Abstract
The Theorem of Pythagoras is employed as a starting point for discussing the irrationality of the square root of 2 and its implications in Mathematics and culture. It motivates to consider the equation of the circle over the field of rational numbers and other fields which leads in a natural way t to the use of modular arithmetic for Diophantine equations.
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Uwe Storch is Professor (emeritus) of Mathematics at Ruhr University Bochum, Germany. He has been a visitor to TIFR, Mumbai, and he has given at various times lectures at the Department of Mathematics, IISc, Bangalore, on subjects of his main interests: Algebra, in particular Commutative Algebra, and Algebraic Geometry.
This is the translation of an article with the same title (“and” replaced by und) published online in a slightly shortened version by the press centre of Ruhr University, Bochum (Germany) on December 22, 2005 as part of a Christmas calendar under the epigraph Was die Menschen vor 2000 Jahren wussten (What men knew 2000 years ago). The notes were added later by the author.
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Storch, U. Pythagoras and Diophantus. Reson 14, 691–703 (2009). https://doi.org/10.1007/s12045-009-0057-x
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DOI: https://doi.org/10.1007/s12045-009-0057-x