Abu Kamil is considered the first mathematician to systematically use and accept irrational numbers as solutions and coefficients to equations.
13 Facts About Abu Kamil
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Abu Kamil was the first Islamic mathematician to work easily with algebraic equations with powers higher than, and solved sets of non-linear simultaneous equations with three unknown variables.
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Abu Kamil wrote all problems rhetorically, and some of his books lacked any mathematical notation beside those of integers.
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Almost nothing is known about the life and career of Abu Kamil except that he was a successor of al-Khwarizmi, whom he never personally met.
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Whereas the Algebra of al-Khwarizmi was geared towards the general public, Abu Kamil was addressing other mathematicians, or readers familiar with Euclid's Elements.
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Abu Kamil describes a number of systematic procedures for finding integral solutions for indeterminate equations.
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However, Abu Kamil explains certain methods not found in any extant copy of the Arithmetica.
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Abu Kamil describes one problem for which he found 2,678 solutions.
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Abu Kamil uses the equation to calculate a numerical approximation for the side of a regular pentagon in a circle of diameter 10.
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Abu Kamil uses the golden ratio in some of his calculations.
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The works of Abu Kamil influenced other mathematicians, like al-Karaji and Fibonacci, and as such had a lasting impact on the development of algebra.
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Unmistakable borrowings, but without Abu Kamil being explicitly mentioned and perhaps mediated by lost treatises, are found in Fibonacci's Liber Abaci.
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Abu Kamil was one of the earliest mathematicians to recognize al-Khwarizmi's contributions to algebra, defending him against Ibn Barza who attributed the authority and precedent in algebra to his grandfather, 'Abd al-Hamid ibn Turk.