Binomial theorem (English Wikipedia)
Analysis of information sources in references of the Wikipedia article "Binomial theorem" in English language version.
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- Aigner, Martin (1979). Combinatorial Theory. Springer. p. 105. ISBN 0-387-90376-3.
- Datta, Bibhutibhushan (1929). "The Jaina School of Mathematics". Bulletin of the Calcutta Mathematical Society. 27. 5. 115–145 (esp. 133–134). Reprinted as "The Mathematical Achievements of the Jainas" in Chattopadhyaya, Debiprasad, ed. (1982). Studies in the History of Science in India. Vol. 2. New Delhi: Editorial Enterprises. pp. 684–716.
- 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.
- Shukla, Kripa Shankar, ed. (1959). "Combinations of Savours". The Patiganita of Sridharacarya. Lucknow University. Vyavahāras 1.9, p. 97 (text), pp. 58–59 (translation).
- 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.
- Martzloff, Jean-Claude (1997) [French ed. 1987]. "Jia Xian and Liu Yi". A History of Chinese Mathematics. Translated by Wilson, Stephen S. Springer. p. 142. ISBN 3-540-54749-5.
- Bourbaki, N. (1994). Elements of the History of Mathematics. Translated by J. Meldrum. Springer. ISBN 3-540-19376-6.
ia800306.us.archive.org
- 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.
books.google.com
- Olver, Peter J. (2000). Applications of Lie Groups to Differential Equations. Springer. pp. 318–319. ISBN 9780387950006.
cambridge.org
- 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.
doi.org
- 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.
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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
repository.ias.ac.in
- 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.
jstor.org
- 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.
math.ca
cms.math.ca
- Sokolowsky, Dan; Rennie, Basil C. (1979). "Problem 352". Crux Mathematicorum. 5 (2): 55–56.
proofs.wiki
- Binomial theorem – inductive proofs Archived February 24, 2015, at the Wayback Machine
researchgate.net
- 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.
st-andrews.ac.uk
mathshistory.st-andrews.ac.uk
utk.edu
archives.math.utk.edu
- Landau, James A. (1999-05-08). "Historia Matematica Mailing List Archive: Re: [HM] Pascal's Triangle". Archives of Historia Matematica. Archived from the original (mailing list email) on 2021-02-24. Retrieved 2007-04-13.
web.archive.org
- Binomial theorem – inductive proofs Archived February 24, 2015, at the Wayback Machine
- Landau, James A. (1999-05-08). "Historia Matematica Mailing List Archive: Re: [HM] Pascal's Triangle". Archives of Historia Matematica. Archived from the original (mailing list email) on 2021-02-24. Retrieved 2007-04-13.