Pi (English Wikipedia)

Analysis of information sources in references of the Wikipedia article "Pi" in English language version.

Last modified: 21:27:08, 30 September 2026 (UTC)

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17centurymaths.com (Global: low place; English: low place)

Euler, Leonhard (1727). "Tentamen explicationis phaenomenorum aeris" (PDF). Commentarii Academiae Scientiarum Imperialis Petropolitana (in Latin). 2: 351. E007. Retrieved 15 October 2017. Sumatur pro ratione radii ad peripheriem, $I : π$ English translation by Ian Bruce: " $π$ is taken for the ratio of the radius to the periphery [note that in this work, Euler's $π$ is double our $π$ .]"
Euler, Leonhard (1747). Henry, Charles (ed.). Lettres inédites d'Euler à d'Alembert. Bullettino di Bibliografia e di Storia delle Scienze Matematiche e Fisiche (in French). Vol. 19 (published 1886). p. 139. E858. Car, soit π la circonference d'un cercle, dout le rayon est $= 1$ English translation in Cajori, Florian (1913). "History of the Exponential and Logarithmic Concepts". The American Mathematical Monthly. 20 (3): 75–84. doi:10.2307/2973441. JSTOR 2973441. Letting $π$ be the circumference (!) of a circle of unit radius
Euler, Leonhard (1736). "Ch. 3 Prop. 34 Cor. 1". Mechanica sive motus scientia analytice exposita. (cum tabulis) (in Latin). Vol. 1. Academiae scientiarum Petropoli. p. 113. E015. Denotet $1 : π$ rationem diametri ad peripheriam English translation by Ian Bruce : "Let $1 : π$ denote the ratio of the diameter to the circumference"

adsabs.harvard.edu (Global: 14^th place; English: 9^th place)

ui.adsabs.harvard.edu

Kennedy, E. S. (1978). "Abu-r-Raihan al-Biruni, 973–1048". Journal for the History of Astronomy. 9: 65. Bibcode:1978JHA.....9...65K. doi:10.1177/002182867800900106. Ptolemy used a three-sexagesimal-digit approximation, and Jamshīd al-Kāshī expanded this to nine digits; see Aaboe, Asger (1998) [1964]. Episodes from the Early History of Mathematics. New Mathematical Library. Vol. 13. New York: Random House. p. 125. ISBN 978-0-88385-613-0.

americanscientist.org (Global: 9,393^rd place; English: 7,744^th place)

Hayes, Brian (September 2014). "Pencil, Paper, and Pi". American Scientist. Vol. 102, no. 5. p. 342. doi:10.1511/2014.110.342. Retrieved 22 January 2022.

ams.org (Global: 434^th place; English: 249^th place)

mathscinet.ams.org

Mollin, R. A. (1999). "Continued fraction gems". Nieuw Archief voor Wiskunde. 17 (3): 383–405. MR 1743850.
Borwein, Jonathan M. (2014). "The life of $π$ : from Archimedes to ENIAC and beyond". In Sidoli, Nathan; Van Brummelen, Glen (eds.). From Alexandria, through Baghdad: Surveys and studies in the ancient Greek and medieval Islamic mathematical sciences in honor of J. L. Berggren. Heidelberg: Springer. pp. 531–561. doi:10.1007/978-3-642-36736-6_24. ISBN 978-3-642-36735-9. MR 3203895.
Gibbons, Jeremy (2006). "Unbounded spigot algorithms for the digits of pi" (PDF). The American Mathematical Monthly. 113 (4): 318–328. doi:10.2307/27641917. JSTOR 27641917. MR 2211758.
Martini, Horst; Montejano, Luis; Oliveros, Déborah (2019). Bodies of Constant Width: An Introduction to Convex Geometry with Applications. Birkhäuser. doi:10.1007/978-3-030-03868-7. ISBN 978-3-030-03866-3. MR 3930585.
See Barbier's theorem, Corollary 5.1.1, p. 98; Reuleaux triangles, pp. 3, 10; smooth curves such as an analytic curve due to Rabinowitz, § 5.3.3, pp. 111–112.
Howe, Roger (1980). "On the role of the Heisenberg group in harmonic analysis". Bulletin of the American Mathematical Society. 3 (2): 821–844. doi:10.1090/S0273-0979-1980-14825-9. MR 0578375.
Tate, John T. (1967). "Fourier analysis in number fields, and Hecke's zeta-functions". In Cassels, J. W. S.; Fröhlich, A. (eds.). Algebraic Number Theory (Proc. Instructional Conf., Brighton, 1965). Thompson, Washington, DC. pp. 305–347. ISBN 978-0-9502734-2-6. MR 0217026.

archive.org (Global: 6^th place; English: 6^th place)

Remmert 2012, p. 148.
Weierstrass, Karl (1841). "Darstellung einer analytischen Function einer complexen Veränderlichen, deren absoluter Betrag zwischen zwei gegebenen Grenzen liegt" [Representation of an analytical function of a complex variable, whose absolute value lies between two given limits]. Mathematische Werke (in German). Vol. 1. Berlin: Mayer & Müller (published 1894). pp. 51–66. Remmert, Reinhold (2012). "Ch. 5 What is π?". In Heinz-Dieter Ebbinghaus; Hans Hermes; Friedrich Hirzebruch; Max Koecher; Klaus Mainzer; Jürgen Neukirch; Alexander Prestel; Reinhold Remmert (eds.). Numbers. Springer. ISBN 978-1-4612-1005-4.
Baltzer, Richard (1870). Die Elemente der Mathematik [The Elements of Mathematics] (in German). Hirzel. p. 195.
Rudin, Walter (1976). Principles of Mathematical Analysis. McGraw-Hill. p. 183. ISBN 978-0-07-054235-8.
Posamentier & Lehmann 2004, p. 25. Posamentier, Alfred S.; Lehmann, Ingmar (2004). $π$ : A Biography of the World's Most Mysterious Number. Prometheus Books. ISBN 978-1-59102-200-8.
Beckmann, Petr (1989) [1974]. History of Pi. St. Martin's Press. p. 37. ISBN 978-0-88029-418-8.
Schlager, Neil; Lauer, Josh (2001). Science and Its Times: Understanding the Social Significance of Scientific Discovery. Gale Group. ISBN 978-0-7876-3933-4. Retrieved 19 December 2019., p. 185.
Boyer & Merzbach 1991, p. 168. Boyer, Carl B.; Merzbach, Uta C. (1991). A History of Mathematics (2 ed.). Wiley. ISBN 978-0-471-54397-8.
Boyer & Merzbach 1991, p. 202. Boyer, Carl B.; Merzbach, Uta C. (1991). A History of Mathematics (2 ed.). Wiley. ISBN 978-0-471-54397-8.
Jones, William (1706). Synopsis Palmariorum Matheseos. London: J. Wale. pp. 243, 263. p. 263: There are various other ways of finding the Lengths, or Areas of particular Curve Lines or Planes, which may very much facilitate the Practice; as for instance, in the Circle, the Diameter is to Circumference as 1 to
${\overline {{\tfrac {16}{5}}-{\tfrac {4}{239}}}}-{\tfrac {1}{3}}{\overline {{\tfrac {16}{5^{3}}}-{\tfrac {4}{239^{3}}}}}+{\tfrac {1}{5}}{\overline {{\tfrac {16}{5^{5}}}-{\tfrac {4}{239^{5}}}}}-,\,\&c.=$
$3.14159, & c. = π$ . This Series (among others for the same purpose, and drawn from the same Principle) I receiv'd from the Excellent Analyst, and my much Esteem'd Friend Mr. John Machin; and by means thereof, Van Ceulen's Number, or that in Art. 64.38. may be Examin'd with all desireable Ease and Dispatch.
Reprinted in Smith, David E. (1929). "William Jones: The First Use of $π$ for the Circle Ratio". A Source Book in Mathematics. McGraw–Hill. pp. 346–347.
Roy, Ranjan (2021) [1st ed. 2011]. Series and Products in the Development of Mathematics. Vol. 1 (2 ed.). Cambridge University Press. pp. 215–216, 219–220.
Newton, Isaac (1971). "De computo serierum" [On the computation of series]. In Whiteside, Derek Thomas (ed.). The Mathematical Papers of Isaac Newton. Vol. 4, 1674–1684. Cambridge University Press. "De transmutatione serierum" [On the transformation of series] § 3.2.2 pp. 604–615.
Sandifer, Ed (2009). "Estimating π" (PDF). How Euler Did It. Reprinted in How Euler Did Even More. Mathematical Association of America. 2014. pp. 109–118.
Euler, Leonhard (1755). "§ 2.2.30". Institutiones Calculi Differentialis (in Latin). Academiae Imperialis Scientiarium Petropolitanae. p. 318. E 212.
Euler, Leonhard (1798) [written 1779]. "Investigatio quarundam serierum, quae ad rationem peripheriae circuli ad diametrum vero proxime definiendam maxime sunt accommodatae". Nova Acta Academiae Scientiarum Petropolitinae. 11: 133–149, 167–168. E 705.
Hwang, Chien-Lih (2004). "88.38 Some Observations on the Method of Arctangents for the Calculation of $π$ ". Mathematical Gazette. 88 (512): 270–278. doi:10.1017/S0025557200175060. JSTOR 3620848.
Hwang, Chien-Lih (2005). "89.67 An elementary derivation of Euler's series for the arctangent function". Mathematical Gazette. 89 (516): 469–470. doi:10.1017/S0025557200178404. JSTOR 3621947.
Posamentier & Lehmann 2004, p. 284. Posamentier, Alfred S.; Lehmann, Ingmar (2004). $π$ : A Biography of the World's Most Mysterious Number. Prometheus Books. ISBN 978-1-59102-200-8.
Lindemann, F. (1882). "Über die Ludolph'sche Zahl". Sitzungsberichte der Königlich Preussischen Akademie der Wissenschaften zu Berlin. 2: 679–682.
Oughtred, William (1648). Clavis Mathematicæ [The key to mathematics] (in Latin). London: Thomas Harper. p. 69. (English translation: Oughtred, William (1694). Key of the Mathematics. J. Salusbury.)
Smith, David E. (1925). History of Mathematics. Vol. 2: Special Topics of Elementary Mathematics. Boston: Ginn & Company. p. 312.
Barrow, Isaac (1860). "Lecture XXIV". In Whewell, William (ed.). The mathematical works of Isaac Barrow (in Latin). Harvard University. Cambridge University press. p. 381.
Gregorius, David (1695). "Ad Reverendum Virum D. Henricum Aldrich S.T.T. Decanum Aedis Christi Oxoniae" (PDF). Philosophical Transactions (in Latin). 19 (231): 637–652. doi:10.1098/rstl.1695.0114. JSTOR 102382.
Arndt & Haenel 2006, pp. 39–40.
Posamentier & Lehmann 2004, p. 105. Arndt, Jörg; Haenel, Christoph (2006). Pi Unleashed. Springer-Verlag. ISBN 978-3-540-66572-4. Retrieved 5 June 2013. English translation by Catriona and David Lischka. Posamentier, Alfred S.; Lehmann, Ingmar (2004). $π$ : A Biography of the World's Most Mysterious Number. Prometheus Books. ISBN 978-1-59102-200-8.
Arndt & Haenel 2006, p. 43.
Posamentier & Lehmann 2004, pp. 105–108. Arndt, Jörg; Haenel, Christoph (2006). Pi Unleashed. Springer-Verlag. ISBN 978-3-540-66572-4. Retrieved 5 June 2013. English translation by Catriona and David Lischka. Posamentier, Alfred S.; Lehmann, Ingmar (2004). $π$ : A Biography of the World's Most Mysterious Number. Prometheus Books. ISBN 978-1-59102-200-8.
For instance, Pickover calls π "the most famous mathematical constant of all time", and Peterson writes, "Of all known mathematical constants, however, pi continues to attract the most attention", citing the Givenchy π perfume, Pi (film), and Pi Day as examples. See: Pickover, Clifford A. (1995). Keys to Infinity. Wiley & Sons. p. 59. ISBN 978-0-471-11857-2. Peterson, Ivars (2002). Mathematical Treks: From Surreal Numbers to Magic Circles. MAA spectrum. Mathematical Association of America. p. 17. ISBN 978-0-88385-537-9.
Posamentier & Lehmann 2004, p. 118.
Arndt & Haenel 2006, p. 50. Posamentier, Alfred S.; Lehmann, Ingmar (2004). $π$ : A Biography of the World's Most Mysterious Number. Prometheus Books. ISBN 978-1-59102-200-8. Arndt, Jörg; Haenel, Christoph (2006). Pi Unleashed. Springer-Verlag. ISBN 978-3-540-66572-4. Retrieved 5 June 2013. English translation by Catriona and David Lischka.
Arndt & Haenel 2006, pp. 211–212.
Posamentier & Lehmann 2004, pp. 36–37.
Hallerberg, Arthur (May 1977). "Indiana's squared circle". Mathematics Magazine. 50 (3): 136–140. doi:10.2307/2689499. JSTOR 2689499. Arndt, Jörg; Haenel, Christoph (2006). Pi Unleashed. Springer-Verlag. ISBN 978-3-540-66572-4. Retrieved 5 June 2013. English translation by Catriona and David Lischka. Posamentier, Alfred S.; Lehmann, Ingmar (2004). $π$ : A Biography of the World's Most Mysterious Number. Prometheus Books. ISBN 978-1-59102-200-8.

arxiv.org (Global: 49^th place; English: 31^st place)

Plouffe, Simon (2022). "A formula for the $n$ th decimal digit or binary of $π$ and powers of $π$ ". arXiv:2201.12601 [math.NT].
L. Esposito; C. Nitsch; C. Trombetti (2011). "Best constants in Poincaré inequalities for convex domains". arXiv:1110.2960 [math.AP].
Benjamin Nill; Andreas Paffenholz (2014). "On the equality case in Erhart's volume conjecture". Advances in Geometry. 14 (4): 579–586. arXiv:1205.1270. doi:10.1515/advgeom-2014-0001.
Friedmann, T.; Hagen, C. R. (2015). "Quantum mechanical derivation of the Wallis formula for pi". Journal of Mathematical Physics. 56 (11) 112101. arXiv:1510.07813. doi:10.1063/1.4930800.

bbc.co.uk (Global: 11^th place; English: 10^th place)

Palmer, Jason (16 September 2010). "Pi record smashed as team finds two-quadrillionth digit". BBC News. Retrieved 26 March 2011.

bnf.fr (Global: 61^st place; English: 357^th place)

gallica.bnf.fr

Euler, Leonhard (1922). Leonhardi Euleri opera omnia. 1, Opera mathematica. Volumen VIII, Leonhardi Euleri introductio in analysin infinitorum. Tomus primus / ediderunt Adolf Krazer et Ferdinand Rudio (in Latin). Lipsae: B. G. Teubneri. pp. 133–134. E101.

books.google.com (Global: 3^rd place; English: 3^rd place)

Oughtred, William (1652). Theorematum in libris Archimedis de sphaera et cylindro declarario (in Latin). Excudebat L. Lichfield, Veneunt apud T. Robinson. $δ . π$ :: semidiameter. semiperipheria
Arndt & Haenel 2006, p. 8. Arndt, Jörg; Haenel, Christoph (2006). Pi Unleashed. Springer-Verlag. ISBN 978-3-540-66572-4. Retrieved 5 June 2013. English translation by Catriona and David Lischka.
Remmert 2012, p. 129. Remmert, Reinhold (2012). "Ch. 5 What is π?". In Heinz-Dieter Ebbinghaus; Hans Hermes; Friedrich Hirzebruch; Max Koecher; Klaus Mainzer; Jürgen Neukirch; Alexander Prestel; Reinhold Remmert (eds.). Numbers. Springer. ISBN 978-1-4612-1005-4.
Remmert 2012, p. 148.
Weierstrass, Karl (1841). "Darstellung einer analytischen Function einer complexen Veränderlichen, deren absoluter Betrag zwischen zwei gegebenen Grenzen liegt" [Representation of an analytical function of a complex variable, whose absolute value lies between two given limits]. Mathematische Werke (in German). Vol. 1. Berlin: Mayer & Müller (published 1894). pp. 51–66. Remmert, Reinhold (2012). "Ch. 5 What is π?". In Heinz-Dieter Ebbinghaus; Hans Hermes; Friedrich Hirzebruch; Max Koecher; Klaus Mainzer; Jürgen Neukirch; Alexander Prestel; Reinhold Remmert (eds.). Numbers. Springer. ISBN 978-1-4612-1005-4.
Arndt & Haenel 2006, p. 5. Arndt, Jörg; Haenel, Christoph (2006). Pi Unleashed. Springer-Verlag. ISBN 978-3-540-66572-4. Retrieved 5 June 2013. English translation by Catriona and David Lischka.
Arndt & Haenel 2006, pp. 22–23. Arndt, Jörg; Haenel, Christoph (2006). Pi Unleashed. Springer-Verlag. ISBN 978-3-540-66572-4. Retrieved 5 June 2013. English translation by Catriona and David Lischka.
Arndt & Haenel 2006, pp. 22, 28–30. Arndt, Jörg; Haenel, Christoph (2006). Pi Unleashed. Springer-Verlag. ISBN 978-3-540-66572-4. Retrieved 5 June 2013. English translation by Catriona and David Lischka.
Arndt & Haenel 2006, p. 3. Arndt, Jörg; Haenel, Christoph (2006). Pi Unleashed. Springer-Verlag. ISBN 978-3-540-66572-4. Retrieved 5 June 2013. English translation by Catriona and David Lischka.
Arndt & Haenel 2006, pp. 6–7. Arndt, Jörg; Haenel, Christoph (2006). Pi Unleashed. Springer-Verlag. ISBN 978-3-540-66572-4. Retrieved 5 June 2013. English translation by Catriona and David Lischka.
Arndt & Haenel 2006, p. 33. Arndt, Jörg; Haenel, Christoph (2006). Pi Unleashed. Springer-Verlag. ISBN 978-3-540-66572-4. Retrieved 5 June 2013. English translation by Catriona and David Lischka.
Arndt & Haenel 2006, p. 240. Arndt, Jörg; Haenel, Christoph (2006). Pi Unleashed. Springer-Verlag. ISBN 978-3-540-66572-4. Retrieved 5 June 2013. English translation by Catriona and David Lischka.
Arndt & Haenel 2006, p. 242. Arndt, Jörg; Haenel, Christoph (2006). Pi Unleashed. Springer-Verlag. ISBN 978-3-540-66572-4. Retrieved 5 June 2013. English translation by Catriona and David Lischka.
Kennedy, E. S. (1978). "Abu-r-Raihan al-Biruni, 973–1048". Journal for the History of Astronomy. 9: 65. Bibcode:1978JHA.....9...65K. doi:10.1177/002182867800900106. Ptolemy used a three-sexagesimal-digit approximation, and Jamshīd al-Kāshī expanded this to nine digits; see Aaboe, Asger (1998) [1964]. Episodes from the Early History of Mathematics. New Mathematical Library. Vol. 13. New York: Random House. p. 125. ISBN 978-0-88385-613-0.
Andrews, Askey & Roy 1999, p. 14. Andrews, George E.; Askey, Richard; Roy, Ranjan (1999). Special Functions. Cambridge: University Press. ISBN 978-0-521-78988-2.
Arndt & Haenel 2006, p. 167. Arndt, Jörg; Haenel, Christoph (2006). Pi Unleashed. Springer-Verlag. ISBN 978-3-540-66572-4. Retrieved 5 June 2013. English translation by Catriona and David Lischka.
Herz-Fischler, Roger (2000). The Shape of the Great Pyramid. Wilfrid Laurier University Press. pp. 67–77, 165–166. ISBN 978-0-88920-324-2. Retrieved 5 June 2013.
Plofker, Kim (2009). Mathematics in India. Princeton University Press. p. 27. ISBN 978-0-691-12067-6.
Arndt & Haenel 2006, p. 170. Arndt, Jörg; Haenel, Christoph (2006). Pi Unleashed. Springer-Verlag. ISBN 978-3-540-66572-4. Retrieved 5 June 2013. English translation by Catriona and David Lischka.
Arndt & Haenel 2006, pp. 175, 205. Arndt, Jörg; Haenel, Christoph (2006). Pi Unleashed. Springer-Verlag. ISBN 978-3-540-66572-4. Retrieved 5 June 2013. English translation by Catriona and David Lischka.
Arndt & Haenel 2006, p. 171. Arndt, Jörg; Haenel, Christoph (2006). Pi Unleashed. Springer-Verlag. ISBN 978-3-540-66572-4. Retrieved 5 June 2013. English translation by Catriona and David Lischka.
Arndt & Haenel 2006, p. 176. Arndt, Jörg; Haenel, Christoph (2006). Pi Unleashed. Springer-Verlag. ISBN 978-3-540-66572-4. Retrieved 5 June 2013. English translation by Catriona and David Lischka.
Arndt & Haenel 2006, pp. 176–177. Arndt, Jörg; Haenel, Christoph (2006). Pi Unleashed. Springer-Verlag. ISBN 978-3-540-66572-4. Retrieved 5 June 2013. English translation by Catriona and David Lischka.
Arndt & Haenel 2006, p. 177. Arndt, Jörg; Haenel, Christoph (2006). Pi Unleashed. Springer-Verlag. ISBN 978-3-540-66572-4. Retrieved 5 June 2013. English translation by Catriona and David Lischka.
Arndt & Haenel 2006, p. 178. Arndt, Jörg; Haenel, Christoph (2006). Pi Unleashed. Springer-Verlag. ISBN 978-3-540-66572-4. Retrieved 5 June 2013. English translation by Catriona and David Lischka.
Arndt & Haenel 2006, p. 179. Arndt, Jörg; Haenel, Christoph (2006). Pi Unleashed. Springer-Verlag. ISBN 978-3-540-66572-4. Retrieved 5 June 2013. English translation by Catriona and David Lischka.
Arndt & Haenel 2006, p. 180. Arndt, Jörg; Haenel, Christoph (2006). Pi Unleashed. Springer-Verlag. ISBN 978-3-540-66572-4. Retrieved 5 June 2013. English translation by Catriona and David Lischka.
Arndt & Haenel 2006, p. 182. Arndt, Jörg; Haenel, Christoph (2006). Pi Unleashed. Springer-Verlag. ISBN 978-3-540-66572-4. Retrieved 5 June 2013. English translation by Catriona and David Lischka.
Arndt & Haenel 2006, pp. 182–183. Arndt, Jörg; Haenel, Christoph (2006). Pi Unleashed. Springer-Verlag. ISBN 978-3-540-66572-4. Retrieved 5 June 2013. English translation by Catriona and David Lischka.
Arndt & Haenel 2006, p. 183. Arndt, Jörg; Haenel, Christoph (2006). Pi Unleashed. Springer-Verlag. ISBN 978-3-540-66572-4. Retrieved 5 June 2013. English translation by Catriona and David Lischka.
Arndt & Haenel 2006, pp. 185–191. Arndt, Jörg; Haenel, Christoph (2006). Pi Unleashed. Springer-Verlag. ISBN 978-3-540-66572-4. Retrieved 5 June 2013. English translation by Catriona and David Lischka.
Arndt & Haenel 2006, pp. 185–186. Arndt, Jörg; Haenel, Christoph (2006). Pi Unleashed. Springer-Verlag. ISBN 978-3-540-66572-4. Retrieved 5 June 2013. English translation by Catriona and David Lischka.
Joseph, George Gheverghese (1991). The Crest of the Peacock: Non-European Roots of Mathematics. Princeton University Press. p. 264. ISBN 978-0-691-13526-7.
Andrews, Askey & Roy 1999, p. 59. Andrews, George E.; Askey, Richard; Roy, Ranjan (1999). Special Functions. Cambridge: University Press. ISBN 978-0-521-78988-2.
Arndt & Haenel 2006, p. 187.
Vieta, Franciscus (1593). Variorum de rebus mathematicis responsorum. Vol. VIII.
OEIS: A060294 Arndt, Jörg; Haenel, Christoph (2006). Pi Unleashed. Springer-Verlag. ISBN 978-3-540-66572-4. Retrieved 5 June 2013. English translation by Catriona and David Lischka.
Arndt & Haenel 2006, p. 187. Arndt, Jörg; Haenel, Christoph (2006). Pi Unleashed. Springer-Verlag. ISBN 978-3-540-66572-4. Retrieved 5 June 2013. English translation by Catriona and David Lischka.
Arndt & Haenel 2006, p. 188. Newton quoted by Arndt. Arndt, Jörg; Haenel, Christoph (2006). Pi Unleashed. Springer-Verlag. ISBN 978-3-540-66572-4. Retrieved 5 June 2013. English translation by Catriona and David Lischka.
Arndt & Haenel 2006, p. 189. Arndt, Jörg; Haenel, Christoph (2006). Pi Unleashed. Springer-Verlag. ISBN 978-3-540-66572-4. Retrieved 5 June 2013. English translation by Catriona and David Lischka.
Arndt & Haenel 2006, pp. 192–193. Arndt, Jörg; Haenel, Christoph (2006). Pi Unleashed. Springer-Verlag. ISBN 978-3-540-66572-4. Retrieved 5 June 2013. English translation by Catriona and David Lischka.
Arndt & Haenel 2006, pp. 72–74. Arndt, Jörg; Haenel, Christoph (2006). Pi Unleashed. Springer-Verlag. ISBN 978-3-540-66572-4. Retrieved 5 June 2013. English translation by Catriona and David Lischka.
Arndt & Haenel 2006, pp. 194–196. Arndt, Jörg; Haenel, Christoph (2006). Pi Unleashed. Springer-Verlag. ISBN 978-3-540-66572-4. Retrieved 5 June 2013. English translation by Catriona and David Lischka.
Arndt & Haenel 2006, pp. 192–196, 205. Arndt, Jörg; Haenel, Christoph (2006). Pi Unleashed. Springer-Verlag. ISBN 978-3-540-66572-4. Retrieved 5 June 2013. English translation by Catriona and David Lischka.
Borwein, J. M.; Borwein, P. B. (1988). "Ramanujan and Pi". Scientific American. 256 (2): 112–117. doi:10.1038/scientificamerican0288-112.
Arndt & Haenel 2006, pp. 15–17, 70–72, 104, 156, 192–197, 201–202. Arndt, Jörg; Haenel, Christoph (2006). Pi Unleashed. Springer-Verlag. ISBN 978-3-540-66572-4. Retrieved 5 June 2013. English translation by Catriona and David Lischka.
Arndt & Haenel 2006, pp. 69–72. Arndt, Jörg; Haenel, Christoph (2006). Pi Unleashed. Springer-Verlag. ISBN 978-3-540-66572-4. Retrieved 5 June 2013. English translation by Catriona and David Lischka.
Arndt & Haenel 2006, Formula 16.10, p. 223. Arndt, Jörg; Haenel, Christoph (2006). Pi Unleashed. Springer-Verlag. ISBN 978-3-540-66572-4. Retrieved 5 June 2013. English translation by Catriona and David Lischka.
Arndt & Haenel 2006, p. 196. Arndt, Jörg; Haenel, Christoph (2006). Pi Unleashed. Springer-Verlag. ISBN 978-3-540-66572-4. Retrieved 5 June 2013. English translation by Catriona and David Lischka.
Oughtred, William (1648). Clavis Mathematicæ [The key to mathematics] (in Latin). London: Thomas Harper. p. 69. (English translation: Oughtred, William (1694). Key of the Mathematics. J. Salusbury.)
Arndt & Haenel 2006, p. 166. Arndt, Jörg; Haenel, Christoph (2006). Pi Unleashed. Springer-Verlag. ISBN 978-3-540-66572-4. Retrieved 5 June 2013. English translation by Catriona and David Lischka.
Cajori, Florian (2007). A History of Mathematical Notations: Vol. II. Cosimo, Inc. pp. 8–13. ISBN 978-1-60206-714-1. the ratio of the length of a circle to its diameter was represented in the fractional form by the use of two letters ... J.A. Segner ... in 1767, he represented $3.14159...$ by $δ : π$ , as did Oughtred more than a century earlier
Arndt & Haenel 2006, p. 165: A facsimile of Jones' text is in Berggren, Borwein & Borwein 1997, pp. 108–109. Arndt, Jörg; Haenel, Christoph (2006). Pi Unleashed. Springer-Verlag. ISBN 978-3-540-66572-4. Retrieved 5 June 2013. English translation by Catriona and David Lischka. Berggren, Lennart; Borwein, Jonathan; Borwein, Peter (1997). Pi: a Source Book. Springer-Verlag. ISBN 978-0-387-20571-7.
Segner, Joannes Andreas (1756). Cursus Mathematicus (in Latin). Halae Magdeburgicae. p. 282.
Euler, Leonhard (1727). "Tentamen explicationis phaenomenorum aeris" (PDF). Commentarii Academiae Scientiarum Imperialis Petropolitana (in Latin). 2: 351. E007. Retrieved 15 October 2017. Sumatur pro ratione radii ad peripheriem, $I : π$ English translation by Ian Bruce: " $π$ is taken for the ratio of the radius to the periphery [note that in this work, Euler's $π$ is double our $π$ .]"
Euler, Leonhard (1747). Henry, Charles (ed.). Lettres inédites d'Euler à d'Alembert. Bullettino di Bibliografia e di Storia delle Scienze Matematiche e Fisiche (in French). Vol. 19 (published 1886). p. 139. E858. Car, soit π la circonference d'un cercle, dout le rayon est $= 1$ English translation in Cajori, Florian (1913). "History of the Exponential and Logarithmic Concepts". The American Mathematical Monthly. 20 (3): 75–84. doi:10.2307/2973441. JSTOR 2973441. Letting $π$ be the circumference (!) of a circle of unit radius
Euler, Leonhard (1736). "Ch. 3 Prop. 34 Cor. 1". Mechanica sive motus scientia analytice exposita. (cum tabulis) (in Latin). Vol. 1. Academiae scientiarum Petropoli. p. 113. E015. Denotet $1 : π$ rationem diametri ad peripheriam English translation by Ian Bruce : "Let $1 : π$ denote the ratio of the diameter to the circumference"
Segner, Johann Andreas von (1761). Cursus Mathematicus: Elementorum Analyseos Infinitorum Elementorum Analyseos Infinitorvm (in Latin). Renger. p. 374. Si autem $π$ notet peripheriam circuli, cuius diameter eſt $2$
Arndt & Haenel 2006, pp. 17–19. Arndt, Jörg; Haenel, Christoph (2006). Pi Unleashed. Springer-Verlag. ISBN 978-3-540-66572-4. Retrieved 5 June 2013. English translation by Catriona and David Lischka.
Arndt & Haenel 2006, pp. 17–18. Arndt, Jörg; Haenel, Christoph (2006). Pi Unleashed. Springer-Verlag. ISBN 978-3-540-66572-4. Retrieved 5 June 2013. English translation by Catriona and David Lischka.
Arndt & Haenel 2006, p. 205. Arndt, Jörg; Haenel, Christoph (2006). Pi Unleashed. Springer-Verlag. ISBN 978-3-540-66572-4. Retrieved 5 June 2013. English translation by Catriona and David Lischka.
Arndt & Haenel 2006, p. 197. Arndt, Jörg; Haenel, Christoph (2006). Pi Unleashed. Springer-Verlag. ISBN 978-3-540-66572-4. Retrieved 5 June 2013. English translation by Catriona and David Lischka.
Arndt & Haenel 2006, pp. 15–17. Arndt, Jörg; Haenel, Christoph (2006). Pi Unleashed. Springer-Verlag. ISBN 978-3-540-66572-4. Retrieved 5 June 2013. English translation by Catriona and David Lischka.
Arndt & Haenel 2006, p. 131. Arndt, Jörg; Haenel, Christoph (2006). Pi Unleashed. Springer-Verlag. ISBN 978-3-540-66572-4. Retrieved 5 June 2013. English translation by Catriona and David Lischka.
Arndt & Haenel 2006, pp. 132, 140. Arndt, Jörg; Haenel, Christoph (2006). Pi Unleashed. Springer-Verlag. ISBN 978-3-540-66572-4. Retrieved 5 June 2013. English translation by Catriona and David Lischka.
Arndt & Haenel 2006, p. 87. Arndt, Jörg; Haenel, Christoph (2006). Pi Unleashed. Springer-Verlag. ISBN 978-3-540-66572-4. Retrieved 5 June 2013. English translation by Catriona and David Lischka.
Arndt & Haenel 2006, p. 111 (5 times); pp. 113–114 (4 times). For details of algorithms, see Borwein, Jonathan; Borwein, Peter (1987). Pi and the AGM: a Study in Analytic Number Theory and Computational Complexity. Wiley. ISBN 978-0-471-31515-5. Arndt, Jörg; Haenel, Christoph (2006). Pi Unleashed. Springer-Verlag. ISBN 978-3-540-66572-4. Retrieved 5 June 2013. English translation by Catriona and David Lischka.
Arndt & Haenel 2006, pp. 103–104. Arndt, Jörg; Haenel, Christoph (2006). Pi Unleashed. Springer-Verlag. ISBN 978-3-540-66572-4. Retrieved 5 June 2013. English translation by Catriona and David Lischka.
Arndt & Haenel 2006, p. 104. Arndt, Jörg; Haenel, Christoph (2006). Pi Unleashed. Springer-Verlag. ISBN 978-3-540-66572-4. Retrieved 5 June 2013. English translation by Catriona and David Lischka.
Arndt & Haenel 2006, pp. 104, 206. Arndt, Jörg; Haenel, Christoph (2006). Pi Unleashed. Springer-Verlag. ISBN 978-3-540-66572-4. Retrieved 5 June 2013. English translation by Catriona and David Lischka.
Arndt & Haenel 2006, pp. 110–111. Arndt, Jörg; Haenel, Christoph (2006). Pi Unleashed. Springer-Verlag. ISBN 978-3-540-66572-4. Retrieved 5 June 2013. English translation by Catriona and David Lischka.
Bailey, David H.; Borwein, Jonathan M. (2016). "15.2 Computational records". Pi: The Next Generation, A Sourcebook on the Recent History of Pi and Its Computation. Springer International Publishing. p. 469. doi:10.1007/978-3-319-32377-0. ISBN 978-3-319-32375-6.
Arndt & Haenel 2006, p. 39. Arndt, Jörg; Haenel, Christoph (2006). Pi Unleashed. Springer-Verlag. ISBN 978-3-540-66572-4. Retrieved 5 June 2013. English translation by Catriona and David Lischka.
Arndt & Haenel 2006, pp. 39–40.
Posamentier & Lehmann 2004, p. 105. Arndt, Jörg; Haenel, Christoph (2006). Pi Unleashed. Springer-Verlag. ISBN 978-3-540-66572-4. Retrieved 5 June 2013. English translation by Catriona and David Lischka. Posamentier, Alfred S.; Lehmann, Ingmar (2004). $π$ : A Biography of the World's Most Mysterious Number. Prometheus Books. ISBN 978-1-59102-200-8.
Arndt & Haenel 2006, p. 43.
Posamentier & Lehmann 2004, pp. 105–108. Arndt, Jörg; Haenel, Christoph (2006). Pi Unleashed. Springer-Verlag. ISBN 978-3-540-66572-4. Retrieved 5 June 2013. English translation by Catriona and David Lischka. Posamentier, Alfred S.; Lehmann, Ingmar (2004). $π$ : A Biography of the World's Most Mysterious Number. Prometheus Books. ISBN 978-1-59102-200-8.
Arndt & Haenel 2006, pp. 77–84. Arndt, Jörg; Haenel, Christoph (2006). Pi Unleashed. Springer-Verlag. ISBN 978-3-540-66572-4. Retrieved 5 June 2013. English translation by Catriona and David Lischka.
Arndt & Haenel 2006, p. 77. Arndt, Jörg; Haenel, Christoph (2006). Pi Unleashed. Springer-Verlag. ISBN 978-3-540-66572-4. Retrieved 5 June 2013. English translation by Catriona and David Lischka.
Arndt & Haenel 2006, pp. 117, 126–128. Arndt, Jörg; Haenel, Christoph (2006). Pi Unleashed. Springer-Verlag. ISBN 978-3-540-66572-4. Retrieved 5 June 2013. English translation by Catriona and David Lischka.
Arndt & Haenel 2006, p. 20.
Bellards formula in: Bellard, Fabrice. "A new formula to compute the n^th binary digit of pi". Archived from the original on 12 September 2007. Retrieved 27 October 2007. Arndt, Jörg; Haenel, Christoph (2006). Pi Unleashed. Springer-Verlag. ISBN 978-3-540-66572-4. Retrieved 5 June 2013. English translation by Catriona and David Lischka.
Arndt & Haenel 2006, pp. 41–43.
This theorem was proved by Ernesto Cesàro in 1881. For a more rigorous proof than the intuitive and informal one given here, see Hardy, G. H. (2008). An Introduction to the Theory of Numbers. Oxford University Press. Theorem 332. ISBN 978-0-19-921986-5. Arndt, Jörg; Haenel, Christoph (2006). Pi Unleashed. Springer-Verlag. ISBN 978-3-540-66572-4. Retrieved 5 June 2013. English translation by Catriona and David Lischka.
Arndt & Haenel 2006, p. 43. Arndt, Jörg; Haenel, Christoph (2006). Pi Unleashed. Springer-Verlag. ISBN 978-3-540-66572-4. Retrieved 5 June 2013. English translation by Catriona and David Lischka.
Itzykson, C.; Zuber, J.-B. (1980). Quantum Field Theory (2005 ed.). Mineola, NY: Dover Publications. ISBN 978-0-486-44568-7. LCCN 2005053026. OCLC 61200849.
Arndt & Haenel 2006, pp. 44–45. Arndt, Jörg; Haenel, Christoph (2006). Pi Unleashed. Springer-Verlag. ISBN 978-3-540-66572-4. Retrieved 5 June 2013. English translation by Catriona and David Lischka.
Danesi, Marcel (January 2021). "Chapter 4: Pi in Popular Culture". Pi ( $π$ ) in Nature, Art, and Culture. Brill. p. 97. doi:10.1163/9789004433397. ISBN 978-90-04-43337-3.
For instance, Pickover calls π "the most famous mathematical constant of all time", and Peterson writes, "Of all known mathematical constants, however, pi continues to attract the most attention", citing the Givenchy π perfume, Pi (film), and Pi Day as examples. See: Pickover, Clifford A. (1995). Keys to Infinity. Wiley & Sons. p. 59. ISBN 978-0-471-11857-2. Peterson, Ivars (2002). Mathematical Treks: From Surreal Numbers to Magic Circles. MAA spectrum. Mathematical Association of America. p. 17. ISBN 978-0-88385-537-9.
Posamentier & Lehmann 2004, p. 118.
Arndt & Haenel 2006, p. 50. Posamentier, Alfred S.; Lehmann, Ingmar (2004). $π$ : A Biography of the World's Most Mysterious Number. Prometheus Books. ISBN 978-1-59102-200-8. Arndt, Jörg; Haenel, Christoph (2006). Pi Unleashed. Springer-Verlag. ISBN 978-3-540-66572-4. Retrieved 5 June 2013. English translation by Catriona and David Lischka.
Arndt & Haenel 2006, p. 14.
Polster, Burkard; Ross, Marty (2012). Math Goes to the Movies. Johns Hopkins University Press. pp. 56–57. ISBN 978-1-4214-0484-4. Arndt, Jörg; Haenel, Christoph (2006). Pi Unleashed. Springer-Verlag. ISBN 978-3-540-66572-4. Retrieved 5 June 2013. English translation by Catriona and David Lischka.
Rubillo, James M. (January 1989). "Disintegrate 'em". The Mathematics Teacher. 82 (1): 10. JSTOR 27966082.
Petroski, Henry (2011). Title An Engineer's Alphabet: Gleanings from the Softer Side of a Profession. Cambridge University Press. p. 47. ISBN 978-1-139-50530-7.
Freiberger, Marianne; Thomas, Rachel (2015). "Tau – the new π". Numericon: A Journey through the Hidden Lives of Numbers. Quercus. p. 159. ISBN 978-1-62365-411-5.
Abbott, Stephen (April 2012). "My Conversion to Tauism" (PDF). Math Horizons. 19 (4): 34. doi:10.4169/mathhorizons.19.4.34.
Arndt & Haenel 2006, pp. 211–212.
Posamentier & Lehmann 2004, pp. 36–37.
Hallerberg, Arthur (May 1977). "Indiana's squared circle". Mathematics Magazine. 50 (3): 136–140. doi:10.2307/2689499. JSTOR 2689499. Arndt, Jörg; Haenel, Christoph (2006). Pi Unleashed. Springer-Verlag. ISBN 978-3-540-66572-4. Retrieved 5 June 2013. English translation by Catriona and David Lischka. Posamentier, Alfred S.; Lehmann, Ingmar (2004). $π$ : A Biography of the World's Most Mysterious Number. Prometheus Books. ISBN 978-1-59102-200-8.

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Cooker, M. J. (2011). "Fast formulas for slowly convergent alternating series" (PDF). Mathematical Gazette. 95 (533): 218–226. doi:10.1017/S0025557200002928. Archived from the original (PDF) on 4 May 2019. Retrieved 23 February 2023.

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Goss, Jamal (13 March 2026). "Pi Day means big business for Pie Bar in Kennesaw". CBS News. Retrieved 14 March 2026. ...the math-themed holiday has also become a sweet tradition at bakeries across the country.

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Haruka Iwao, Emma (14 March 2019). "Pi in the sky: Calculating a record-breaking 31.4 trillion digits of Archimedes' constant on Google Cloud". Google Cloud Platform. Retrieved 12 April 2019.

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Klebanoff, Aaron (2001). "Pi in the Mandelbrot set" (PDF). Fractals. 9 (4): 393–402. doi:10.1142/S0218348X01000828. Archived from the original (PDF) on 27 October 2011. Retrieved 14 April 2012.
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dbnl.org (Global: 1,412^th place; English: 1,636^th place)

Brezinski, C. (2009). "Some pioneers of extrapolation methods". In Bultheel, Adhemar; Cools, Ronald (eds.). The Birth of Numerical Analysis. World Scientific. pp. 1–22. doi:10.1142/9789812836267_0001. ISBN 978-981-283-625-0.
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Kennedy, E. S. (1978). "Abu-r-Raihan al-Biruni, 973–1048". Journal for the History of Astronomy. 9: 65. Bibcode:1978JHA.....9...65K. doi:10.1177/002182867800900106. Ptolemy used a three-sexagesimal-digit approximation, and Jamshīd al-Kāshī expanded this to nine digits; see Aaboe, Asger (1998) [1964]. Episodes from the Early History of Mathematics. New Mathematical Library. Vol. 13. New York: Random House. p. 125. ISBN 978-0-88385-613-0.
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Yoder, Joella G. (1996). "Following in the footsteps of geometry: The mathematical world of Christiaan Huygens". De Zeventiende Eeuw. 12: 83–93 – via Digital Library for Dutch Literature.
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Euler, Leonhard (1755). "§ 2.2.30". Institutiones Calculi Differentialis (in Latin). Academiae Imperialis Scientiarium Petropolitanae. p. 318. E 212.
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Arndt & Haenel 2006, pp. 15–17, 70–72, 104, 156, 192–197, 201–202. Arndt, Jörg; Haenel, Christoph (2006). Pi Unleashed. Springer-Verlag. ISBN 978-3-540-66572-4. Retrieved 5 June 2013. English translation by Catriona and David Lischka.
Borwein, J. M.; Borwein, P. B.; Dilcher, K. (1989). "Pi, Euler Numbers, and Asymptotic Expansions". American Mathematical Monthly. 96 (8): 681–687. doi:10.2307/2324715. hdl:1959.13/1043679. JSTOR 2324715.
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Euler, Leonhard (1747). Henry, Charles (ed.). Lettres inédites d'Euler à d'Alembert. Bullettino di Bibliografia e di Storia delle Scienze Matematiche e Fisiche (in French). Vol. 19 (published 1886). p. 139. E858. Car, soit π la circonference d'un cercle, dout le rayon est $= 1$ English translation in Cajori, Florian (1913). "History of the Exponential and Logarithmic Concepts". The American Mathematical Monthly. 20 (3): 75–84. doi:10.2307/2973441. JSTOR 2973441. Letting $π$ be the circumference (!) of a circle of unit radius
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Martini, Horst; Montejano, Luis; Oliveros, Déborah (2019). Bodies of Constant Width: An Introduction to Convex Geometry with Applications. Birkhäuser. doi:10.1007/978-3-030-03868-7. ISBN 978-3-030-03866-3. MR 3930585.
See Barbier's theorem, Corollary 5.1.1, p. 98; Reuleaux triangles, pp. 3, 10; smooth curves such as an analytic curve due to Rabinowitz, § 5.3.3, pp. 111–112.
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Euler, Leonhard (1755). "§ 2.2.30". Institutiones Calculi Differentialis (in Latin). Academiae Imperialis Scientiarium Petropolitanae. p. 318. E 212.
Euler, Leonhard (1798) [written 1779]. "Investigatio quarundam serierum, quae ad rationem peripheriae circuli ad diametrum vero proxime definiendam maxime sunt accommodatae". Nova Acta Academiae Scientiarum Petropolitinae. 11: 133–149, 167–168. E 705.
Hwang, Chien-Lih (2004). "88.38 Some Observations on the Method of Arctangents for the Calculation of $π$ ". Mathematical Gazette. 88 (512): 270–278. doi:10.1017/S0025557200175060. JSTOR 3620848.
Hwang, Chien-Lih (2005). "89.67 An elementary derivation of Euler's series for the arctangent function". Mathematical Gazette. 89 (516): 469–470. doi:10.1017/S0025557200178404. JSTOR 3621947.
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Lehmer, D. H. (1938). "On Arccotangent Relations for π" (PDF). American Mathematical Monthly. 45 (10): 657–664 Published by: Mathematical Association of America. doi:10.1080/00029890.1938.11990873. JSTOR 2302434. Archived from the original (PDF) on 7 March 2023. Retrieved 21 February 2023.
Freiberger, Marianne; Thomas, Rachel (2015). "Tau – the new π". Numericon: A Journey through the Hidden Lives of Numbers. Quercus. p. 159. ISBN 978-1-62365-411-5.
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pubmed.ncbi.nlm.nih.gov

Raz, A.; Packard, M. G. (2009). "A slice of pi: An exploratory neuroimaging study of digit encoding and retrieval in a superior memorist". Neurocase. 15 (5): 361–372. doi:10.1080/13554790902776896. PMC 4323087. PMID 19585350.

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Sandifer, Ed (2009). "Estimating π" (PDF). How Euler Did It. Reprinted in How Euler Did Even More. Mathematical Association of America. 2014. pp. 109–118.
Euler, Leonhard (1755). "§ 2.2.30". Institutiones Calculi Differentialis (in Latin). Academiae Imperialis Scientiarium Petropolitanae. p. 318. E 212.
Euler, Leonhard (1798) [written 1779]. "Investigatio quarundam serierum, quae ad rationem peripheriae circuli ad diametrum vero proxime definiendam maxime sunt accommodatae". Nova Acta Academiae Scientiarum Petropolitinae. 11: 133–149, 167–168. E 705.
Hwang, Chien-Lih (2004). "88.38 Some Observations on the Method of Arctangents for the Calculation of $π$ ". Mathematical Gazette. 88 (512): 270–278. doi:10.1017/S0025557200175060. JSTOR 3620848.
Hwang, Chien-Lih (2005). "89.67 An elementary derivation of Euler's series for the arctangent function". Mathematical Gazette. 89 (516): 469–470. doi:10.1017/S0025557200178404. JSTOR 3621947.

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Itzykson, C.; Zuber, J.-B. (1980). Quantum Field Theory (2005 ed.). Mineola, NY: Dover Publications. ISBN 978-0-486-44568-7. LCCN 2005053026. OCLC 61200849.

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jstor.org (Global: 23rd place; English: 15th place)

lbl.gov (Global: 3,154th place; English: 3,216th place)

crd-legacy.lbl.gov

loc.gov (Global: 63rd place; English: 47th place)

lccn.loc.gov

maa.org (Global: 4,358th place; English: 2,907th place)

eulerarchive.maa.org

maa.org

nih.gov (Global: 5th place; English: 5th place)

ncbi.nlm.nih.gov

pubmed.ncbi.nlm.nih.gov

nytimes.com (Global: 7th place; English: 7th place)

oeis.org (Global: 1,188th place; English: 866th place)

openstax.org (Global: 8,731st place; English: 6,059th place)

ox.ac.uk (Global: 541st place; English: 356th place)

cs.ox.ac.uk

pacific.edu (Global: low place; English: low place)

scholarlycommons.pacific.edu

plouffe.fr (Global: low place; English: low place)

probability.ca (Global: low place; English: low place)

reference.com (Global: 1,491st place; English: 1,468th place)

dictionary.reference.com

sciencenews.org (Global: 4,656th place; English: 3,908th place)

st-and.ac.uk (Global: 4,765th place; English: 5,091st place)

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

telegraphindia.com (Global: 640th place; English: 331st place)

thenewstack.io (Global: low place; English: low place)

usatoday.com (Global: 55th place; English: 36th place)

utah.edu (Global: 2,766th place; English: 1,555th place)

math.utah.edu

web.archive.org (Global: 1st place; English: 1st place)

wolfram.com (Global: 1,091st place; English: 1,169th place)

mathworld.wolfram.com

worldcat.org (Global: 4th place; English: 4th place)

search.worldcat.org

worldscientific.com (Global: low place; English: 6,878th place)

adsabs.harvard.edu (Global: 14^th place; English: 9^th place)

americanscientist.org (Global: 9,393^rd place; English: 7,744^th place)

ams.org (Global: 434^th place; English: 249^th place)

archive.org (Global: 6^th place; English: 6^th place)

arxiv.org (Global: 49^th place; English: 31^st place)

bbc.co.uk (Global: 11^th place; English: 10^th place)

bnf.fr (Global: 61^st place; English: 357^th place)

books.google.com (Global: 3^rd place; English: 3^rd place)

cambridge.org (Global: 209^th place; English: 151^st place)

cbsnews.com (Global: 136^th place; English: 93^rd place)

cloud.google.com (Global: low place; English: 8,446^th place)

comcast.net (Global: 5,430^th place; English: 3,786^th place)

dbnl.org (Global: 1,412^th place; English: 1,636^th place)

doi.org (Global: 2^nd place; English: 2^nd place)

elte.hu (Global: 5,662^nd place; English: 8,968^th place)

free.fr (Global: 283^rd place; English: 705^th place)

guinnessworldrecords.com (Global: 873^rd place; English: 697^th place)

hdl.handle.net (Global: 66^th place; English: 34^th place)

independent.co.uk (Global: 46^th place; English: 29^th place)

japantimes.co.jp (Global: 407^th place; English: 286^th place)

jstor.org (Global: 23^rd place; English: 15^th place)

lbl.gov (Global: 3,154^th place; English: 3,216^th place)

loc.gov (Global: 63^rd place; English: 47^th place)

maa.org (Global: 4,358^th place; English: 2,907^th place)

nih.gov (Global: 5^th place; English: 5^th place)

nytimes.com (Global: 7^th place; English: 7^th place)

oeis.org (Global: 1,188^th place; English: 866^th place)

openstax.org (Global: 8,731^st place; English: 6,059^th place)

ox.ac.uk (Global: 541^st place; English: 356^th place)

reference.com (Global: 1,491^st place; English: 1,468^th place)

sciencenews.org (Global: 4,656^th place; English: 3,908^th place)

st-and.ac.uk (Global: 4,765^th place; English: 5,091^st place)

telegraphindia.com (Global: 640^th place; English: 331^st place)

usatoday.com (Global: 55^th place; English: 36^th place)

utah.edu (Global: 2,766^th place; English: 1,555^th place)

web.archive.org (Global: 1^st place; English: 1^st place)

wolfram.com (Global: 1,091^st place; English: 1,169^th place)

worldcat.org (Global: 4^th place; English: 4^th place)

worldscientific.com (Global: low place; English: 6,878^th place)