Revisiting AlSamaw'al’s table of binomial coefficients: Greek inspiration, diagrammatic reasoning and mathematical induction (2015)
Type of Content
Journal ArticlePublisher
University of Canterbury. Mathematics and StatisticsCollections
Abstract
In a famous passage from his alBahir, alSamaw'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 alSamaw'al's presentation, and the role that diagrams might have played in helping alSamaw'al's readers follow his arguments, including his supposed use of an early form of mathematical induction.
Citation
Bajri, S., Hannah. J., Montelle, C. (2015) Revisiting AlSamaw'al’s table of binomial coefficients: Greek inspiration, diagrammatic reasoning and mathematical induction. Archive for History of Exact Sciences, 69(6), pp. 537576.This citation is automatically generated and may be unreliable. Use as a guide only.
Keywords
Islamic algebra; Greek influence; diagrammatic reasoning; mathematical induction; the Pascal triangle; binomial theoremANZSRC Fields of Research
49  Mathematical sciences::4904  Pure mathematics::490401  Algebra and number theoryRelated items
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