Pi sayısı (Turkish Wikipedia)

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

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Euler, Leonhard (1727). "Tentamen explicationis phaenomenorum aeris" (PDF). Commentarii Academiae Scientiarum Imperialis Petropolitana (Latince). 2: 351. E007. 1 Nisan 2016 tarihinde kaynağından arşivlendi (PDF). Erişim tarihi: 15 Ekim 2017. Sumatur pro ratione radii ad peripheriem, $I : π$ English translation by Ian Bruce 10 Haziran 2016 tarihinde Wayback Machine sitesinde arşivlendi.: " $π$ 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 (1736). "Ch. 3 Prop. 34 Cor. 1". Mechanica sive motus scientia analytice exposita. (cum tabulis) (Latince). 1. Academiae scientiarum Petropoli. s. 113. E015. Denotet $1 : π$ rationem diametri ad peripheriam English translation by Ian Bruce 10 Haziran 2016 tarihinde Wayback Machine sitesinde arşivlendi. : "Let $1 : π$ denote the ratio of the diameter to the circumference"

americanscientist.org

Hayes, Brian (September 2014). "Pencil, Paper, and Pi". American Scientist. 102 (5). s. 342. doi:10.1511/2014.110.342. 22 Ocak 2022 tarihinde kaynağından arşivlendi. Erişim tarihi: 22 Ocak 2022.

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". Sidoli, Nathan; Van Brummelen, Glen (Ed.). From Alexandria, through Baghdad: Surveys and studies in the ancient Greek and medieval Islamic mathematical sciences in honor of J. L. Berggren. Heidelberg: Springer. ss. 531-561. doi:10.1007/978-3-642-36736-6_24. 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. 23 Mart 2023 tarihinde kaynağından arşivlendi (PDF). Erişim tarihi: 15 Nisan 2023.
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.

archive.org

Jones, William (1706). Synopsis Palmariorum Matheseos. Londra: J. Wale. ss. 243, 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 Eugene (1929). "William Jones: The First Use of $π$ for the Circle Ratio". A Source Book in Mathematics. McGraw–Hill. ss. 346-347.
Bailey, David H.; Plouffe, Simon M.; Borwein, Peter B.; Borwein, Jonathan M. (1997). "The quest for PI". The Mathematical Intelligencer. 19 (1): 50-56. CiteSeerX 10.1.1.138.7085 $2. doi:10.1007/BF03024340. ISSN 0343-6993.
Baltzer, Richard (1870). Die Elemente der Mathematik [The Elements of Mathematics] (Almanca). Hirzel. s. 195. 14 Eylül 2016 tarihinde kaynağından arşivlendi.
Rudin, Walter (1976). Principles of Mathematical Analysis. McGraw-Hill. s. 183. ISBN 978-0-07-054235-8.
Ahlfors, Lars (1966). Complex analysis. McGraw-Hill. s. 46.
Beckmann, Peter (1989) [1974]. History of Pi. St. Martin's Press. s. 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. 13 Aralık 2019 tarihinde kaynağından arşivlendi. Erişim tarihi: 19 Aralık 2019. , p. 185.
Lange, L.J. (May 1999). "An Elegant Continued Fraction for $π$ ". The American Mathematical Monthly. 106 (5): 456-458. doi:10.2307/2589152. JSTOR 2589152.
Tweddle, Ian (1991). "John Machin and Robert Simson on Inverse-tangent Series for $π$ ". Archive for History of Exact Sciences. 42 (1): 1-14. doi:10.1007/BF00384331. JSTOR 41133896.
Sandifer, Ed (2009). "Estimating π" (PDF). How Euler Did It. 19 Mart 2014 tarihinde kaynağından (PDF) arşivlendi. Reprinted in Sandifer, Ed (2014). How Euler Did Even More. Mathematical Association of America. ss. 109-118.
Euler, Leonhard (1755). "§2.2.30". Institutiones Calculi Differentialis (Latince). Academiae Imperialis Scientiarium Petropolitanae. s. 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.

Chien-Lih, Hwang (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.

Chien-Lih, Hwang (2005). "89.67 An elementary derivation of Euler's series for the arctangent function". Mathematical Gazette. 89 (516): 469-470. doi:10.1017/S0025557200178404.
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.
Wells, David (1997). The Penguin Dictionary of Curious and Interesting Numbers (revised bas.). Penguin. s. 35. ISBN 978-0-14-026149-3.
Lindemann, F. (1882). "Über die Ludolph'sche Zahl". Sitzungsberichte der Königlich Preussischen Akademie der Wissenschaften zu Berlin. 2: 679-682.
Archibald, R.C. (1921). "Historical Notes on the Relation $e -(π /2) = i i$ ". The American Mathematical Monthly. 28 (3): 116-121. doi:10.2307/2972388. JSTOR 2972388. It is noticeable that these letters are never used separately, that is, $π$ is not used for 'Semiperipheria'
See, for example, Oughtred, William (1648). Clavis Mathematicæ [The key to mathematics] (Latince). Londra: Thomas Harper. s. 69. (English translation: Oughtred, William (1694). Key of the Mathematics (İngilizce). J. Salusbury. )
Barrow, Isaac (1860). "Lecture XXIV". Whewell, William (Ed.). The mathematical works of Isaac Barrow (Latince). Harvard University. Cambridge University press. s. 381.
Rabinowitz, Stanley; Wagon, Stan (March 1995). "A spigot algorithm for the digits of Pi". American Mathematical Monthly. 102 (3): 195-203. doi:10.2307/2975006. JSTOR 2975006.

bbc.co.uk

Palmer, Jason (16 Eylül 2010). "Pi record smashed as team finds two-quadrillionth digit". BBC News. 17 Mart 2011 tarihinde kaynağından arşivlendi. Erişim tarihi: 26 Mart 2011.

bnf.fr

gallica.bnf.fr

Euler, Leonhard (1707–1783) (1922). Leonhardi Euleri opera omnia. 1, Opera mathematica. Volumen VIII, Leonhardi Euleri introductio in analysin infinitorum. Tomus primus / ediderunt Adolf Krazer et Ferdinand Rudio (Latince). Lipsae: B.G. Teubneri. ss. 133-134. E101. 16 Ekim 2017 tarihinde kaynağından arşivlendi. Erişim tarihi: 15 Ekim 2017.

books.google.com

Oughtred, William (1652). Theorematum in libris Archimedis de sphaera et cylindro declarario (Latince). Excudebat L. Lichfield, Veneunt apud T. Robinson. $δ . π$ :: semidiameter. semiperipheria
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. 13. New York: Random House. s. 125. ISBN 978-0-88385-613-0. 29 Kasım 2016 tarihinde kaynağından arşivlendi.
Herz-Fischler, Roger (2000). The Shape of the Great Pyramid. Wilfrid Laurier University Press. ss. 67-77, 165-166. ISBN 978-0-88920-324-2. 29 Kasım 2016 tarihinde kaynağından arşivlendi. Erişim tarihi: 5 Haziran 2013.
Plofker, Kim (2009). Mathematics in India. Princeton University Press. s. 27. ISBN 978-0691120676.
Joseph, George Gheverghese (1991). The Crest of the Peacock: Non-European Roots of Mathematics. Princeton University Press. s. 264. ISBN 978-0-691-13526-7.
Vieta, Franciscus (1593). Variorum de rebus mathematicis responsorum. VIII.
Cajori, Florian (2007). A History of Mathematical Notations: Vol. II (İngilizce). Cosimo, Inc. ss. 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
Smith, David E. (1958). History of Mathematics (İngilizce). Courier Corporation. s. 312. ISBN 978-0-486-20430-7.
See, for example, Oughtred, William (1648). Clavis Mathematicæ [The key to mathematics] (Latince). Londra: Thomas Harper. s. 69. (English translation: Oughtred, William (1694). Key of the Mathematics (İngilizce). J. Salusbury. )
Segner, Joannes Andreas (1756). Cursus Mathematicus (Latince). Halae Magdeburgicae. s. 282. 15 Ekim 2017 tarihinde kaynağından arşivlendi. Erişim tarihi: 15 Ekim 2017.
Euler, Leonhard (1747). Henry, Charles (Ed.). Lettres inédites d'Euler à d'Alembert. Bullettino di Bibliografia e di Storia delle Scienze Matematiche e Fisiche (Fransızca). 19 (1886 tarihinde yayınlandı). s. 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) (Latince). 1. Academiae scientiarum Petropoli. s. 113. E015. Denotet $1 : π$ rationem diametri ad peripheriam English translation by Ian Bruce 10 Haziran 2016 tarihinde Wayback Machine sitesinde arşivlendi. : "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 (Latince). Renger. s. 374. Si autem $π$ notet peripheriam circuli, cuius diameter eſt $2$
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. s. 469. doi:10.1007/978-3-319-32377-0. ISBN 978-3-319-32375-6.

cambridge.org

Cooker, M.J. (2011). "Fast formulas for slowly convergent alternating series" (PDF). Mathematical Gazette. 95 (533): 218-226. doi:10.1017/S0025557200002928. 4 Mayıs 2019 tarihinde kaynağından (PDF) arşivlendi. Erişim tarihi: 15 Nisan 2023.

cloud.google.com

Haruka Iwao, Emma (14 Mart 2019). "Pi in the sky: Calculating a record-breaking 31.4 trillion digits of Archimedes' constant on Google Cloud". Google Cloud Platform. 19 Ekim 2019 tarihinde kaynağından arşivlendi. Erişim tarihi: 12 Nisan 2019.

comune.palermo.it

librarsi.comune.palermo.it

Grienbergerus, Christophorus (1630). Elementa Trigonometrica (PDF) (Latince). 1 Şubat 2014 tarihinde kaynağından (PDF) arşivlendi. His evaluation was 3.14159 26535 89793 23846 26433 83279 50288 4196 < $π$ < 3.14159 26535 89793 23846 26433 83279 50288 4199.

dbnl.org

Yoder, Joella G. (1996). "Following in the footsteps of geometry: The mathematical world of Christiaan Huygens". De Zeventiende Eeuw. 12: 83-93. 12 Mayıs 2021 tarihinde kaynağından arşivlendi. Erişim tarihi: 15 Nisan 2023 – Digital Library for Dutch Literature vasıtasıyla.

doi.org

Bailey, David H.; Plouffe, Simon M.; Borwein, Peter B.; Borwein, Jonathan M. (1997). "The quest for PI". The Mathematical Intelligencer. 19 (1): 50-56. CiteSeerX 10.1.1.138.7085 $2. doi:10.1007/BF03024340. ISSN 0343-6993.
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.
Lange, L.J. (May 1999). "An Elegant Continued Fraction for $π$ ". The American Mathematical Monthly. 106 (5): 456-458. doi:10.2307/2589152. JSTOR 2589152.
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. 13. New York: Random House. s. 125. ISBN 978-0-88385-613-0. 29 Kasım 2016 tarihinde kaynağından arşivlendi.
Borwein, Jonathan M. (2014). "The life of $π$ : from Archimedes to ENIAC and beyond". Sidoli, Nathan; Van Brummelen, Glen (Ed.). From Alexandria, through Baghdad: Surveys and studies in the ancient Greek and medieval Islamic mathematical sciences in honor of J. L. Berggren. Heidelberg: Springer. ss. 531-561. doi:10.1007/978-3-642-36736-6_24. MR 3203895.
Azarian, Mohammad K. (2010). "al-Risāla al-muhītīyya: A Summary". Missouri Journal of Mathematical Sciences. 22 (2): 64-85. doi:10.35834/mjms/1312233136 .
Brezinski, C. (2009). "Some pioneers of extrapolation methods". Bultheel, Adhemar; Cools, Ronald (Ed.). The Birth of Numerical Analysis. World Scientific. ss. 1-22. doi:10.1142/9789812836267_0001. ISBN 978-981-283-625-0. 25 Mart 2023 tarihinde kaynağından arşivlendi. Erişim tarihi: 15 Nisan 2023.
Roy, Ranjan (1990). "The Discovery of the Series Formula for $π$ by Leibniz, Gregory and Nilakantha" (PDF). Mathematics Magazine. 63 (5): 291-306. doi:10.1080/0025570X.1990.11977541. 14 Mart 2023 tarihinde kaynağından arşivlendi (PDF). Erişim tarihi: 15 Nisan 2023.
Cooker, M.J. (2011). "Fast formulas for slowly convergent alternating series" (PDF). Mathematical Gazette. 95 (533): 218-226. doi:10.1017/S0025557200002928. 4 Mayıs 2019 tarihinde kaynağından (PDF) arşivlendi. Erişim tarihi: 15 Nisan 2023.
Tweddle, Ian (1991). "John Machin and Robert Simson on Inverse-tangent Series for $π$ ". Archive for History of Exact Sciences. 42 (1): 1-14. doi:10.1007/BF00384331. JSTOR 41133896.
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. 7 Mart 2023 tarihinde kaynağından arşivlendi (PDF). Erişim tarihi: 15 Nisan 2023.
Sandifer, Ed (2009). "Estimating π" (PDF). How Euler Did It. 19 Mart 2014 tarihinde kaynağından (PDF) arşivlendi. Reprinted in Sandifer, Ed (2014). How Euler Did Even More. Mathematical Association of America. ss. 109-118.
Euler, Leonhard (1755). "§2.2.30". Institutiones Calculi Differentialis (Latince). Academiae Imperialis Scientiarium Petropolitanae. s. 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.

Chien-Lih, Hwang (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.

Chien-Lih, Hwang (2005). "89.67 An elementary derivation of Euler's series for the arctangent function". Mathematical Gazette. 89 (516): 469-470. doi:10.1017/S0025557200178404.
Hayes, Brian (September 2014). "Pencil, Paper, and Pi". American Scientist. 102 (5). s. 342. doi:10.1511/2014.110.342. 22 Ocak 2022 tarihinde kaynağından arşivlendi. Erişim tarihi: 22 Ocak 2022.
Borwein, J.M.; Borwein, P.B. (1988). "Ramanujan and Pi". Scientific American. 256 (2): 112-117. Bibcode:1988SciAm.258b.112B. doi:10.1038/scientificamerican0288-112.
Arndt & Haenel 2006, ss. 15–17, 70–72, 104, 156, 192–197, 201–202
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.
Archibald, R.C. (1921). "Historical Notes on the Relation $e -(π /2) = i i$ ". The American Mathematical Monthly. 28 (3): 116-121. doi:10.2307/2972388. JSTOR 2972388. It is noticeable that these letters are never used separately, that is, $π$ is not used for 'Semiperipheria'
Gregorius, David (1695). "Ad Reverendum Virum D. Henricum Aldrich S.T.T. Decanum Aedis Christi Oxoniae". Philosophical Transactions (Latince). 19 (231): 637-652. Bibcode:1695RSPT...19..637G. doi:10.1098/rstl.1695.0114 . JSTOR 102382.
Euler, Leonhard (1747). Henry, Charles (Ed.). Lettres inédites d'Euler à d'Alembert. Bullettino di Bibliografia e di Storia delle Scienze Matematiche e Fisiche (Fransızca). 19 (1886 tarihinde yayınlandı). s. 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
Reitwiesner, George (1950). "An ENIAC Determination of pi and e to 2000 Decimal Places". Mathematical Tables and Other Aids to Computation. 4 (29): 11-15. doi:10.2307/2002695. JSTOR 2002695.
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. s. 469. doi:10.1007/978-3-319-32377-0. ISBN 978-3-319-32375-6.
Grünbaum, B. (1960). "Projection Constants". Transactions of the American Mathematical Society. 95 (3): 451-465. doi:10.1090/s0002-9947-1960-0114110-9 .
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. 23 Mart 2023 tarihinde kaynağından arşivlendi (PDF). Erişim tarihi: 15 Nisan 2023.
Rabinowitz, Stanley; Wagon, Stan (March 1995). "A spigot algorithm for the digits of Pi". American Mathematical Monthly. 102 (3): 195-203. doi:10.2307/2975006. JSTOR 2975006.
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.

free.fr

fabrice.bellard.free.fr

Arndt & Haenel 2006, s. 20
Bellards formula in: Bellard, Fabrice. "A new formula to compute the n^th binary digit of pi". 12 Eylül 2007 tarihinde kaynağından arşivlendi. Erişim tarihi: 27 Ekim 2007.

handle.net

hdl.handle.net

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.

harvard.edu

adsabs.harvard.edu

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.
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. 13. New York: Random House. s. 125. ISBN 978-0-88385-613-0. 29 Kasım 2016 tarihinde kaynağından arşivlendi.
Borwein, J.M.; Borwein, P.B. (1988). "Ramanujan and Pi". Scientific American. 256 (2): 112-117. Bibcode:1988SciAm.258b.112B. doi:10.1038/scientificamerican0288-112.
Arndt & Haenel 2006, ss. 15–17, 70–72, 104, 156, 192–197, 201–202
Gregorius, David (1695). "Ad Reverendum Virum D. Henricum Aldrich S.T.T. Decanum Aedis Christi Oxoniae". Philosophical Transactions (Latince). 19 (231): 637-652. Bibcode:1695RSPT...19..637G. doi:10.1098/rstl.1695.0114 . JSTOR 102382.

independent.co.uk

Connor, Steve (8 Ocak 2010). "The Big Question: How close have we come to knowing the precise value of pi?". The Independent. Londra. 2 Nisan 2012 tarihinde kaynağından arşivlendi. Erişim tarihi: 14 Nisan 2012.

jstor.org

Lange, L.J. (May 1999). "An Elegant Continued Fraction for $π$ ". The American Mathematical Monthly. 106 (5): 456-458. doi:10.2307/2589152. JSTOR 2589152.
Tweddle, Ian (1991). "John Machin and Robert Simson on Inverse-tangent Series for $π$ ". Archive for History of Exact Sciences. 42 (1): 1-14. doi:10.1007/BF00384331. JSTOR 41133896.
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. 7 Mart 2023 tarihinde kaynağından arşivlendi (PDF). Erişim tarihi: 15 Nisan 2023.
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lbl.gov

crd-legacy.lbl.gov

Bailey, David H. (16 Mayıs 2003). "Some Background on Kanada's Recent Pi Calculation" (PDF). 15 Nisan 2012 tarihinde kaynağından arşivlendi (PDF). Erişim tarihi: 12 Nisan 2012.

maa.org

eulerarchive.maa.org

Sandifer, Ed (2009). "Estimating π" (PDF). How Euler Did It. 19 Mart 2014 tarihinde kaynağından (PDF) arşivlendi. Reprinted in Sandifer, Ed (2014). How Euler Did Even More. Mathematical Association of America. ss. 109-118.
Euler, Leonhard (1755). "§2.2.30". Institutiones Calculi Differentialis (Latince). Academiae Imperialis Scientiarium Petropolitanae. s. 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.

Chien-Lih, Hwang (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.

Chien-Lih, Hwang (2005). "89.67 An elementary derivation of Euler's series for the arctangent function". Mathematical Gazette. 89 (516): 469-470. doi:10.1017/S0025557200178404.
Euler, Leonhard (1727). "Tentamen explicationis phaenomenorum aeris" (PDF). Commentarii Academiae Scientiarum Imperialis Petropolitana (Latince). 2: 351. E007. 1 Nisan 2016 tarihinde kaynağından arşivlendi (PDF). Erişim tarihi: 15 Ekim 2017. Sumatur pro ratione radii ad peripheriem, $I : π$ English translation by Ian Bruce 10 Haziran 2016 tarihinde Wayback Machine sitesinde arşivlendi.: " $π$ 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 (Fransızca). 19 (1886 tarihinde yayınlandı). s. 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) (Latince). 1. Academiae scientiarum Petropoli. s. 113. E015. Denotet $1 : π$ rationem diametri ad peripheriam English translation by Ian Bruce 10 Haziran 2016 tarihinde Wayback Machine sitesinde arşivlendi. : "Let $1 : π$ denote the ratio of the diameter to the circumference"
Euler, Leonhard (1707–1783) (1922). Leonhardi Euleri opera omnia. 1, Opera mathematica. Volumen VIII, Leonhardi Euleri introductio in analysin infinitorum. Tomus primus / ediderunt Adolf Krazer et Ferdinand Rudio (Latince). Lipsae: B.G. Teubneri. ss. 133-134. E101. 16 Ekim 2017 tarihinde kaynağından arşivlendi. Erişim tarihi: 15 Ekim 2017.

maa.org

Roy, Ranjan (1990). "The Discovery of the Series Formula for $π$ by Leibniz, Gregory and Nilakantha" (PDF). Mathematics Magazine. 63 (5): 291-306. doi:10.1080/0025570X.1990.11977541. 14 Mart 2023 tarihinde kaynağından arşivlendi (PDF). Erişim tarihi: 15 Nisan 2023.
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. 7 Mart 2023 tarihinde kaynağından arşivlendi (PDF). Erişim tarihi: 15 Nisan 2023.

matematikciler.org

"Pi Sayısı". 9 Temmuz 2015 tarihinde kaynağından arşivlendi. Erişim tarihi: 8 Temmuz 2015.

oeis.org

A060294

openstax.org

Abramson 2014, Section 8.5: Polar form of complex numbers.
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Abramson 2014, Section 5.1: Angles.

ox.ac.uk

cs.ox.ac.uk

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. 23 Mart 2023 tarihinde kaynağından arşivlendi (PDF). Erişim tarihi: 15 Nisan 2023.

pacific.edu

scholarlycommons.pacific.edu

Sandifer, Ed (2009). "Estimating π" (PDF). How Euler Did It. 19 Mart 2014 tarihinde kaynağından (PDF) arşivlendi. Reprinted in Sandifer, Ed (2014). How Euler Did Even More. Mathematical Association of America. ss. 109-118.
Euler, Leonhard (1755). "§2.2.30". Institutiones Calculi Differentialis (Latince). Academiae Imperialis Scientiarium Petropolitanae. s. 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.

Chien-Lih, Hwang (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.

Chien-Lih, Hwang (2005). "89.67 An elementary derivation of Euler's series for the arctangent function". Mathematical Gazette. 89 (516): 469-470. doi:10.1017/S0025557200178404.

pi2e.ch

"π^e trillion digits of π". pi2e.ch. 6 Aralık 2016 tarihinde kaynağından arşivlendi.

pi314.net

"The world of Pi - Newton". www.pi314.net. 13 Temmuz 2010 tarihinde kaynağından arşivlendi. Erişim tarihi: 13 Mart 2022.
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plouffe.fr

Plouffe, Simon (April 2006). "Identities inspired by Ramanujan's Notebooks (part 2)" (PDF). 14 Ocak 2012 tarihinde kaynağından arşivlendi (PDF). Erişim tarihi: 10 Nisan 2009.

psu.edu

citeseerx.ist.psu.edu

Bailey, David H.; Plouffe, Simon M.; Borwein, Peter B.; Borwein, Jonathan M. (1997). "The quest for PI". The Mathematical Intelligencer. 19 (1): 50-56. CiteSeerX 10.1.1.138.7085 $2. doi:10.1007/BF03024340. ISSN 0343-6993.

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dictionary.reference.com

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thenewstack.io

Cassel, David (11 Haziran 2022). "How Google's Emma Haruka Iwao Helped Set a New Record for Pi". The New Stack. 11 Haziran 2022 tarihinde kaynağından arşivlendi. Erişim tarihi: 15 Nisan 2023.

web.archive.org

"Pi Sayısı". 9 Temmuz 2015 tarihinde kaynağından arşivlendi. Erişim tarihi: 8 Temmuz 2015.
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Haruka Iwao, Emma (14 Mart 2019). "Pi in the sky: Calculating a record-breaking 31.4 trillion digits of Archimedes' constant on Google Cloud". Google Cloud Platform. 19 Ekim 2019 tarihinde kaynağından arşivlendi. Erişim tarihi: 12 Nisan 2019.
"pi". Dictionary.reference.com. 2 Mart 1993. 28 Temmuz 2014 tarihinde kaynağından arşivlendi. Erişim tarihi: 18 Haziran 2012.
Baltzer, Richard (1870). Die Elemente der Mathematik [The Elements of Mathematics] (Almanca). Hirzel. s. 195. 14 Eylül 2016 tarihinde kaynağından arşivlendi.
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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 (1964). Episodes from the Early History of Mathematics. New Mathematical Library. 13. New York: Random House. s. 125. ISBN 978-0-88385-613-0. 29 Kasım 2016 tarihinde kaynağından arşivlendi.
Herz-Fischler, Roger (2000). The Shape of the Great Pyramid. Wilfrid Laurier University Press. ss. 67-77, 165-166. ISBN 978-0-88920-324-2. 29 Kasım 2016 tarihinde kaynağından arşivlendi. Erişim tarihi: 5 Haziran 2013.
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Grienbergerus, Christophorus (1630). Elementa Trigonometrica (PDF) (Latince). 1 Şubat 2014 tarihinde kaynağından (PDF) arşivlendi. His evaluation was 3.14159 26535 89793 23846 26433 83279 50288 4196 < $π$ < 3.14159 26535 89793 23846 26433 83279 50288 4199.
Brezinski, C. (2009). "Some pioneers of extrapolation methods". Bultheel, Adhemar; Cools, Ronald (Ed.). The Birth of Numerical Analysis. World Scientific. ss. 1-22. doi:10.1142/9789812836267_0001. ISBN 978-981-283-625-0. 25 Mart 2023 tarihinde kaynağından arşivlendi. Erişim tarihi: 15 Nisan 2023.
Yoder, Joella G. (1996). "Following in the footsteps of geometry: The mathematical world of Christiaan Huygens". De Zeventiende Eeuw. 12: 83-93. 12 Mayıs 2021 tarihinde kaynağından arşivlendi. Erişim tarihi: 15 Nisan 2023 – Digital Library for Dutch Literature vasıtasıyla.
Roy, Ranjan (1990). "The Discovery of the Series Formula for $π$ by Leibniz, Gregory and Nilakantha" (PDF). Mathematics Magazine. 63 (5): 291-306. doi:10.1080/0025570X.1990.11977541. 14 Mart 2023 tarihinde kaynağından arşivlendi (PDF). Erişim tarihi: 15 Nisan 2023.
Cooker, M.J. (2011). "Fast formulas for slowly convergent alternating series" (PDF). Mathematical Gazette. 95 (533): 218-226. doi:10.1017/S0025557200002928. 4 Mayıs 2019 tarihinde kaynağından (PDF) arşivlendi. Erişim tarihi: 15 Nisan 2023.
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. 7 Mart 2023 tarihinde kaynağından arşivlendi (PDF). Erişim tarihi: 15 Nisan 2023.
Sandifer, Ed (2009). "Estimating π" (PDF). How Euler Did It. 19 Mart 2014 tarihinde kaynağından (PDF) arşivlendi. Reprinted in Sandifer, Ed (2014). How Euler Did Even More. Mathematical Association of America. ss. 109-118.
Euler, Leonhard (1755). "§2.2.30". Institutiones Calculi Differentialis (Latince). Academiae Imperialis Scientiarium Petropolitanae. s. 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.

Chien-Lih, Hwang (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.

Chien-Lih, Hwang (2005). "89.67 An elementary derivation of Euler's series for the arctangent function". Mathematical Gazette. 89 (516): 469-470. doi:10.1017/S0025557200178404.
Hayes, Brian (September 2014). "Pencil, Paper, and Pi". American Scientist. 102 (5). s. 342. doi:10.1511/2014.110.342. 22 Ocak 2022 tarihinde kaynağından arşivlendi. Erişim tarihi: 22 Ocak 2022.
Segner, Joannes Andreas (1756). Cursus Mathematicus (Latince). Halae Magdeburgicae. s. 282. 15 Ekim 2017 tarihinde kaynağından arşivlendi. Erişim tarihi: 15 Ekim 2017.
Euler, Leonhard (1727). "Tentamen explicationis phaenomenorum aeris" (PDF). Commentarii Academiae Scientiarum Imperialis Petropolitana (Latince). 2: 351. E007. 1 Nisan 2016 tarihinde kaynağından arşivlendi (PDF). Erişim tarihi: 15 Ekim 2017. Sumatur pro ratione radii ad peripheriem, $I : π$ English translation by Ian Bruce 10 Haziran 2016 tarihinde Wayback Machine sitesinde arşivlendi.: " $π$ 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 (1736). "Ch. 3 Prop. 34 Cor. 1". Mechanica sive motus scientia analytice exposita. (cum tabulis) (Latince). 1. Academiae scientiarum Petropoli. s. 113. E015. Denotet $1 : π$ rationem diametri ad peripheriam English translation by Ian Bruce 10 Haziran 2016 tarihinde Wayback Machine sitesinde arşivlendi. : "Let $1 : π$ denote the ratio of the diameter to the circumference"
Euler, Leonhard (1707–1783) (1922). Leonhardi Euleri opera omnia. 1, Opera mathematica. Volumen VIII, Leonhardi Euleri introductio in analysin infinitorum. Tomus primus / ediderunt Adolf Krazer et Ferdinand Rudio (Latince). Lipsae: B.G. Teubneri. ss. 133-134. E101. 16 Ekim 2017 tarihinde kaynağından arşivlendi. Erişim tarihi: 15 Ekim 2017.
Bailey, David H. (16 Mayıs 2003). "Some Background on Kanada's Recent Pi Calculation" (PDF). 15 Nisan 2012 tarihinde kaynağından arşivlendi (PDF). Erişim tarihi: 12 Nisan 2012.
Connor, Steve (8 Ocak 2010). "The Big Question: How close have we come to knowing the precise value of pi?". The Independent. Londra. 2 Nisan 2012 tarihinde kaynağından arşivlendi. Erişim tarihi: 14 Nisan 2012.
Cassel, David (11 Haziran 2022). "How Google's Emma Haruka Iwao Helped Set a New Record for Pi". The New Stack. 11 Haziran 2022 tarihinde kaynağından arşivlendi. Erişim tarihi: 15 Nisan 2023.
Plouffe, Simon (April 2006). "Identities inspired by Ramanujan's Notebooks (part 2)" (PDF). 14 Ocak 2012 tarihinde kaynağından arşivlendi (PDF). Erişim tarihi: 10 Nisan 2009.
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. 23 Mart 2023 tarihinde kaynağından arşivlendi (PDF). Erişim tarihi: 15 Nisan 2023.
Arndt & Haenel 2006, s. 20
Bellards formula in: Bellard, Fabrice. "A new formula to compute the n^th binary digit of pi". 12 Eylül 2007 tarihinde kaynağından arşivlendi. Erişim tarihi: 27 Ekim 2007.
Palmer, Jason (16 Eylül 2010). "Pi record smashed as team finds two-quadrillionth digit". BBC News. 17 Mart 2011 tarihinde kaynağından arşivlendi. Erişim tarihi: 26 Mart 2011.
"The world of Pi - Newton". www.pi314.net. 13 Temmuz 2010 tarihinde kaynağından arşivlendi. Erişim tarihi: 13 Mart 2022.
"The world of Pi - Bellard". www.pi314.net. 2 Temmuz 2011 tarihinde kaynağından arşivlendi. Erişim tarihi: 13 Mart 2022.

worldcat.org

Bailey, David H.; Plouffe, Simon M.; Borwein, Peter B.; Borwein, Jonathan M. (1997). "The quest for PI". The Mathematical Intelligencer. 19 (1): 50-56. CiteSeerX 10.1.1.138.7085 $2. doi:10.1007/BF03024340. ISSN 0343-6993.
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.

worldscientific.com

Brezinski, C. (2009). "Some pioneers of extrapolation methods". Bultheel, Adhemar; Cools, Ronald (Ed.). The Birth of Numerical Analysis. World Scientific. ss. 1-22. doi:10.1142/9789812836267_0001. ISBN 978-981-283-625-0. 25 Mart 2023 tarihinde kaynağından arşivlendi. Erişim tarihi: 15 Nisan 2023.