Approximations of π (English Wikipedia)

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

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Jadhav, Dipak (1 January 2018). "On The Value Implied in the Data Referred To in the Mahābhārata for π". Vidyottama Sanatana: International Journal of Hindu Science and Religious Studies. 2 (1): 18. doi:10.25078/ijhsrs.v2i1.511. ISSN 2550-0651. S2CID 146074061.

americanscientist.org

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

ams.org

mathscinet.ams.org

See #Imputed biblical value. Beckmann 1971 "There has been concern over the apparent biblical statement of $π$ ≈ 3 from the early times of rabbinical Judaism, addressed by Rabbi Nehemiah in the 2nd century."^{[page needed]} Beckmann, Petr (1971). A History of $π$ . New York: St. Martin's Press. ISBN 978-0-88029-418-8. MR 0449960.
See also Beckmann 1971, pp. 12, 21–22 "in 1936, a tablet was excavated some 200 miles from Babylon. ... The mentioned tablet, whose translation was partially published only in 1950, ... states that the ratio of the perimeter of a regular hexagon to the circumference of the circumscribed circle equals a number which in modern notation is given by 57/60+36/(60)² [i.e. $π$ = 3/0.96 = 25/8]". Beckmann, Petr (1971). A History of $π$ . New York: St. Martin's Press. ISBN 978-0-88029-418-8. MR 0449960.
Lam, Lay Yong; Ang, Tian Se (1986), "Circle measurements in ancient China", Historia Mathematica, 13 (4): 325–340, doi:10.1016/0315-0860(86)90055-8, MR 0875525. Reprinted in Berggren, J. L.; Borwein, Jonathan M.; Borwein, Peter, eds. (2004). Pi: A Source Book. Springer. pp. 20–35. ISBN 978-0387205717.. See in particular pp. 333–334 (pp. 28–29 of the reprint).
Beckmann 1971, p. 66 Beckmann, Petr (1971). A History of $π$ . New York: St. Martin's Press. ISBN 978-0-88029-418-8. MR 0449960.
Beckmann 1971, pp. 94–95 Beckmann, Petr (1971). A History of $π$ . New York: St. Martin's Press. ISBN 978-0-88029-418-8. MR 0449960.
Ramanujan, S. (1914). "Modular equations and approximations to $π$ ". Quarterly Journal of Mathematics. 45: 350–372. Reprinted in Berggren, Lennart; Borwein, Jonathan; Borwein, Peter (2004). "Modular equations and approximations to $π$ ". Pi: A Source Book (3rd ed.). New York: Springer-Verlag. pp. 241–257. doi:10.1007/978-1-4757-4217-6_29. ISBN 0-387-20571-3. MR 2065455.

ams.org

Capra, B. "Digits of Pi" (PDF). Retrieved 13 January 2018.

archive.org

Jones, William (1706). Synopsis Palmariorum Matheseos. London: J. Wale. pp. 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. pp. 346–347.
Vega, Géorge (1795) [1789]. "Detérmination de la demi-circonférence d'un cercle dont le diameter est $= 1$ , exprimée en $140$ figures decimals". Supplement. Nova Acta Academiae Scientiarum Petropolitanae. 11: 41–44.
Sandifer, Edward (2006). "Why 140 Digits of Pi Matter" (PDF). Jurij baron Vega in njegov čas: Zbornik ob 250-letnici rojstva [Baron Jurij Vega and His Times: Celebrating 250 Years]. Ljubljana: DMFA. ISBN 978-961-6137-98-0. LCCN 2008467244. OCLC 448882242. Archived from the original (PDF) on 28 August 2006. We should note that Vega's value contains an error in the 127th digit. Vega gives a 4 where there should be an [6], and all digits after that are incorrect.
Shanks, William (1853). Contributions to Mathematics: Comprising Chiefly the Rectification of the Circle to 607 Places of Decimals. Macmillan Publishers. p. viii – via the Internet Archive.
Unpublished work by Newton (1684), later independently discovered by others, and popularized by Euler (1755).
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.

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.

Newton, Isaac (1971). Whiteside, Derek Thomas (ed.). The Mathematical Papers of Isaac Newton. Vol. 4, 1674–1684. Cambridge University Press. pp. 526–653.

Euler, Leonhard (1755). "§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 (2005), "An elementary derivation of Euler's series for the arctangent function", The Mathematical Gazette, 89 (516): 469–470, doi:10.1017/S0025557200178404, S2CID 123395287

arxiv.org

Damini, D.B.; Abhishek, Dhar (2020). "How Archimedes showed that π is approximately equal to 22/7". p. 8. arXiv:2008.07995 [math.HO].
Treub, Peter (30 November 2016). "Digit Statistics of the First 22.4 Trillion Decimal Digits of Pi". arXiv:1612.00489 [math.NT].
Trueb, Peter (2020). The Borwein brothers, Pi and the AGM. Springer Proceedings in Mathematics & Statistics. Vol. 313. arXiv:1802.07558. doi:10.1007/978-3-030-36568-4. ISBN 978-3-030-36567-7. S2CID 214742997.
Plouffe, Simon (2009). "On the computation of the n^th decimal digit of various transcendental numbers". arXiv:0912.0303v1 [math.NT].

bellard.org

"Pi Computation Record".
"Computation of the n'th digit of in any base in O(n^2)". bellard.org. Retrieved 30 September 2024.
Bellard, Fabrice. "TachusPi". Retrieved 20 March 2020.

biu.ac.il

u.cs.biu.ac.il

Tsaban, Boaz; Garber, David (February 1998). "On the rabbinical approximation of $π$ " (PDF). Historia Mathematica. 25 (1): 75–84. doi:10.1006/hmat.1997.2185. ISSN 0315-0860. Retrieved 14 July 2009.

books.google.com

Romano, David Gilman (1993). Athletics and Mathematics in Archaic Corinth: The Origins of the Greek Stadion. American Philosophical Society. p. 78. ISBN 978-0871692061. A group of mathematical clay tablets from the Old Babylonian Period, excavated at Susa in 1936, and published by E.M. Bruins in 1950, provide the information that the Babylonian approximation of $π$ was 3 1/8 or 3.125.
Chaitanya, Krishna. A profile of Indian culture. Indian Book Company (1975). p. 133.
Lam, Lay Yong; Ang, Tian Se (1986), "Circle measurements in ancient China", Historia Mathematica, 13 (4): 325–340, doi:10.1016/0315-0860(86)90055-8, MR 0875525. Reprinted in Berggren, J. L.; Borwein, Jonathan M.; Borwein, Peter, eds. (2004). Pi: A Source Book. Springer. pp. 20–35. ISBN 978-0387205717.. See in particular pp. 333–334 (pp. 28–29 of the reprint).

britannica.com

"Bhāskara II | 12th Century Indian Mathematician & Astronomer | Britannica". www.britannica.com. 1 January 2025. Retrieved 28 February 2025.

cloud.google.com

"Even more pi in the sky: Calculating 100 trillion digits of pi on Google Cloud". Google Cloud Platform. 8 June 2022. Retrieved 10 June 2022.

demon.co.uk

legon.demon.co.uk

Legon, J. A. R. (1991). On Pyramid Dimensions and Proportions. Discussions in Egyptology. Vol. 20. pp. 25–34. Archived from the original on 18 July 2011. Retrieved 7 June 2011.

doi.org

Hayes, Brian (September 2014). "Pencil, Paper, and Pi". American Scientist. Vol. 102, no. 5. p. 342. doi:10.1511/2014.110.342.
Jadhav, Dipak (1 January 2018). "On The Value Implied in the Data Referred To in the Mahābhārata for π". Vidyottama Sanatana: International Journal of Hindu Science and Religious Studies. 2 (1): 18. doi:10.25078/ijhsrs.v2i1.511. ISSN 2550-0651. S2CID 146074061.
Lam, Lay Yong; Ang, Tian Se (1986), "Circle measurements in ancient China", Historia Mathematica, 13 (4): 325–340, doi:10.1016/0315-0860(86)90055-8, MR 0875525. Reprinted in Berggren, J. L.; Borwein, Jonathan M.; Borwein, Peter, eds. (2004). Pi: A Source Book. Springer. pp. 20–35. ISBN 978-0387205717.. See in particular pp. 333–334 (pp. 28–29 of the reprint).
Azarian, Mohammad K. (2010). "al-Risāla al-muhītīyya: A Summary". Missouri Journal of Mathematical Sciences. 22 (2): 64–85. doi:10.35834/mjms/1312233136.
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. S2CID 121087222.
Ferguson, D. F. (16 March 1946). "Value of π". Nature. 157 (3985): 342. Bibcode:1946Natur.157..342F. doi:10.1038/157342c0. ISSN 1476-4687. S2CID 4085398.
Shanks, William (1873). "V. On the extension of the numerical value of π". Proceedings of the Royal Society of London. 21 (139–147). Royal Society Publishing: 318–319. doi:10.1098/rspl.1872.0066. S2CID 120851313.
Ferguson 1946a, doi:10.2307/3608485
Shanks, D.; Wrench, J. W. Jr. (1962). "Calculation of $π$ to 100,000 decimals". Mathematics of Computation. 16 (77): 76–99. doi:10.2307/2003813. JSTOR 2003813.
Hallerberg, Arthur E. (1977). "Indiana's Squared Circle". Mathematics Magazine. 50 (3): 136–140. doi:10.1080/0025570X.1977.11976632.
Tsaban, Boaz; Garber, David (February 1998). "On the rabbinical approximation of $π$ " (PDF). Historia Mathematica. 25 (1): 75–84. doi:10.1006/hmat.1997.2185. ISSN 0315-0860. Retrieved 14 July 2009.
Unpublished work by Newton (1684), later independently discovered by others, and popularized by Euler (1755).
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.

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.

Newton, Isaac (1971). Whiteside, Derek Thomas (ed.). The Mathematical Papers of Isaac Newton. Vol. 4, 1674–1684. Cambridge University Press. pp. 526–653.

Euler, Leonhard (1755). "§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 (2005), "An elementary derivation of Euler's series for the arctangent function", The Mathematical Gazette, 89 (516): 469–470, doi:10.1017/S0025557200178404, S2CID 123395287
Trueb, Peter (2020). The Borwein brothers, Pi and the AGM. Springer Proceedings in Mathematics & Statistics. Vol. 313. arXiv:1802.07558. doi:10.1007/978-3-030-36568-4. ISBN 978-3-030-36567-7. S2CID 214742997.
Popper, K. R. (August 1952). "The nature of philosophical problems and their roots in science". The British Journal for the Philosophy of Science. 3 (10). University of Chicago Press: 124–156. doi:10.1093/bjps/iii.10.124. JSTOR 685553. See p. 150.
Ramanujan, S. (1914). "Modular equations and approximations to $π$ ". Quarterly Journal of Mathematics. 45: 350–372. Reprinted in Berggren, Lennart; Borwein, Jonathan; Borwein, Peter (2004). "Modular equations and approximations to $π$ ". Pi: A Source Book (3rd ed.). New York: Springer-Verlag. pp. 241–257. doi:10.1007/978-1-4757-4217-6_29. ISBN 0-387-20571-3. MR 2065455.
Dutka, J. (1982). "Wallis's product, Brouncker's continued fraction, and Leibniz's series". Archive for History of Exact Sciences. 26 (2): 115–126. doi:10.1007/BF00348349. S2CID 121628039.
Rabinowitz, Stanley; Wagon, Stan (1995). "A Spigot Algorithm for the Digits of π". The American Mathematical Monthly. 102 (3): 195–203. doi:10.2307/2975006. ISSN 0002-9890. JSTOR 2975006.
Hwang Chien-Lih (2005), "An elementary derivation of Euler's series for the arctangent function", The Mathematical Gazette, 89 (516): 469–470, doi:10.1017/S0025557200178404, S2CID 123395287

extremetech.com

Anthony, Sebastian (15 March 2012). "What can you do with a supercomputer? – ExtremeTech". Extremetech.

fhgr.ch

"Die FH Graubünden kennt Pi am genauesten – Weltrekord!". Retrieved 31 August 2021.

free.fr

numbers.computation.free.fr

"PiFast timings"

guinnessworldrecords.com

"Most accurate value of pi". Guinness World Records. Archived from the original on 8 May 2025. Retrieved 16 May 2025.

gutenberg.org

Hemphill, Scott (1993). Pi.
Kanada, Yasumasa (1996). One Divided by Pi.

harvard.edu

ui.adsabs.harvard.edu

Ferguson, D. F. (16 March 1946). "Value of π". Nature. 157 (3985): 342. Bibcode:1946Natur.157..342F. doi:10.1038/157342c0. ISSN 1476-4687. S2CID 4085398.

hathitrust.org

babel.hathitrust.org

Ramanujan, S. (1914). "Modular equations and approximations to $π$ ". Quarterly Journal of Mathematics. 45: 350–372. Reprinted in Berggren, Lennart; Borwein, Jonathan; Borwein, Peter (2004). "Modular equations and approximations to $π$ ". Pi: A Source Book (3rd ed.). New York: Springer-Verlag. pp. 241–257. doi:10.1007/978-1-4757-4217-6_29. ISBN 0-387-20571-3. MR 2065455.

ijpam.eu

Chakrabarti, Gopal; Hudson, Richard (2003). "An Improvement of Archimedes Method of Approximating π" (PDF). International Journal of Pure and Applied Mathematics. 7 (2): 207–212.

illinois.edu

faculty.math.illinois.edu

"Continued Fraction Approximations to Pi" (PDF). Illinois Department of Mathematics. University of Illinois Board of Trustees. Archived from the original (PDF) on 23 January 2021. Retrieved 16 March 2020.

johndcook.com

John D., Cook (22 May 2018). "Best Rational Approximations for Pi". John D. Cook Consulting. Retrieved 16 March 2020.

jstor.org

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. S2CID 121087222.
Shanks, D.; Wrench, J. W. Jr. (1962). "Calculation of $π$ to 100,000 decimals". Mathematics of Computation. 16 (77): 76–99. doi:10.2307/2003813. JSTOR 2003813.
Popper, K. R. (August 1952). "The nature of philosophical problems and their roots in science". The British Journal for the Philosophy of Science. 3 (10). University of Chicago Press: 124–156. doi:10.1093/bjps/iii.10.124. JSTOR 685553. See p. 150.
Hoffman, David W. (November 2009). "A pi curiosity". College Mathematics Journal. 40 (5). JSTOR 25653799.
Rabinowitz, Stanley; Wagon, Stan (1995). "A Spigot Algorithm for the Digits of π". The American Mathematical Monthly. 102 (3): 195–203. doi:10.2307/2975006. ISSN 0002-9890. JSTOR 2975006.

knaw.nl

dwc.knaw.nl

Bruins, E. M. (1950). "Quelques textes mathématiques de la Mission de Suse" (PDF).

laya.com

qin.laya.com

"Fractional Approximations of Pi".

lbl.gov

crd.lbl.gov

"David H Bailey". crd.LBL.gov. Archived from the original on 10 April 2011. Retrieved 11 December 2017.

livemint.com

How Aryabhata got the earth's circumference right Archived 15 January 2017 at the Wayback Machine

loc.gov

lccn.loc.gov

Vega, Géorge (1795) [1789]. "Detérmination de la demi-circonférence d'un cercle dont le diameter est $= 1$ , exprimée en $140$ figures decimals". Supplement. Nova Acta Academiae Scientiarum Petropolitanae. 11: 41–44.
Sandifer, Edward (2006). "Why 140 Digits of Pi Matter" (PDF). Jurij baron Vega in njegov čas: Zbornik ob 250-letnici rojstva [Baron Jurij Vega and His Times: Celebrating 250 Years]. Ljubljana: DMFA. ISBN 978-961-6137-98-0. LCCN 2008467244. OCLC 448882242. Archived from the original (PDF) on 28 August 2006. We should note that Vega's value contains an error in the 127th digit. Vega gives a 4 where there should be an [6], and all digits after that are incorrect.

maa.org

eulerarchive.maa.org

Unpublished work by Newton (1684), later independently discovered by others, and popularized by Euler (1755).
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.

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.

Newton, Isaac (1971). Whiteside, Derek Thomas (ed.). The Mathematical Papers of Isaac Newton. Vol. 4, 1674–1684. Cambridge University Press. pp. 526–653.

Euler, Leonhard (1755). "§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 (2005), "An elementary derivation of Euler's series for the arctangent function", The Mathematical Gazette, 89 (516): 469–470, doi:10.1017/S0025557200178404, S2CID 123395287

mathforum.org

Math Forum – Ask Dr. Math

mschneider.cc

Schneider, Martin (6 July 2011). "A nested radical approximation for $π$ " (PDF). Archived from the original (PDF) on 6 July 2011.

newscientist.com

Glenn (19 October 2011). "Short Sharp Science: Epic pi quest sets 10 trillion digit record". New Scientist. Retrieved 18 April 2016.

northwestern.edu

mccormick.northwestern.edu

McCormick Grad Sets New Pi Record Archived 28 September 2011 at the Wayback Machine

numberworld.org

"Pi – 5 Trillion Digits".
Yee, Alexander J.; Kondo, Shigeru (22 October 2011). "Round 2... 10 Trillion Digits of Pi".
Yee, Alexander J.; Kondo, Shigeru (28 December 2013). "12.1 Trillion Digits of Pi".
Yee, Alexander J. (2018). "y-cruncher: A Multi-Threaded Pi Program". numberworld.org. Retrieved 14 March 2018.
"Google Cloud Topples the Pi Record". numberworld.org. Retrieved 14 March 2019.
"The Pi Record Returns to the Personal Computer". Retrieved 30 January 2020.
Yee, Alexander J. (14 March 2024). "Limping to a new Pi Record of 105 Trillion Digits". NumberWorld.org. Retrieved 16 March 2024.

oeis.org

Sloane, N. J. A. (ed.). "Sequence A002485 (Numerators of convergents to Pi)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
Sloane, N. J. A. (ed.). "Sequence A002486 (Denominators of convergents to Pi)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
For related results see The circle problem: number of points (x,y) in square lattice with x^2 + y^2 <= n.

pacific.edu

scholarlycommons.pacific.edu

Unpublished work by Newton (1684), later independently discovered by others, and popularized by Euler (1755).
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.

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.

Newton, Isaac (1971). Whiteside, Derek Thomas (ed.). The Mathematical Papers of Isaac Newton. Vol. 4, 1674–1684. Cambridge University Press. pp. 526–653.

Euler, Leonhard (1755). "§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 (2005), "An elementary derivation of Euler's series for the arctangent function", The Mathematical Gazette, 89 (516): 469–470, doi:10.1017/S0025557200178404, S2CID 123395287

pi314.net

"The world of Pi – Bellard". Pi314.net. 13 April 2013. Retrieved 18 April 2016.

projecteuclid.org

Azarian, Mohammad K. (2010). "al-Risāla al-muhītīyya: A Summary". Missouri Journal of Mathematical Sciences. 22 (2): 64–85. doi:10.35834/mjms/1312233136.

recoveredscience.com

Aleff, H. Peter. "Ancient Creation Stories told by the Numbers: Solomon's Pi". recoveredscience.com. Archived from the original on 14 October 2007. Retrieved 30 October 2007.

royalsocietypublishing.org

Shanks, William (1873). "V. On the extension of the numerical value of π". Proceedings of the Royal Society of London. 21 (139–147). Royal Society Publishing: 318–319. doi:10.1098/rspl.1872.0066. S2CID 120851313.

semanticscholar.org

api.semanticscholar.org

Jadhav, Dipak (1 January 2018). "On The Value Implied in the Data Referred To in the Mahābhārata for π". Vidyottama Sanatana: International Journal of Hindu Science and Religious Studies. 2 (1): 18. doi:10.25078/ijhsrs.v2i1.511. ISSN 2550-0651. S2CID 146074061.
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. S2CID 121087222.
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