Revisiting Al-Samaw'al’s table of binomial coefficients: Greek inspiration, diagrammatic reasoning and mathematical induction

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dc.contributor.authorBajri, S.
dc.contributor.authorHannah. J.
dc.contributor.authorMontelle, C.
dc.date.accessioned2016-01-31T22:28:31Z
dc.date.available2016-01-31T22:28:31Z
dc.date.issued2015en
dc.description.abstractIn a famous passage from his al-Bahir, al-Samaw'al proves the identity which we would now write as (ab)^n = a^n b^n for the cases n = 3; 4. He also calculates the equivalent of the expansion of the binomial (a + b)^n for the same values of n, and describes the construction of what we now call the Pascal Triangle, showing the table up to its 12th row. We give a literal translation of the whole passage, along with paraphrases in more modern or symbolic form. We discuss the influence of the Euclidean tradition on al-Samaw'al's presentation, and the role that diagrams might have played in helping al-Samaw'al's readers follow his arguments, including his supposed use of an early form of mathematical induction.en
dc.identifier.citationBajri, S., Hannah. J., Montelle, C. (2015) Revisiting Al-Samaw'al’s table of binomial coefficients: Greek inspiration, diagrammatic reasoning and mathematical induction. Archive for History of Exact Sciences, 69(6), pp. 537-576.en
dc.identifier.doihttps://doi.org/10.1007/s00407-015-0156-x
dc.identifier.urihttp://hdl.handle.net/10092/11738
dc.language.isoen
dc.publisherUniversity of Canterbury. Mathematics and Statisticsen
dc.rights.urihttps://hdl.handle.net/10092/17651
dc.subjectIslamic algebraen
dc.subjectGreek influenceen
dc.subjectdiagrammatic reasoningen
dc.subjectmathematical inductionen
dc.subjectthe Pascal triangleen
dc.subjectbinomial theoremen
dc.subject.anzsrcFields of Research::49 - Mathematical sciences::4904 - Pure mathematics::490401 - Algebra and number theoryen
dc.titleRevisiting Al-Samaw'al’s table of binomial coefficients: Greek inspiration, diagrammatic reasoning and mathematical inductionen
dc.typeJournal Article
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