عدد پی
ارجاعات

↑  Jones, William (1706). Synopsis Palmariorum Matheseos: or, a New Introduction to the Mathematics (به انگلیسی). pp. 243, 263. Archived from the original on 25 March 2012. Retrieved 15 October 2017.
↑  "Compendium of Mathematical Symbols". Math Vault (به انگلیسی). 2020-03-01. Retrieved 2020-08-10.
1 2  Weisstein, Eric W. "Pi". mathworld.wolfram.com (به انگلیسی). Retrieved 2020-08-10.
↑  Bogart, Steven. "What Is Pi, and How Did It Originate?". Scientific American (به انگلیسی). Retrieved 2020-08-10.
↑  Andrews, Askey & Roy 1999, p. 59.
↑  Gupta 1992, pp. 68–71.
↑  "πe trillion digits of π". pi2e.ch. Archived from the original on 6 December 2016.
↑  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. Archived from the original on 19 October 2019. Retrieved 12 April 2019.
↑  Arndt & Haenel 2006, p. 17.
↑  Bailey et al. 1997, pp. 50–56.
↑  Boeing, Niels (14 مارس 2016). "Die Welt ist Pi" [The World is Pi]. Zeit Online (به آلمانی). Archived from the original on 17 March 2016. Die Ludolphsche Zahl oder Kreiszahl erhielt nun auch das Symbol, unter dem wir es heute kennen: William Jones schlug 1706 den griechischen Buchstaben π vor, in Anlehnung an perimetros, griechisch für Umfang. Leonhard Euler etablierte π schließlich in seinen mathematischen Schriften. [The Ludolphian number or circle number now also received the symbol under which we know it today: William Jones proposed in 1706 the Greek letter π, based on perimetros [περίμετρος], Greek for perimeter. Leonhard Euler firmly established π in his mathematical writings.]
1 2 3  (Arndt و Haenel 2006، ص. 8)
↑  Apostol, Tom (1967). Calculus, volume 1 (2nd ed.). Wiley.. p. 102: "From a logical point of view, this is unsatisfactory at the present stage because we have not yet discussed the concept of arc length." Arc length is introduced on p. 529.
1 2 3  Remmert, Reinhold (1991), "What is  \pi ?", Numbers, Springer, p. 129
↑  (Remmert 1991). انتگرال دقیق وایرشتراس عبارت است از  \pi =\int _{-\infty }^{\infty }{\frac {dx}{1+x^{2}}}.
↑  Remmert 1991.
↑  Baltzer, Richard (1870), Die Elemente der Mathematik [The Elements of Mathematics] (به آلمانی), Hirzel, p. 195, archived from the original on 14 September 2016
↑  Landau, Edmund (1934), Einführung in die Differentialrechnung und Integralrechnung (به آلمانی), Noordoff, p. 193
1 2  Rudin, Walter (1976). Principles of Mathematical Analysis. McGraw-Hill. ISBN 978-0-07-054235-8., p. 183.
↑  Rudin, Walter (1986). Real and complex analysis. McGraw-Hill., p. 2.
↑  Ahlfors, Lars (1966), Complex analysis, McGraw-Hill, p. 46
↑  Bourbaki, Nicolas (1981), Topologie generale, Springer, §VIII.2.
↑  Bourbaki, Nicolas (1979), Fonctions d'une variable réelle (به فرانسوی), Springer, §II.3.
↑  (Arndt و Haenel 2006، ص. 5)
↑  Salikhov, V. (2008). "On the Irrationality Measure of pi". Russian Mathematical Surveys. 53 (3): 570–572. Bibcode:2008RuMaS..63..570S. doi:10.1070/RM2008v063n03ABEH004543. ISSN 0036-0279.
1 2  (Arndt و Haenel 2006، صص. 22–23)
Preuss, Paul (23 ژوئیه 2001). "Are The Digits of Pi Random? Lab Researcher May Hold The Key". آزمایشگاه ملی لارنس برکلی. Archived from the original on 20 October 2007. Retrieved 10 November 2007.
↑  (Arndt و Haenel 2006، صص. 22, 28–30)
↑  (Arndt و Haenel 2006، ص. 3)
↑  Mayer, Steve. "The Transcendence of [[عدد پی| \pi ]]". Archived from the original on 2000-09-29. Retrieved 4 November 2007. {{cite web}}: URL–wikilink conflict (help)
↑  (Posamentier و Lehmann 2004، ص. 25)
↑  (Eymard و Lafon 1999، ص. 129)
↑  (Beckmann 1989، ص. 37)
Schlager, Neil; Lauer, Josh (2001). Science and Its Times: Understanding the Social Significance of Scientific Discovery. Gale Group. ISBN 978-0-7876-3933-4., p. 185.
1 2  (Eymard و Lafon 1999، ص. 78)
↑  Sloane, N. J. A. (ed.). "Sequence A001203 (Continued fraction for Pi)". دانشنامه برخط دنباله‌های صحیح. OEIS Foundation. Retrieved 12 April 2012.
↑  Lange, L.J. (May 1999). "An Elegant Continued Fraction for [[عدد پی| \pi ]]". The American Mathematical Monthly. 106 (5): 456–458. doi:10.2307/2589152. JSTOR 2589152. {{cite journal}}: URL–wikilink conflict (help)
↑  (Arndt و Haenel 2006، ص. 240)
↑  (Arndt و Haenel 2006، ص. 242)
↑  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 (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, archived from the original on 29 November 2016
↑  (Ayers 1964، ص. 100)
1 2  (Bronshteĭn و Semendiaev 1971، ص. 592)
↑  Maor, Eli, E: The Story of a Number, Princeton University Press, 2009, p. 160, شابک ‎۹۷۸−۰−۶۹۱−۱۴۱۳۴−۳ ("five most important" constants).
↑  Weisstein, Eric W. "Roots of Unity". MathWorld.
↑  (Arndt و Haenel ۲۰۰۶، ص. ۱۶۷)
1 2  JM فقط ریاضی بایگانی‌شده  در ۲۱ ژوئن ۲۰۱۵ توسط Wayback Machine عدد پی