圆周率近似值 (Chinese Wikipedia)

Analysis of information sources in references of the Wikipedia article "圆周率近似值" in Chinese language version.

refsWebsite

Global rank Chinese rank

24web.archive.org

1^st place

8doi.org

2^nd place

23^rd place

6archive.org

6^th place

4^th place

4books.google.com

3^rd place

8^th place

3harvard.edu

18^th place

57^th place

2oeis.org

742^nd place

1,026^th place

2demon.co.uk

3,292^nd place

3,188^th place

2wikipedia.org

low place

2lbl.gov

2,509^th place

1,602^nd place

2wolfram.com

513^th place

358^th place

1163.com

372^nd place

16^th place

1jstor.org

26^th place

113^th place

1mathworks.com

6,214^th place

3,185^th place

1uz.ac.zw

low place

1wikisource.org

27^th place

30^th place

1projecteuclid.org

3,707^th place

5,418^th place

1st-and.ac.uk

3,503^rd place

2,468^th place

1comune.palermo.it

low place

1independent.co.uk

36^th place

153^rd place

1semanticscholar.org

11^th place

332^nd place

1numberworld.org

low place

1plouffe.fr

low place

1ox.ac.uk

613^th place

708^th place

1free.fr

321^st place

1,231^st place

1bbc.co.uk

8^th place

32^nd place

1mschneider.cc

low place

1iamned.com

low place

1bellard.org

low place

163.com

62.8万亿个数字：瑞士大学创造了新的圆周率计算记录. [2021-08-20]. （原始内容存档于2021-08-26）（中文）.

archive.org

George E. Andrews, Richard Askey, Ranjan Roy. Special Functions. Cambridge University Press. 1999: 58. ISBN 0-521-78988-5.
"We can conclude that although the ancient Egyptians could not precisely define the value of $π$ , in practice they used it". Verner, M. The Pyramids: Their Archaeology and History. 2003. ，第70页。
Petrie. Wisdom of the Egyptians. 1940. ，第30页。
参见Legon, J. A. R. On Pyramid Dimensions and Proportions. Discussions in Egyptology. 1991, 20: 第25–34页 [2016-09-13]. （原始内容存档于2011-07-18）. .
参见Petrie, W. M. F. Surveys of the Great Pyramids. Nature. 1925, 116 (2930期): 第942页. Bibcode:1925Natur.116..942P. doi:10.1038/116942a0.
Borwein, J. M.; Borwein, P. B.; Dilcher, K. Pi, Euler Numbers, and Asymptotic Expansions. American Mathematical Monthly. 1989, 96 (8): 681–687. doi:10.2307/2324715.
Arndt & Haenel 2006，第223頁, (formula 16.10). Note that (n − 1)n(n + 1) = n³ − n.
Wells, David. The Penguin Dictionary of Curious and Interesting Numbers revised. Penguin. 1997: 35. ISBN 978-0-140-26149-3.
Rabinowitz, Stanley; Wagon, Stan. A spigot algorithm for the digits of Pi. American Mathematical Monthly. 1995-03, 102 (3): 195–203. doi:10.2307/2975006. A computer program has been created that implements Wagon's spigot algorithm in only 120 characters of software.
Gardner, Martin. New Mathematical Diversions. Mathematical Association of America: 92. 1995. .

bbc.co.uk

Palmer, Jason. Pi record smashed as team finds two-quadrillionth digit. BBC News. 2010-09-16 [2011-03-26]. （原始内容存档于2011-03-17）.

bellard.org

Bellard's Website:Bellard.org （页面存档备份，存于互联网档案馆）

books.google.com

Kennedy, E. S., Abu-r-Raihan al-Biruni, 973-1048, Journal for the History of Astronomy: 65, Bibcode:1978JHA.....9...65K, doi:10.1177/002182867800900106 。克劳狄乌斯·托勒密使用了60进制下的三位小数去近似，随后卡西将其扩展到了九位小数。参见Aaboe, Asger, Episodes from the Early History of Mathematics, New Mathematical Library 13, 纽约: Random House: 125, 1964 [2017-12-08], （原始内容存档于2017-02-01）
Egyptologist: Rossi, Corinna, Architecture and Mathematics in Ancient Egypt, Cambridge University Press, 2004, 第60-70页，200, ISBN 9780521829540.
对此的怀疑：Shermer, Michael（英语：Michael Shermer）, The Skeptic Encyclopedia of Pseudoscience, ABC-CLIO, 2002, 第407-408页, ISBN 9781576076538.
参见Fagan, Garrett G., Archaeological Fantasies: How Pseudoarchaeology Misrepresents The Past and Misleads the Public, Routledge, 2006, ISBN 9780415305938.
若需要一个没有 $π$ 参与的解释的列表，请见Roger Herz-Fischler. The Shape of the Great Pyramid. Wilfrid Laurier University Press. 2000: 第67–77页，第165–166页 [2013-06-05]. ISBN 9780889203242. （原始内容存档于2016-11-29）.
Chaitanya, Krishna. A profile of Indian culture. （页面存档备份，存于互联网档案馆） Indian Book Company (1975). 第133页。
此零非彼O. 臺灣商務印書館. 2006: 286. ISBN 978-957-05-2072-9.

comune.palermo.it

librarsi.comune.palermo.it

Grienbergerus, Christophorus. Elementa Trigonometrica (PDF). 1630 [2016-09-13]. （原始内容 (PDF)存档于2014-02-01）（拉丁语）. 。其計算結果是3.14159 26535 89793 23846 26433 83279 50288 4196 < $π$ < 3.14159 26535 89793 23846 26433 83279 50288 4199

demon.co.uk

legon.demon.co.uk

Legon, J. A. R. On Pyramid Dimensions and Proportions (1991) Discussions in Egyptology (20) 第25-34页 [1] （页面存档备份，存于互联网档案馆）
"We can conclude that although the ancient Egyptians could not precisely define the value of $π$ , in practice they used it". Verner, M. The Pyramids: Their Archaeology and History. 2003. ，第70页。
Petrie. Wisdom of the Egyptians. 1940. ，第30页。
参见Legon, J. A. R. On Pyramid Dimensions and Proportions. Discussions in Egyptology. 1991, 20: 第25–34页 [2016-09-13]. （原始内容存档于2011-07-18）. .
参见Petrie, W. M. F. Surveys of the Great Pyramids. Nature. 1925, 116 (2930期): 第942页. Bibcode:1925Natur.116..942P. doi:10.1038/116942a0.

doi.org

David Bailey; Jonathan Borwein; Peter Borwein; Simon Plouffe, The Quest for Pi, The Mathematical Intelligencer, 1997, 19 (1): 50–56, doi:10.1007/bf03024340
Kennedy, E. S., Abu-r-Raihan al-Biruni, 973-1048, Journal for the History of Astronomy: 65, Bibcode:1978JHA.....9...65K, doi:10.1177/002182867800900106 。克劳狄乌斯·托勒密使用了60进制下的三位小数去近似，随后卡西将其扩展到了九位小数。参见Aaboe, Asger, Episodes from the Early History of Mathematics, New Mathematical Library 13, 纽约: Random House: 125, 1964 [2017-12-08], （原始内容存档于2017-02-01）
Lange, L. J. An Elegant Continued Fraction for π. The American Mathematical Monthly. 1999-05, 106 (5): 456–458. JSTOR 2589152. doi:10.2307/2589152.
"We can conclude that although the ancient Egyptians could not precisely define the value of $π$ , in practice they used it". Verner, M. The Pyramids: Their Archaeology and History. 2003. ，第70页。
Petrie. Wisdom of the Egyptians. 1940. ，第30页。
参见Legon, J. A. R. On Pyramid Dimensions and Proportions. Discussions in Egyptology. 1991, 20: 第25–34页 [2016-09-13]. （原始内容存档于2011-07-18）. .
参见Petrie, W. M. F. Surveys of the Great Pyramids. Nature. 1925, 116 (2930期): 第942页. Bibcode:1925Natur.116..942P. doi:10.1038/116942a0.
Borwein, J. M.; Borwein, P. B. Ramanujan and Pi. Scientific American. 1988, 256 (2): 112–117. Bibcode:1988SciAm.258b.112B. doi:10.1038/scientificamerican0288-112.
Borwein, J. M.; Borwein, P. B.; Dilcher, K. Pi, Euler Numbers, and Asymptotic Expansions. American Mathematical Monthly. 1989, 96 (8): 681–687. doi:10.2307/2324715.
Rabinowitz, Stanley; Wagon, Stan. A spigot algorithm for the digits of Pi. American Mathematical Monthly. 1995-03, 102 (3): 195–203. doi:10.2307/2975006. A computer program has been created that implements Wagon's spigot algorithm in only 120 characters of software.
Bailey, David H; Borwein, Peter B; and Plouffe, Simon. On the Rapid Computation of Various Polylogarithmic Constants (PDF). Mathematics of Computation. 1997-04, 66 (218): 903–913 [2016-09-13]. doi:10.1090/S0025-5718-97-00856-9. （原始内容存档 (PDF)于2012-07-22）.

free.fr

fabrice.bellard.free.fr

Bellards formula in: Bellard, Fabrice. A new formula to compute the n^th binary digit of pi. [2007-10-27]. （原始内容存档于2007-09-12）.

harvard.edu

ui.adsabs.harvard.edu

Kennedy, E. S., Abu-r-Raihan al-Biruni, 973-1048, Journal for the History of Astronomy: 65, Bibcode:1978JHA.....9...65K, doi:10.1177/002182867800900106 。克劳狄乌斯·托勒密使用了60进制下的三位小数去近似，随后卡西将其扩展到了九位小数。参见Aaboe, Asger, Episodes from the Early History of Mathematics, New Mathematical Library 13, 纽约: Random House: 125, 1964 [2017-12-08], （原始内容存档于2017-02-01）
"We can conclude that although the ancient Egyptians could not precisely define the value of $π$ , in practice they used it". Verner, M. The Pyramids: Their Archaeology and History. 2003. ，第70页。
Petrie. Wisdom of the Egyptians. 1940. ，第30页。
参见Legon, J. A. R. On Pyramid Dimensions and Proportions. Discussions in Egyptology. 1991, 20: 第25–34页 [2016-09-13]. （原始内容存档于2011-07-18）. .
参见Petrie, W. M. F. Surveys of the Great Pyramids. Nature. 1925, 116 (2930期): 第942页. Bibcode:1925Natur.116..942P. doi:10.1038/116942a0.
Borwein, J. M.; Borwein, P. B. Ramanujan and Pi. Scientific American. 1988, 256 (2): 112–117. Bibcode:1988SciAm.258b.112B. doi:10.1038/scientificamerican0288-112.

iamned.com

CetinHakimoglu–Brown. [2013-02-18]. （原始内容存档于2009-03-29）.

independent.co.uk

Connor, Steve. The Big Question: How close have we come to knowing the precise value of pi?. The Independent (London). 2010-01-08 [2012-04-14]. （原始内容存档于2012-04-02）.

jstor.org

Lange, L. J. An Elegant Continued Fraction for π. The American Mathematical Monthly. 1999-05, 106 (5): 456–458. JSTOR 2589152. doi:10.2307/2589152.

lbl.gov

crd-legacy.lbl.gov

Bailey, David H. Some Background on Kanada’s Recent Pi Calculation (PDF). 2003-05-16 [2012-04-12]. （原始内容存档 (PDF)于2012-04-15）.
Bailey, David H; Borwein, Peter B; and Plouffe, Simon. On the Rapid Computation of Various Polylogarithmic Constants (PDF). Mathematics of Computation. 1997-04, 66 (218): 903–913 [2016-09-13]. doi:10.1090/S0025-5718-97-00856-9. （原始内容存档 (PDF)于2012-07-22）.

mathworks.com

The Computation of Pi by Archimedes: The Computation of Pi by Archimedes – File Exchange – MATLAB Central. Mathworks.com. [2013-03-12]. （原始内容存档于2013-02-25）.

mschneider.cc

A nested radical approximation for pi (PDF). [2013-02-18]. （原始内容 (PDF)存档于2011-07-06）.

numberworld.org

Pi - 12.1 Trillion Digits. www.numberworld.org. [2012-05-30]. （原始内容存档于2014-01-01）.

oeis.org

Sloane, N.J.A. (编). Sequence A001203 (Continued fraction for Pi). The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 12 April 2012.
A060294

ox.ac.uk

cs.ox.ac.uk

Gibbons, Jeremy, "Unbounded Spigot Algorithms for the Digits of Pi" （页面存档备份，存于互联网档案馆）, 2005. Gibbons produced an improved version of Wagon's algorithm.

plouffe.fr

Plouffe, Simon. Identities inspired by Ramanujan's Notebooks (part 2) (PDF). 2006-04 [2009-04-10]. （原始内容存档 (PDF)于2012-01-14）.

projecteuclid.org

Azarian, Mohammad K. al-Risāla al-muhītīyya: A Summary. Missouri Journal of Mathematical Sciences. 2010, 22 (2): 64–85 [2016-09-13]. （原始内容存档于2015-01-14）.

semanticscholar.org

Fabrice Bellard. Computation of 2700 billion decimal digits of Pi using a Desktop Computer - Semantic Scholar. www.semanticscholar.org. 2010-02-11 [2017-04-10].

st-and.ac.uk

www-history.mcs.st-and.ac.uk

O'Connor, John J.; Robertson, Edmund F. Ghiyath al-Din Jamshid Mas'ud al-Kashi. MacTutor History of Mathematics archive. 1999 [2012-08-11]. （原始内容存档于2011-04-12）.

uz.ac.zw

uzweb.uz.ac.zw

Lazarus Mudehwe. The story of pi. Zimaths. Feb 1997. （原始内容存档于8 January 2013）.

web.archive.org

62.8万亿个数字：瑞士大学创造了新的圆周率计算记录. [2021-08-20]. （原始内容存档于2021-08-26）（中文）.
Kennedy, E. S., Abu-r-Raihan al-Biruni, 973-1048, Journal for the History of Astronomy: 65, Bibcode:1978JHA.....9...65K, doi:10.1177/002182867800900106 。克劳狄乌斯·托勒密使用了60进制下的三位小数去近似，随后卡西将其扩展到了九位小数。参见Aaboe, Asger, Episodes from the Early History of Mathematics, New Mathematical Library 13, 纽约: Random House: 125, 1964 [2017-12-08], （原始内容存档于2017-02-01）
Legon, J. A. R. On Pyramid Dimensions and Proportions (1991) Discussions in Egyptology (20) 第25-34页 [1] （页面存档备份，存于互联网档案馆）
"We can conclude that although the ancient Egyptians could not precisely define the value of $π$ , in practice they used it". Verner, M. The Pyramids: Their Archaeology and History. 2003. ，第70页。
Petrie. Wisdom of the Egyptians. 1940. ，第30页。
参见Legon, J. A. R. On Pyramid Dimensions and Proportions. Discussions in Egyptology. 1991, 20: 第25–34页 [2016-09-13]. （原始内容存档于2011-07-18）. .
参见Petrie, W. M. F. Surveys of the Great Pyramids. Nature. 1925, 116 (2930期): 第942页. Bibcode:1925Natur.116..942P. doi:10.1038/116942a0.
Egyptologist: Rossi, Corinna, Architecture and Mathematics in Ancient Egypt, Cambridge University Press, 2004, 第60-70页，200, ISBN 9780521829540.
对此的怀疑：Shermer, Michael（英语：Michael Shermer）, The Skeptic Encyclopedia of Pseudoscience, ABC-CLIO, 2002, 第407-408页, ISBN 9781576076538.
参见Fagan, Garrett G., Archaeological Fantasies: How Pseudoarchaeology Misrepresents The Past and Misleads the Public, Routledge, 2006, ISBN 9780415305938.
若需要一个没有 $π$ 参与的解释的列表，请见Roger Herz-Fischler. The Shape of the Great Pyramid. Wilfrid Laurier University Press. 2000: 第67–77页，第165–166页 [2013-06-05]. ISBN 9780889203242. （原始内容存档于2016-11-29）.
Chaitanya, Krishna. A profile of Indian culture. （页面存档备份，存于互联网档案馆） Indian Book Company (1975). 第133页。
The Computation of Pi by Archimedes: The Computation of Pi by Archimedes – File Exchange – MATLAB Central. Mathworks.com. [2013-03-12]. （原始内容存档于2013-02-25）.
Lazarus Mudehwe. The story of pi. Zimaths. Feb 1997. （原始内容存档于8 January 2013）.
Azarian, Mohammad K. al-Risāla al-muhītīyya: A Summary. Missouri Journal of Mathematical Sciences. 2010, 22 (2): 64–85 [2016-09-13]. （原始内容存档于2015-01-14）.
O'Connor, John J.; Robertson, Edmund F. Ghiyath al-Din Jamshid Mas'ud al-Kashi. MacTutor History of Mathematics archive. 1999 [2012-08-11]. （原始内容存档于2011-04-12）.
Grienbergerus, Christophorus. Elementa Trigonometrica (PDF). 1630 [2016-09-13]. （原始内容 (PDF)存档于2014-02-01）（拉丁语）. 。其計算結果是3.14159 26535 89793 23846 26433 83279 50288 4196 < $π$ < 3.14159 26535 89793 23846 26433 83279 50288 4199
Bailey, David H. Some Background on Kanada’s Recent Pi Calculation (PDF). 2003-05-16 [2012-04-12]. （原始内容存档 (PDF)于2012-04-15）.
Connor, Steve. The Big Question: How close have we come to knowing the precise value of pi?. The Independent (London). 2010-01-08 [2012-04-14]. （原始内容存档于2012-04-02）.
Pi - 12.1 Trillion Digits. www.numberworld.org. [2012-05-30]. （原始内容存档于2014-01-01）.
Plouffe, Simon. Identities inspired by Ramanujan's Notebooks (part 2) (PDF). 2006-04 [2009-04-10]. （原始内容存档 (PDF)于2012-01-14）.
Weisstein, Eric W. (编). Random Walk--1-Dimensiona. at MathWorld--A Wolfram Web Resource. Wolfram Research, Inc. [2016-09-18]. （原始内容存档于2016-11-18）（英语）.
Gibbons, Jeremy, "Unbounded Spigot Algorithms for the Digits of Pi" （页面存档备份，存于互联网档案馆）, 2005. Gibbons produced an improved version of Wagon's algorithm.
Bailey, David H; Borwein, Peter B; and Plouffe, Simon. On the Rapid Computation of Various Polylogarithmic Constants (PDF). Mathematics of Computation. 1997-04, 66 (218): 903–913 [2016-09-13]. doi:10.1090/S0025-5718-97-00856-9. （原始内容存档 (PDF)于2012-07-22）.
Bellards formula in: Bellard, Fabrice. A new formula to compute the n^th binary digit of pi. [2007-10-27]. （原始内容存档于2007-09-12）.
Palmer, Jason. Pi record smashed as team finds two-quadrillionth digit. BBC News. 2010-09-16 [2011-03-26]. （原始内容存档于2011-03-17）.
A nested radical approximation for pi (PDF). [2013-02-18]. （原始内容 (PDF)存档于2011-07-06）.
CetinHakimoglu–Brown. [2013-02-18]. （原始内容存档于2009-03-29）.
Weisstein, Eric W. (编). BBP Formula. at MathWorld--A Wolfram Web Resource. Wolfram Research, Inc. （原始内容存档于2010-02-25）（英语）.
Bellard's Website:Bellard.org （页面存档备份，存于互联网档案馆）

wikipedia.org

en.wikipedia.org

Egyptologist: Rossi, Corinna, Architecture and Mathematics in Ancient Egypt, Cambridge University Press, 2004, 第60-70页，200, ISBN 9780521829540.
对此的怀疑：Shermer, Michael（英语：Michael Shermer）, The Skeptic Encyclopedia of Pseudoscience, ABC-CLIO, 2002, 第407-408页, ISBN 9781576076538.
参见Fagan, Garrett G., Archaeological Fantasies: How Pseudoarchaeology Misrepresents The Past and Misleads the Public, Routledge, 2006, ISBN 9780415305938.
若需要一个没有 $π$ 参与的解释的列表，请见Roger Herz-Fischler. The Shape of the Great Pyramid. Wilfrid Laurier University Press. 2000: 第67–77页，第165–166页 [2013-06-05]. ISBN 9780889203242. （原始内容存档于2016-11-29）.
Grünbaum, B., Projection Constants, Trans. Amer. Math. Soc., 1960, 95: 451–465

wikisource.org

zh.wikisource.org

隋書/卷16

wolfram.com

mathworld.wolfram.com

Weisstein, Eric W. (编). Random Walk--1-Dimensiona. at MathWorld--A Wolfram Web Resource. Wolfram Research, Inc. [2016-09-18]. （原始内容存档于2016-11-18）（英语）.
Weisstein, Eric W. (编). BBP Formula. at MathWorld--A Wolfram Web Resource. Wolfram Research, Inc. （原始内容存档于2010-02-25）（英语）.