Binomial theorem (English Wikipedia)

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

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  • Barth, Nils R. (2004). "Computing Cavalieri's Quadrature Formula by a Symmetry of the n-Cube". The American Mathematical Monthly. 111 (9): 811–813. doi:10.2307/4145193. JSTOR 4145193.
  • Coolidge, J. L. (1949). "The Story of the Binomial Theorem". The American Mathematical Monthly. 56 (3): 147–157. doi:10.2307/2305028. JSTOR 2305028.
  • Biggs, Norman L. (1979). "The roots of combinatorics". Historia Mathematica. 6 (2): 109–136. doi:10.1016/0315-0860(79)90074-0.
  • Bag, Amulya Kumar (1966). "Binomial theorem in ancient India" (PDF). Indian Journal of History of Science. 1 (1): 68–74.
    Shah, Jayant (2013). "A History of Piṅgala's Combinatorics". Gaṇita Bhāratī. 35 (1–4): 43–96. ResearchGate:353496244. (Preprint)
    Survey sources:
    Edwards, A. W. F. (1987). "The combinatorial numbers in India". Pascal's Arithmetical Triangle. London: Charles Griffin. pp. 27–33. ISBN 0-19-520546-4.
    Divakaran, P. P. (2018). "Combinatorics". The Mathematics of India: Concepts, Methods, Connections. Springer; Hindustan Book Agency. §5.5 pp. 135–140. doi:10.1007/978-981-13-1774-3_5. ISBN 978-981-13-1773-6.
    Roy, Ranjan (2021). "The Binomial Theorem". Series and Products in the Development of Mathematics. Vol. 1 (2 ed.). Cambridge University Press. Ch. 4, pp. 77–104. doi:10.1017/9781108709453.005. ISBN 978-1-108-70945-3.
  • Gupta, Radha Charan (1992). "Varāhamihira's Calculation of and the Discovery of Pascal's Triangle". Gaṇita Bhāratī. 14 (1–4): 45–49. Reprinted in Ramasubramanian, K., ed. (2019). Gaṇitānanda. Springer. pp. 285–289. doi:10.1007/978-981-13-1229-8_29.
  • Yadegari, Mohammad (1980). "The Binomial Theorem: A Widespread Concept in Medieval Islamic Mathematics". Historia Mathematica. 7 (4): 401–406. doi:10.1016/0315-0860(80)90004-X.
  • Rashed, Roshdi (1972). "L'induction mathématique: al-Karajī, al-Samawʾal". Archive for History of Exact Sciences (in French). 9 (1): 1–21. doi:10.1007/BF00348537. JSTOR 41133347. Translated into English by A. F. W. Armstrong in Rashed, Roshdi (1994). "Mathematical Induction: al-Karajī and al-Samawʾal". The Development of Arabic Mathematics: Between Arithmetic and Algebra. Kluwer. §1.4, pp. 62–81. doi:10.1007/978-94-017-3274-1_2. ISBN 0-7923-2565-6. The first formulation of the binomial and the table of binomial coefficients, to our knowledge, is to be found in a text by al-Karajī, cited by al-Samawʾal in al-Bāhir.
  • Sesiano, Jacques (1997). "Al-Karajī". In Selin, Helaine (ed.). Encyclopaedia of the History of Science, Technology, and Medicine in Non-Western Cultures. Springer. pp. 475–476. doi:10.1007/978-94-017-1416-7_11. ISBN 978-94-017-1418-1. Another [lost work of Karajī's] contained the first known explanation of the arithmetical (Pascal's) triangle; the passage in question survived through al-Samawʾal's Bāhir (twelfth century) which heavily drew from the Badīʿ.
  • Berggren, John Lennart (1985). "History of mathematics in the Islamic world: The present state of the art". Review of Middle East Studies. 19 (1): 9–33. doi:10.1017/S0026318400014796. Republished in Sidoli, Nathan; Brummelen, Glen Van, eds. (2014). From Alexandria, Through Baghdad. Springer. pp. 51–71. doi:10.1007/978-3-642-36736-6_4. ISBN 978-3-642-36735-9. [...] since the table of binomial coefficients had been previously found in such late works as those of al-Kāshī (fifteenth century) and Naṣīr al-Dīn al-Ṭūsī (thirteenth century), some had suggested that the table was a Chinese import. However, the use of the binomial coefficients by Islamic mathematicians of the eleventh century, in a context which had deep roots in Islamic mathematics, suggests strongly that the table was a local discovery – most probably of al-Karajī.
  • Hughes, Barnabas (1989). "The arithmetical triangle of Jordanus de Nemore". Historia Mathematica. 16 (3): 213–223. doi:10.1016/0315-0860(89)90018-9.
  • Whiteside, D. T. (1961). "Newton's Discovery of the General Binomial Theorem". The Mathematical Gazette. 45 (353): 175–180. doi:10.2307/3612767. JSTOR 3612767.
  • Cover, Thomas M.; Thomas, Joy A. (1991). "Data Compression". Elements of Information Theory. Wiley. Ch. 5, pp. 78–124. doi:10.1002/0471200611.ch5. ISBN 9780471062592.

ias.ac.in (Global: 6,086th place; English: 4,310th place)

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jstor.org (Global: 26th place; English: 20th place)

  • Barth, Nils R. (2004). "Computing Cavalieri's Quadrature Formula by a Symmetry of the n-Cube". The American Mathematical Monthly. 111 (9): 811–813. doi:10.2307/4145193. JSTOR 4145193.
  • Coolidge, J. L. (1949). "The Story of the Binomial Theorem". The American Mathematical Monthly. 56 (3): 147–157. doi:10.2307/2305028. JSTOR 2305028.
  • Rashed, Roshdi (1972). "L'induction mathématique: al-Karajī, al-Samawʾal". Archive for History of Exact Sciences (in French). 9 (1): 1–21. doi:10.1007/BF00348537. JSTOR 41133347. Translated into English by A. F. W. Armstrong in Rashed, Roshdi (1994). "Mathematical Induction: al-Karajī and al-Samawʾal". The Development of Arabic Mathematics: Between Arithmetic and Algebra. Kluwer. §1.4, pp. 62–81. doi:10.1007/978-94-017-3274-1_2. ISBN 0-7923-2565-6. The first formulation of the binomial and the table of binomial coefficients, to our knowledge, is to be found in a text by al-Karajī, cited by al-Samawʾal in al-Bāhir.
  • Whiteside, D. T. (1961). "Newton's Discovery of the General Binomial Theorem". The Mathematical Gazette. 45 (353): 175–180. doi:10.2307/3612767. JSTOR 3612767.

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  • Sokolowsky, Dan; Rennie, Basil C. (1979). "Problem 352". Crux Mathematicorum. 5 (2): 55–56.

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