecimal Digits are Correct! – pi2e trillion digits of pi|work=pi2e.ch|date=31 October 2016|access-date=15 November 2016}}</ref> |
|||
|105 days |
|||
|align="right"|'''22,459,157,718,361'''<br />{{math|1== {{floor|''{{pi}}<sup>e</sup>''{{x10^|12}}}}}} |
|||
|- |
|||
|14 March 2019 |
|||
|[[Emma Haruka Iwao]]<ref>{{cite web|url=http://www.numberworld.org/blogs/2019_3_14_pi_record/|title=Google Cloud Topples the Pi Record|access-date=14 March 2019}}</ref> |
|||
| |
|||
* using [[y-cruncher]] v0.7.6 |
|||
* Computation: 1× n1-megamem-96 (96 vCPU, 1.4 TB) with 30 TB of SSD |
|||
* Storage: 24× n1-standard-16 (16 vCPU, 60 GB) with 10 TB of SSD |
|||
* Windows Server 2016 (x64) |
|||
* Verification: 20 hours using Bellard's 7-term formula, and 28 hours using Plouffe's 4-term formula |
|||
|121 days |
|||
|align="right"|'''31,415,926,535,897'''<br />{{math|1== {{floor|''{{pi}}''{{x10^|13}}}}}} |
|||
|- |
|||
|29 January 2020 |
|||
|Timothy Mullican<ref>{{cite web|url=http://numberworld.org/y-cruncher/news/2020.html#2020_1_29|title=The Pi Record Returns to the Personal Computer|access-date=30 January 2020}}</ref><ref>{{cite web|url=https://blog.timothymullican.com/calculating-pi-my-attempt-breaking-pi-record|title=Calculating Pi: My attempt at breaking the Pi World Record|date=26 June 2019|access-date=30 January 2020}}</ref> |
|||
| |
|||
* using [[y-cruncher]] v0.7.7 |
|||
* Computation: 4× Intel Xeon CPU E7-4880 v2 @ 2.5 GHz (60 cores, 320 GB DDR3-1066 RAM) |
|||
* Storage: 406.5 TB – 48× 6 TB HDDs (Computation) + 47× LTO Ultrium 5 1.5 TB Tapes (Checkpoint Backups) + 12× 4 TB HDDs (Digit Storage) |
|||
* Ubuntu 18.10 (x64) |
|||
* Verification: 17 hours using Bellard's 7-term formula, 24 hours using Plouffe's 4-term formula |
|||
|303 days |
|||
|align="right"|'''50,000,000,000,000'''<br /> = {{val|5|e=13}} |
|||
|- |
|||
|14 August 2021 |
|||
|Team DAViS of the [[University of Applied Sciences of Eastern Switzerland|University of Applied Sciences of the Grisons]]<ref>{{cite web|date=2021-08-14|title=Pi-Challenge - world record attempt by UAS Grisons - University of Applied Sciences of the Grisons|url=https://www.fhgr.ch/en/specialist-areas/applied-future-technologies/davis-centre/pi-challenge/|url-status=dead|access-date=2021-08-17|website=www.fhgr.ch|archive-url=https://web.archive.org/web/20210817040515/https://www.fhgr.ch/en/specialist-areas/applied-future-technologies/davis-centre/pi-challenge/ |archive-date=2021-08-17 }}</ref><ref>{{cite web|date=2021-08-16|title=Die FH Graubünden kennt Pi am genauesten – Weltrekord! - News - FH Graubünden|url=https://www.fhgr.ch/news/newsdetail/die-fh-graubuenden-kennt-pi-am-genauesten-weltrekord/|url-status=live|access-date=2021-08-17|website=www.fhgr.ch|language=de|archive-url=https://web.archive.org/web/20210817060326/https://www.fhgr.ch/news/newsdetail/die-fh-graubuenden-kennt-pi-am-genauesten-weltrekord/ |archive-date=2021-08-17 }}</ref> |
|||
| |
|||
* using [[y-cruncher]] v0.7.8 |
|||
* Computation: AMD Epyc 7542 @ 2.9 GHz (32 cores, 1 TiB RAM) |
|||
* Storage: 608 TB (38× 16 TB HDDs, 34 are used for [[Swapping (computing)|swapping]] and 4 used for storage) |
|||
* Ubuntu 20.04 (x64) |
|||
* Verification using the 4-term BBP formula: 34 hours |
|||
|108 days |
|||
|align="right"|'''62,831,853,071,796'''<br />{{math|1== {{ceil|2''{{pi}}''{{x10^|13}}}}}} |
|||
|- |
|||
|21 March 2022 |
|||
|[[Emma Haruka Iwao]]<ref>{{cite web |title=Calculating 100 trillion digits of pi on Google Cloud |url=https://cloud.google.com/blog/products/compute/calculating-100-trillion-digits-of-pi-on-google-cloud/ |access-date=2022-06-10 |website=Google Cloud Blog |language=en}}</ref><ref>{{cite web |title=100 Trillion Digits of Pi |url=http://numberworld.org/y-cruncher/news/2022.html#2022_6_8 |access-date=2022-06-10 |website=numberworld.org}}</ref> |
|||
| |
|||
* using [[y-cruncher]] v0.7.8 |
|||
* Computation: n2-highmem-128 (128 vCPU and 864 GB RAM) |
|||
* Storage: 663 TB |
|||
* Debian Linux 11 (x64) |
|||
* Verification: 12.6 hours using BBP formula |
|||
|158 days |
|||
|align="right"|'''100,000,000,000,000'''<br /> = {{val|e=14}} |
|||
|- |
|||
|18 April 2023 |
|||
|Jordan Ranous<ref>{{cite web |title=StorageReview Calculated 100 Trillion Digits of Pi in 54 days, Besting Google Cloud |url=https://www.storagereview.com/review/storagereview-calculated-100-trillion-digits-of-pi-in-54-days-besting-google-cloud |access-date=2023-12-02 |website=storagereview.com |language=en}}</ref><ref>{{cite web |title=The Need for Speed! |date=19 April 2023 |url=http://www.numberworld.org/y-cruncher/news/2023.html#2023_4_19 |access-date=2023-12-25 |website=numberworld.org}}</ref> |
|||
| |
|||
* using [[y-cruncher]] v0.7.10 |
|||
* Computation: 2 x AMD EPYC 9654 @ 2.4 GHz (96 cores, 1.5 TiB RAM) |
|||
* Storage: 583 TB (19× 30.72 TB) |
|||
* Windows Server 2022 (x64) |
|||
|59 days |
|||
|align="right"|100,000,000,000,000<br /> = {{val|e=14}} |
|||
|- |
|||
|14 March 2024 |
|||
|Jordan Ranous, Kevin O’Brien and Brian Beeler<ref>{{Cite web |last=Ranous |first=Jordan |date=2024-03-13 |title=105 Trillion Pi Digits: The Journey to a New Pi Calculation Record |url=https://www.storagereview.com/review/breaking-records-storagereviews-105-trillion-digit-pi-calculation |access-date=2024-03-14 |website=StorageReview.com |language=en-US}}</ref><ref>{{Cite web |first=Alexander J. |last=Yee |date=2024-03-14 |title=Limping to a new Pi Record of 105 Trillion Digits |url=http://www.numberworld.org/y-cruncher/news/2024.html#2024_3_13 |website=NumberWorld.org |access-date=2024-03-16}}</ref> |
|||
| |
|||
* using [[y-cruncher]] v0.8.3 |
|||
* Computation: 2 x AMD EPYC 9754 @ 2.25 GHz (128 cores, 1.5 TiB RAM) |
|||
* Storage: 1,105 TB (36× 30.72 TB) |
|||
* Windows Server 2022 (x64) |
|||
|75 days |
|||
|align="right"|'''105,000,000,000,000'''<br /> = {{val|1.05|e=14}} |
|||
|- |
|||
|28 June 2024 |
|||
|Jordan Ranous, Kevin O’Brien and Brian Beeler<ref>{{Cite web |last=Ranous |first=Jordan |date=2024-06-28 |title=StorageReview Lab Breaks Pi Calculation World Record with Over 202 Trillion Digits |url=https://www.storagereview.com/news/storagereview-lab-breaks-pi-calculation-world-record-with-over-202-trillion-digits |access-date=2024-07-02 |website=StorageReview.com |language=en-US}}</ref><ref>{{Cite web |first=Alexander J. |last=Yee |date=2024-06-28 |title=Pi Record Smashed at 202 Trillion Digits |url=http://www.numberworld.org/y-cruncher/news/2024.html#2024_6_28 |website=NumberWorld.org |access-date=2024-06-30}}</ref> |
|||
| |
|||
* using [[y-cruncher]] v0.8.3 |
|||
* Computation: 2 x Intel Xeon Platinum 8592+ @ 1.9 GHz (128 cores, 1.0 TiB DDR5 RAM) |
|||
* Storage: 1.5 PB (28× 61.44 TB) |
|||
* Windows 10 (x64) |
|||
|104 days |
|||
|align="right"|'''202,112,290,000,000'''<br /> = {{val|2.0211229|e=14}} |
|||
|} |
|} |
||
==See also== |
==See also== |
||
* [[History of pi |
* [[History of pi]] |
||
*[[Approximations of π]] |
|||
==References== |
==References== |
||
{{Reflist}} |
{{Reflist|2}} |
||
==External links== |
==External links== |
||
* [http://www.cecm.sfu.ca/ |
* Borwein, Jonathan, "[http://www.cecm.sfu.ca/~jborwein/pi-slides.pdf The Life of Pi] {{Webarchive|url=https://web.archive.org/web/20061207191617/http://www.cecm.sfu.ca/~jborwein/pi-slides.pdf |date=2006-12-07 }}" |
||
* [https://web.archive.org/web/20110824110203/http://pi2.cc.u-tokyo.ac.jp/index.html Kanada Laboratory home page] |
|||
* [http://members.shaw.ca/francislyster/pi/supercomputer.html Stu's Pi page] |
|||
* [ |
* [https://web.archive.org/web/20160303221814/http://members.shaw.ca/francislyster/pi/supercomputer.html Stu's Pi page] |
||
* [https://web.archive.org/web/20090823020534/http://www.hpcs.is.tsukuba.ac.jp/~daisuke/pi.html Takahashi's page] |
|||
* [https://pi.delivery/ Google's web service making all 100 trillion digits available] |
|||
{{DEFAULTSORT:Chronology Of Computation Of Pi}} |
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[[Category:Pi]] |
[[Category:Pi]] |
||
[[Category:History of mathematics]] |
[[Category:History of mathematics]] |
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[[Category:Record progressions|Pi]] |
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[[Category:Pi algorithms]] |
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Latest revision as of 15:23, 16 December 2024
 | This article needs additional citations for verification. (October 2014) |
| Part of a series of articles on the |
| mathematical constant π |
|---|
| 3.1415926535897932384626433... |
| Uses |
| Properties |
| Value |
| People |
| History |
| In culture |
| Related topics |
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.
As of July 2024, π has been calculated to 202,112,290,000,000 (approximately 202 trillion) decimal digits. The last 100 decimal digits of the latest world record computation are:[1]
7034341087 5351110672 0525610978 1945263024 9604509887 5683914937 4658179610 2004394122 9823988073 3622511852
Before 1400
[edit]| Date | Who | Description/Computation method used | Value | Decimal places (world records in bold) |
|---|---|---|---|---|
| 2000? BC | Ancient Egyptians[2] | 4 × (8⁄9)2 | 3.1605... | 1 |
| 2000? BC | Ancient Babylonians[2] | 3 + 1⁄8 | 3.125 | 1 |
| 2000? BC | Ancient Sumerians[3] | 3 + 23/216 | 3.1065 | 1 |
| 1200? BC | Ancient Chinese[2] | 3 | 3 | 0 |
| 800–600 BC | Shatapatha Brahmana – 7.1.1.18 [4] | Instructions on how to construct a circular altar from oblong bricks:
"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."[5] |
25⁄8 = 3.125 | 1 |
| 800? BC | Shulba Sutras[6] | (6⁄(2 + √2))2 | 3.088311 ... | 0 |
| 550? BC | Bible (1 Kings 7:23)[2] | "...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 | 0 |
| 434 BC | Anaxagoras attempted to square the circle[9] | compass and straightedge | Anaxagoras did not offer a solution | 0 |
| 400 BC to AD 400 | Vyasa[10] |
verses: 6.12.40-45 of the Bhishma Parva of the Mahabharata offer: |
3 | 0 |
| c. 250 BC | Archimedes[2] | 223⁄71 < π < 22⁄7 | 3.140845... < π < 3.142857... | 2 |
| 15 BC | Vitruvius[7] | 25⁄8 | 3.125 | 1 |
| Between 1 BC and AD 5 | Liu Xin[7][11][12] | Unknown method giving a figure for a jialiang which implies a value for π ≈ 162⁄(√50+0.095)2. | 3.1547... | 1 |
| AD 130 | Zhang Heng (Book of the Later Han)[2] | √10 = 3.162277... 736⁄232 |
3.1622... | 1 |
| 150 | Ptolemy[2] | 377⁄120 | 3.141666... | 3 |
| 250 | Wang Fan[2] | 142⁄45 | 3.155555... | 1 |
| 263 | Liu Hui[2] | 3.141024 < π < 3.142074 3927⁄1250 |
3.1416 | 3 |
| 400 | He Chengtian[7] | 111035⁄35329 | 3.142885... | 2 |
| 480 | Zu Chongzhi[2] | 3.1415926 < π < 3.1415927 355⁄113 |
3.1415926 | 7 |
| 499 | Aryabhata[2] | 62832⁄20000 | 3.1416 | 3 |
| 640 | Brahmagupta[2] | √10 | 3.162277... | 1 |
| 800 | Al Khwarizmi[2] | 3.1416 | 3 | |
| 1150 | Bhāskara II[7] | 3927⁄1250 and 754⁄240 | 3.1416 | 3 |
| 1220 | Fibonacci[2] | 3.141818 | 3 | |
| 1320 | Zhao Youqin[7] | 3.141592 | 6 |
1400–1949
[edit]| 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[13] | 10 |
| 1424 | Jamshīd al-Kāshī[14] | 16 | |
| 1573 | Valentinus Otho | 355⁄113 | 6 |
| 1579 | François Viète[15] | 9 | |
| 1593 | Adriaan van Roomen[16] | 15 | |
| 1596 | Ludolph van Ceulen | 20 | |
| 1615 | 32 | ||
| 1621 | Willebrord Snell (Snellius) | Pupil of Van Ceulen | 35 |
| 1630 | Christoph Grienberger[17][18] | 38 | |
| 1654 | Christiaan Huygens | Used a geometrical method equivalent to Richardson extrapolation | 10 |
| 1665 | Isaac Newton[2] | 16 | |
| 1681 | Takakazu Seki[19] | 11 16 | |
| 1699 | Abraham Sharp[2] | Calculated pi to 72 digits, but not all were correct | 71 |
| 1706 | John Machin[2] | 100 | |
| 1706 | William Jones | Introduced the Greek letter 'π' | |
| 1719 | Thomas Fantet de Lagny[2] | Calculated 127 decimal places, but not all were correct | 112 |
| 1721 | Anonymous | Calculation made in Philadelphia, Pennsylvania, giving the value of pi to 154 digits, 152 of which were correct. First discovered by F. X. von Zach in a library in Oxford, England in the 1780s, and reported to Jean-Étienne Montucla, who published an account of it.[20] | 152 |
| 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[21] | Calculated 140 decimal places, but not all were correct | 126 |
| 1794 | Adrien-Marie Legendre | Showed that π2 (and hence π) is irrational, and mentioned the possibility that π might be transcendental. | |
| 1824 | William Rutherford[2] | Calculated 208 decimal places, but not all were correct | 152 |
| 1844 | Zacharias Dase and Strassnitzky[2] | Calculated 205 decimal places, but not all were correct | 200 |
| 1847 | Thomas Clausen[2] | Calculated 250 decimal places, but not all were correct | 248 |
| 1853 | Lehmann[2] | 261 | |
| 1853 | Rutherford[2] | 440 | |
| 1853 | William Shanks[22] | Expanded his calculation to 707 decimal places in 1873, but an error introduced at the beginning of his new calculation rendered all of the subsequent digits invalid (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.[23] | 0 |
| 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 | Made use of a desk calculator[24] | 620 |
| 1947 | Ivan Niven | Gave a very elementary proof that π is irrational | |
| January 1947 | D. F. Ferguson | Made use of a desk calculator[24] | 710 |
| September 1947 | D. F. Ferguson | Made use of a desk calculator[24] | 808 |
| 1949 | Levi B. Smith and John Wrench | Made use of a desk calculator | 1,120 |
1949–2009
[edit]| Date | Who | Implementation | Time | Decimal places (world records in bold) |
|---|---|---|---|---|
| All records from 1949 onwards were calculated with electronic computers. | ||||
| September 1949 | G. W. Reitwiesner et al. | The first to use an electronic computer (the ENIAC) to calculate π [25] | 70 hours | 2,037 |
| 1953 | Kurt Mahler | Showed that π is not a Liouville number | ||
| 1954 | S. C. Nicholson & J. Jeenel | Using the NORC[26] | 13 minutes | 3,093 |
| 1957 | George E. Felton | Ferranti Pegasus computer (London), calculated 10,021 digits, but not all were correct[27][28] | 33 hours | 7,480 |
| January 1958 | Francois Genuys | IBM 704[29] | 1.7 hours | 10,000 |
| May 1958 | George E. Felton | Pegasus computer (London) | 33 hours | 10,021 |
| 1959 | Francois Genuys | IBM 704 (Paris)[30] | 4.3 hours | 16,167 |
| 1961 | Daniel Shanks and John Wrench | IBM 7090 (New York)[31] | 8.7 hours | 100,265 |
| 1961 | J.M. Gerard | IBM 7090 (London) | 39 minutes | 20,000 |
| February 1966 | Jean Guilloud and J. Filliatre | IBM 7030 (Paris)[28] | 41.92 hours | 250,000 |
| 1967 | Jean Guilloud and M. Dichampt | CDC 6600 (Paris) | 28 hours | 500,000 |
| 1973 | Jean Guilloud and Martine Bouyer | CDC 7600 | 23.3 hours | 1,001,250 |
| 1981 | Kazunori Miyoshi and Yasumasa Kanada | FACOM M-200[28] | 137.3 hours | 2,000,036 |
| 1981 | Jean Guilloud | Not known | 2,000,050 | |
| 1982 | Yoshiaki Tamura | MELCOM 900II[28] | 7.23 hours | 2,097,144 |
| 1982 | Yoshiaki Tamura and Yasumasa Kanada | HITAC M-280H[28] | 2.9 hours | 4,194,288 |
| 1982 | Yoshiaki Tamura and Yasumasa Kanada | HITAC M-280H[28] | 6.86 hours | 8,388,576 |
| 1983 | Yasumasa Kanada, Sayaka Yoshino and Yoshiaki Tamura | HITAC M-280H[28] | <30 hours | 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[28] | 28 hours | 29,360,111 |
| September 1986 | Yasumasa Kanada, Yoshiaki Tamura | HITAC S-810/20[28] | 6.6 hours | 33,554,414 |
| October 1986 | Yasumasa Kanada, Yoshiaki Tamura | HITAC S-810/20[28] | 23 hours | 67,108,839 |
| January 1987 | Yasumasa Kanada, Yoshiaki Tamura, Yoshinobu Kubo and others | NEC SX-2[28] | 35.25 hours | 134,214,700 |
| January 1988 | Yasumasa Kanada and Yoshiaki Tamura | HITAC S-820/80[32] | 5.95 hours | 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[33] | 1,073,740,799 | |
| August 1991 | Gregory V. Chudnovsky & David V. Chudnovsky | Homemade parallel computer (details unknown, not verified) [34][33] | 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) [35] | 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 and Daisuke Takahashi | HITAC S-3800/480 (dual CPU) [36][37] | 56.74 hours? | 4,294,960,000 |
| 11 October 1995 | Yasumasa Kanada and Daisuke Takahashi | HITAC S-3800/480 (dual CPU) [38][37] | 116.63 hours | 6,442,450,000 |
| 6 July 1997 | Yasumasa Kanada and Daisuke Takahashi | HITACHI SR2201 (1024 CPU) [39][40] | 29.05 hours | 51,539,600,000 |
| 5 April 1999 | Yasumasa Kanada and Daisuke Takahashi | HITACHI SR8000 (64 of 128 nodes) [41][42] | 32.9 hours | 68,719,470,000 |
| 20 September 1999 | Yasumasa Kanada and Daisuke Takahashi | HITACHI SR8000/MPP (128 nodes) [43][44] | 37.35 hours | 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[45] | 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[46] | 29.09 hours | 2,576,980,377,524 |
2009–present
[edit]| Date | Who | Implementation | Time | Decimal places (world records in bold) |
|---|---|---|---|---|
| All records from Dec 2009 onwards are calculated and verified on commodity x86 computers with commercially available parts. All use the Chudnovsky algorithm for the main computation, and Bellard's formula, the Bailey–Borwein–Plouffe formula, or both for verification. | ||||
| 31 December 2009 | Fabrice Bellard[47][48] |
|
131 days | 2,699,999,990,000 = 2.7×1012 − 104 |
| 2 August 2010 | Shigeru Kondo[49] |
|
90 days | 5,000,000,000,000 = 5×1012 |
| 17 October 2011 | Shigeru Kondo[52] |
|
371 days | 10,000,000,000,050 = 1013 + 50 |
| 28 December 2013 | Shigeru Kondo[53] |
|
94 days | 12,100,000,000,050 = 1.21×1013 + 50 |
| 8 October 2014 | Sandon Nash Van Ness "houkouonchi"[54] |
|
208 days | 13,300,000,000,000 = 1.33×1013 |
| 11 November 2016 | Peter Trueb[55][56] |
|
105 days | 22,459,157,718,361 = ⌊πe×1012⌋ |
| 14 March 2019 | Emma Haruka Iwao[58] |
|
121 days | 31,415,926,535,897 = ⌊π×1013⌋ |
| 29 January 2020 | Timothy Mullican[59][60] |
|
303 days | 50,000,000,000,000 = 5×1013 |
| 14 August 2021 | Team DAViS of the University of Applied Sciences of the Grisons[61][62] |
|
108 days | 62,831,853,071,796 = ⌈2π×1013⌉ |
| 21 March 2022 | Emma Haruka Iwao[63][64] |
|
158 days | 100,000,000,000,000 = 1014 |
| 18 April 2023 | Jordan Ranous[65][66] |
|
59 days | 100,000,000,000,000 = 1014 |
| 14 March 2024 | Jordan Ranous, Kevin O’Brien and Brian Beeler[67][68] |
|
75 days | 105,000,000,000,000 = 1.05×1014 |
| 28 June 2024 | Jordan Ranous, Kevin O’Brien and Brian Beeler[69][70] |
|
104 days | 202,112,290,000,000 = 2.0211229×1014 |
See also
[edit]References
[edit]- ^ "y-cruncher validation file".
- ^ a b c d e f g h i j k l m n o p q r s t u v w David H. Bailey; Jonathan M. Borwein; Peter B. Borwein; Simon Plouffe (1997). "The quest for pi" (PDF). Mathematical Intelligencer. 19 (1): 50–57. doi:10.1007/BF03024340. S2CID 14318695.
- ^ "Origins: 3.14159265..." Biblical Archaeology Society. 2022-03-14. Retrieved 2022-06-08.
- ^ Eggeling, Julius (1882–1900). The Satapatha-brahmana, according to the text of the Madhyandina school. Princeton Theological Seminary Library. Oxford, The Clarendon Press. pp. 302–303.
{{cite book}}: CS1 maint: date and year (link) - ^ 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.
- ^ "4 II. Sulba Sutras". www-history.mcs.st-and.ac.uk.
- ^ 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.
- ^ Plofker, Kim (2009). Mathematics in India. Princeton University Press. p. 18. ISBN 978-0691120676.
- ^ Wilson, David (2000). "The History of Pi". sites.math.rutgers.edu. University Of Rutgers. Archived from the original on 7 May 2023.
- ^ Jadhav, Dipak (2018-01-01). "On The Value Implied In The Data Referred To In The Mahābhārata for π". Vidyottama Sanatana: International Journal of Hindu Science and Religious Studies. 2 (1): 18. doi:10.25078/ijhsrs.v2i1.511. ISSN 2550-0651. S2CID 146074061.
- ^ 趙良五 (1991). 中西數學史的比較. 臺灣商務印書館. ISBN 978-9570502688 – via Google Books.
- ^ Needham, Joseph (1986). Science and Civilization in China: Volume 3, Mathematics and the Sciences of the Heavens and the Earth. Taipei: Caves Books, Ltd. Volume 3, 100.
- ^ 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. 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. doi:10.35834/mjms/1312233136.
- ^ Viète, François (1579). Canon mathematicus seu ad triangula : cum adpendicibus (in Latin).
- ^ Romanus, Adrianus (1593). Ideae mathematicae pars prima, sive methodus polygonorum (in Latin). apud Ioannem Keerbergium. hdl:2027/ucm.5320258006.
- ^ Grienbergerus, Christophorus (1630). Elementa Trigonometrica (PDF) (in Latin). Archived from the original (PDF) on 2014-02-01.
- ^ Hobson, Ernest William (1913). 'Squaring the Circle': a History of the Problem (PDF). Cambridge University Press. p. 27.
- ^ Yoshio, Mikami; Eugene Smith, David (2004) [1914]. A History of Japanese Mathematics (paperback ed.). Dover Publications. ISBN 0-486-43482-6.
- ^ Benjamin Wardhaugh, "Filling a Gap in the History of π: An Exciting Discovery", Mathematical Intelligencer 38(1) (2016), 6-7
- ^ Vega, Géorge (1795) [1789]. "Detérmination de la demi-circonférence d'un cercle dont le diameter est = 1, exprimée en 140 figures decimals". Supplement. Nova Acta Academiae Scientiarum Petropolitanae. 11: 41–44.
Sandifer, Ed (2006). "Why 140 Digits of Pi Matter" (PDF). Southern Connecticut State University. Archived from the original (PDF) on 2012-02-04.
- ^ Hayes, Brian (September 2014). "Pencil, Paper, and Pi". American Scientist. Vol. 102, no. 5. p. 342. doi:10.1511/2014.110.342. Retrieved 13 February 2022.
- ^ 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. Archived from the original on 2005-01-09. Retrieved 2009-02-01.
- ^ a b c Wells, D. G. (May 1, 1998). The Penguin Dictionary of Curious and Interesting Numbers (Revised ed.). Penguin Books. p. 33. ISBN 978-0140261493.
- ^ Reitwiesner, G. (1950). "An ENIAC determination of 𝜋 and 𝑒 to more than 2000 decimal places". Mathematics of Computation. 4 (29): 11–15. doi:10.1090/S0025-5718-1950-0037597-6.
- ^ Nicholson, S. C.; Jeenel, J. (1955). "Some comments on a NORC computation of 𝜋". Mathematics of Computation. 9 (52): 162–164. doi:10.1090/S0025-5718-1955-0075672-5.
- ^ 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 π see Wrench, J. W. Jr. (1960). "The evolution of extended decimal approximations to π". The Mathematics Teacher. 53 (8): 644–650. doi:10.5951/MT.53.8.0644. JSTOR 27956272.
- ^ a b c d e f g h i j k Arndt, Jörg; Haenel, Christoph (2001). Pi - Unleashed. Springer. ISBN 978-3-642-56735-3.
- ^ Genuys, F. (1958). "Dix milles decimales de π". Chiffres. 1: 17–22.
- ^ This unpublished value of x to 16167D was computed on an IBM 704 system at the French Alternative Energies and Atomic Energy Commission in Paris, by means of the program of Genuys
- ^ Shanks, Daniel; Wrench, John W. J.r (1962). "Calculation of π to 100,000 decimals". Mathematics of Computation. 16 (77): 76–99. doi:10.1090/S0025-5718-1962-0136051-9.
- ^ Kanada, Y. (November 1988). "Vectorization of multiple-precision arithmetic program and 201,326,000 decimal digits of pi calculation". Proceedings Supercomputing Vol.II: Science and Applications. pp. 117–128 vol.2. doi:10.1109/SUPERC.1988.74139. ISBN 0-8186-8923-4. S2CID 122820709.
- ^ a b "Computers". Science News. 24 August 1991. Retrieved 2022-08-04.
- ^ 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[permanent dead link]
- ^ ftp://pi.super-computing.org/README.our_last_record_4b[permanent dead link]
- ^ a b "GENERAL COMPUTATIONAL UPDATE". www.cecm.sfu.ca. Retrieved 2022-08-04.
- ^ ftp://pi.super-computing.org/README.our_last_record_6b[permanent dead link]
- ^ ftp://pi.super-computing.org/README.our_last_record_51b[permanent dead link]
- ^ "Record for pi : 51.5 billion decimal digits". 2005-12-24. Archived from the original on 2005-12-24. Retrieved 2022-08-04.
- ^ ftp://pi.super-computing.org/README.our_last_record_68b[permanent dead link]
- ^ Kanada, Yasumasa. "plouffe.fr/simon/constants/Pi68billion.txt". www.plouffe.fr. Archived from the original on 5 August 2022.
- ^ ftp://pi.super-computing.org/README.our_latest_record_206b[permanent dead link]
- ^ "Record for pi : 206 billion decimal digits". www.cecm.sfu.ca. Retrieved 2022-08-04.
- ^ "Archived copy". Archived from the original on 2011-03-12. Retrieved 2010-07-08.
{{cite web}}: CS1 maint: archived copy as title (link) - ^ "Archived copy". Archived from the original on 2009-08-23. Retrieved 2009-08-18.
{{cite web}}: CS1 maint: archived copy as title (link) - ^ Bellard, Fabrice (11 Feb 2010). "Computation of 2700 billion decimal digits of Pi using a Desktop Computer" (PDF). 4th revision. S2CID 12242318.
- ^ "TachusPI". bellard.org. Retrieved 2024-10-10.
- ^ "PI-world". calico.jp. Archived from the original on 31 August 2015. Retrieved 28 August 2015.
- ^ "y-cruncher – A Multi-Threaded 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.
- ^ "Pi: Notable large computations". numberworld.org. Retrieved 16 March 2024.
- ^ "pi2e". pi2e.ch. Retrieved 15 November 2016.
- ^ "Pi: Notable large computations". numberworld.org. Retrieved 16 March 2024.
- ^ "Hexadecimal Digits are Correct! – pi2e trillion digits of pi". pi2e.ch. 31 October 2016. Retrieved 15 November 2016.
- ^ "Google Cloud Topples the Pi Record". Retrieved 14 March 2019.
- ^ "The Pi Record Returns to the Personal Computer". Retrieved 30 January 2020.
- ^ "Calculating Pi: My attempt at breaking the Pi World Record". 26 June 2019. Retrieved 30 January 2020.
- ^ "Pi-Challenge - world record attempt by UAS Grisons - University of Applied Sciences of the Grisons". www.fhgr.ch. 2021-08-14. Archived from the original on 2021-08-17. Retrieved 2021-08-17.
- ^ "Die FH Graubünden kennt Pi am genauesten – Weltrekord! - News - FH Graubünden". www.fhgr.ch (in German). 2021-08-16. Archived from the original on 2021-08-17. Retrieved 2021-08-17.
- ^ "Calculating 100 trillion digits of pi on Google Cloud". Google Cloud Blog. Retrieved 2022-06-10.
- ^ "100 Trillion Digits of Pi". numberworld.org. Retrieved 2022-06-10.
- ^ "StorageReview Calculated 100 Trillion Digits of Pi in 54 days, Besting Google Cloud". storagereview.com. Retrieved 2023-12-02.
- ^ "The Need for Speed!". numberworld.org. 19 April 2023. Retrieved 2023-12-25.
- ^ Ranous, Jordan (2024-03-13). "105 Trillion Pi Digits: The Journey to a New Pi Calculation Record". StorageReview.com. Retrieved 2024-03-14.
- ^ Yee, Alexander J. (2024-03-14). "Limping to a new Pi Record of 105 Trillion Digits". NumberWorld.org. Retrieved 2024-03-16.
- ^ Ranous, Jordan (2024-06-28). "StorageReview Lab Breaks Pi Calculation World Record with Over 202 Trillion Digits". StorageReview.com. Retrieved 2024-07-02.
- ^ Yee, Alexander J. (2024-06-28). "Pi Record Smashed at 202 Trillion Digits". NumberWorld.org. Retrieved 2024-06-30.
External links
[edit]- Borwein, Jonathan, "The Life of Pi Archived 2006-12-07 at the Wayback Machine"
- Kanada Laboratory home page
- Stu's Pi page
- Takahashi's page
- Google's web service making all 100 trillion digits available