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

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    Author
    Bajri, S.
    Hannah. J.
    Montelle, C.
    Date
    2015
    Permanent Link
    http://hdl.handle.net/10092/11738

    In 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.

    Subjects
    Islamic algebra
     
    Greek influence
     
    diagrammatic reasoning
     
    mathematical induction
     
    the Pascal triangle
     
    binomial theorem
     
    Field of Research::01 - Mathematical Sciences::0101 - Pure Mathematics::010101 - Algebra and Number Theory
    Collections
    • Engineering: Journal Articles [1125]
    Rights
    https://hdl.handle.net/10092/17651

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