Pai : Tofauti kati ya masahihisho
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Mstari 9:
[[Wanahisabati]] duniani husheherekea [[sikukuu ya Pi]] tarehe [[14 Machi]] au pia [[22 Julai]].
==Tanbihi==
{{Reflist|20em}}
{{refbegin|30em}}
* {{cite book|last=Arndt|first=Jörg|last2=Haenel|first2=Christoph|title=Pi Unleashed|publisher=Springer-Verlag|year=2006|isbn=978-3-540-66572-4 <!--isbn only volume 1-->|url=http://books.google.com/?id=QwwcmweJCDQC&printsec=frontcover#v=onepage&q&f=false|ref=harv|accessdate=2013-06-05}} English translation by Catriona and David Lischka.
* {{cite book|last=Ayers|first=Frank|title=Calculus|publisher=McGraw-Hill|year=1964|isbn=978-0-070-02653-7|ref=harv}}
* {{cite book|last=Berggren|first=Lennart|last2=Borwein|first2=Jonathan|author2-link=Jonathan Borwein|last3=Borwein|first3=Peter|author3-link=Peter Borwein|title=Pi: a Source Book|publisher=Springer-Verlag|year=1997|isbn=978-0-387-20571-7|ref=harv}}
* {{cite book|last=Beckmann|first=Peter|title=History of Pi|publisher=St. Martin's Press|year=1989|origyear=1974|isbn=978-0-88029-418-8|ref=harv}}
* {{cite book|last=Borwein|first=Jonathan|author1-link=|last2=Borwein|first2=Peter|author2-link=|title=Pi and the AGM: a Study in Analytic Number Theory and Computational Complexity|publisher=Wiley|year=1987|isbn=978-0-471-31515-5|ref=harv}}
* {{cite book|last=Boyer|first=Carl B.|last2=Merzbach|first2=Uta C.|year=1991|title=A History of Mathematics|edition=2|publisher=Wiley|isbn=978-0-471-54397-8|ref=harv}}<!-- Year from ISBN. Original citatation was just to Boyer. Possible that edition is wrong and therefore page is wrong. Editions: Boyer 1968, Boyer/Merzbach 1989, Boyer/Merzbach 1991, Merzbach/Boyer 2010, Merzbach/Boyer 2011. Verify second: Hui and 3072-sided polygon is on cited page 202 of 1991 edition; page 228 of 1968 edition. Google snippet has a hit for 3.1456 on page 168 for 1991, but does not show the number. -->
* {{cite book|last=Bronshteĭn|first=Ilia|last2=Semendiaev|first2=K. A.|title=A Guide Book to Mathematics|publisher=H. Deutsch|year=1971|isbn= 978-3-871-44095-3|ref=harv}}
* {{cite book|last=Eymard|first=Pierre|last2=Lafon|first2=Jean Pierre|title=The Number Pi|publisher=American Mathematical Society|year=1999|isbn=978-0-8218-3246-2|ref=harv}}, English translation by Stephen Wilson.
* {{cite book|last=Joseph|first=George Gheverghese|title=The Crest of the Peacock: Non-European Roots of Mathematics|publisher=Princeton University Press|year=1991|isbn=978-0-691-13526-7|url=http://books.google.com/?id=c-xT0KNJp0cC&printsec=frontcover#v=onepage&q&f=false%7C|ref=harv|accessdate=2013-06-05}}<!-- This ISBN is for the third edition from 2011! -->
* {{cite book|last=Posamentier|first=Alfred S.|last2=Lehmann|first2=Ingmar|title=Pi: A Biography of the World's Most Mysterious Number|publisher=Prometheus Books|year=2004|isbn=978-1-59102-200-8|ref=harv}}
* {{cite journal|last=Reitwiesner|first=George|title=An ENIAC Determination of pi and e to 2000 Decimal Places|journal=Mathematical Tables and Other Aids to Computation|year=1950|volume=4|issue= 29|pages=11–15|doi=10.2307/2002695|ref=harv }}
* {{cite journal|last=Roy|first=Ranjan|title=The Discovery of the Series Formula for pi by Leibniz, Gregory, and Nilakantha|journal=Mathematics Magazine|volume=63|issue=5|year=1990|pages=291–306|doi=10.2307/2690896|ref=harv }}
* {{cite journal|last=Schepler|first=H. C.|title=The Chronology of Pi|journal=Mathematics Magazine|publisher=Mathematical Association of America|year=1950|volume=23|issue=3|pages=165–170 (Jan/Feb), 216–228 (Mar/Apr), and 279–283 (May/Jun)|doi=10.2307/3029284|ref=harv }}. [<!-- http://www.jstor.org/stable/3029284 -->http://www.jstor.org/discover/10.2307/3029284 issue 3 Jan/Feb], [http://www.jstor.org/stable/3029832 issue 4 Mar/Apr], [http://www.jstor.org/stable/3029000 issue 5 May/Jun]
{{refend}}
==Marejeo==
{{refbegin|30em}}
* {{cite book|last=Blatner|first=David|title=The Joy of Pi|publisher=Walker & Company|year=1999|isbn=978-0-8027-7562-7|doi= }}
* [[Jonathan Borwein|Borwein, Jonathan]] and [[Peter Borwein|Borwein, Peter]], "The Arithmetic-Geometric Mean and Fast Computation of Elementary Functions", ''SIAM Review'', '''26'''(1984) 351–365
* Borwein, Jonathan, Borwein, Peter, and [[David H. Bailey|Bailey, David H.]], ''Ramanujan, Modular Equations, and Approximations to Pi or How to Compute One Billion Digits of Pi", ''The American Mathematical Monthly'', '''96'''(1989) 201–219
* [[Chudnovsky brothers|Chudnovsky, David V.]] and [[Chudnovsky brothers|Chudnovsky, Gregory V.]], "Approximations and Complex Multiplication According to Ramanujan", in ''Ramanujan Revisited'' (G.E. Andrews et al. Eds), Academic Press, 1988, pp 375–396, 468–472
* Cox, David A., "The Arithmetic-Geometric Mean of Gauss", ''L' Ensignement Mathematique'', '''30'''(1984) 275–330
* [[Jean-Paul Delahaye|Delahaye, Jean-Paul]], "Le Fascinant Nombre Pi", Paris: Bibliothèque Pour la Science (1997) ISBN 2902918259
* Engels, Hermann, "Quadrature of the Circle in Ancient Egypt", ''Historia Mathematica'' '''4'''(1977) 137–140
* [[Leonhard Euler|Euler, Leonhard]], "On the Use of the Discovered Fractions to Sum Infinite Series", in ''Introduction to Analysis of the Infinite. Book I'', translated from the Latin by J. D. Blanton, Springer-Verlag, 1964, pp 137–153
* Heath, T. L., ''The Works of Archimedes'', Cambridge, 1897; reprinted in ''The Works of Archimedes with The Method of Archimedes'', Dover, 1953, pp 91–98
* [[Christiaan Huygens|Huygens, Christiaan]], "De Circuli Magnitudine Inventa", ''Christiani Hugenii Opera Varia I'', Leiden 1724, pp 384–388
* [[Lam Lay Yong|Lay-Yong, Lam]] and Tian-Se, Ang, "Circle Measurements in Ancient China", ''Historia Mathematica'' '''13'''(1986) 325–340
* [[Ferdinand von Lindemann|Lindemann, Ferdinand]], [http://gdz.sub.uni-goettingen.de/index.php?id=11&PPN=PPN235181684_0020&DMDID=DMDLOG_0031&L=1 "Ueber die Zahl pi"], ''Mathematische Annalen'' '''20'''(1882) 213–225
* Matar, K. Mukunda, and Rajagonal, C., "On the Hindu Quadrature of the Circle" (Appendix by K. Balagangadharan). ''Journal of the Bombay Branch of the Royal Asiatic Society'' '''20'''(1944) 77–82
* [[Ivan M. Niven|Niven, Ivan]], "A Simple Proof that pi Is Irrational", ''Bulletin of the American Mathematical Society'', '''53''':7 (July 1947), 507
* [[Srinivasa Ramanujan|Ramanujan, Srinivasa]], "Modular Equations and Approximations to π", ''Quarterly Journal of Pure and Applied Mathematics'', '''XLV''', 1914, 350–372. Reprinted in G.H. Hardy, P.V. Seshu Aiyar, and B. M. Wilson (eds), ''Srinivasa Ramanujan: Collected Papers'', 1927 (reprinted 2000), pp 23–29
* [[William Shanks|Shanks, William]], ''Contributions to Mathematics {{sic|hide=y|Comprising}} Chiefly of the Rectification of the Circle to 607 Places of Decimals'', 1853, pp. i–xvi, 10
* [[Daniel Shanks|Shanks, Daniel]] and [[John Wrench|Wrench, John William]], "Calculation of pi to 100,000 Decimals", ''Mathematics of Computation'' '''16'''(1962) 76–99
* Tropfke, Johannes, ''Geschichte Der Elementar-Mathematik in Systematischer Darstellung'' (''The history of elementary mathematics''), BiblioBazaar, 2009 (reprint), ISBN 978-1-113-08573-3
* [[François Viète|Viete, Francois]], ''Variorum de Rebus Mathematicis Reponsorum Liber VII. F. Viete, Opera Mathematica'' (reprint), Georg Olms Verlag, 1970, pp 398–401, 436–446
* [[Stan Wagon|Wagon, Stan]], "Is Pi Normal?", ''The Mathematical Intelligencer'', '''7''':3(1985) 65–67
* [[John Wallis|Wallis, John]], ''Arithmetica Infinitorum, sive Nova Methodus Inquirendi in Curvilineorum Quadratum, aliaque difficiliora Matheseos Problemata'', Oxford 1655–6. Reprinted in vol. 1 (pp 357–478) of ''Opera Mathematica'', Oxford 1693
* Zebrowski, Ernest, ''A History of the Circle: Mathematical Reasoning and the Physical Universe'', Rutgers Univ Press, 1999, ISBN 978-0-8135-2898-4
{{refend}}
==Viungo vya nje==
{{Commons category}}
* {{dmoz|Science/Math/Recreations/Specific_Numbers/Pi/Digits/|Digits of Pi}}
* [http://mathworld.wolfram.com/Pi.html "Pi"] at Wolfram Mathworld
* [http://www.wolframalpha.com/input/?i=Representations+of+Pi Representations of Pi] at [[Wolfram Alpha]]
* [http://www.subidiom.com/pi Pi Search Engine] 2 billion searchable digits of {{pi}}, {{math|{{sqrt|2}}}}, and {{math|''e''}}
* {{cite web|last=Eaves|first=Laurence|title={{pi}} – Pi|url=http://www.sixtysymbols.com/videos/pi.htm|work=Sixty Symbols|publisher=[[Brady Haran]] for the [[University of Nottingham]]|authorlink=Laurence Eaves|year=2009}}
* {{cite web|last=Grime|first=Dr. James|title=Pi is Beautiful – Numberphile|url=http://www.youtube.com/watch?v=NPoj8lk9Fo4|work=Numberphile|publisher=[[Brady Haran]]|year=2014}}
{{mbegu}}
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