Pythagorean side and diagonal numbers

Filep, László (1999) Pythagorean side and diagonal numbers. ACTA MATHEMATICA ACADEMIAE PAEDAGOGICAE NYÍREGYHÁZIENSIS, 0866-0. pp. 1-7. ISSN 0866-0174

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Abstract

The Pythagorean discovery that the ratio of the diagonal (diameter) and side of a square cannot be expressed as the ratio of two positive integers means in modern language that is not a rational number. The above incommensurability had a great e ect on Greek philosophy and mathematics. Many papers deal with it and its impact, but relatively few with the approximation of the ratio in question. Even not Euclid's Elements that was purely theoretical and neglected the calculation methods. The aim of our paper to analyse the sources and the literature on this problem and give a new (and hopefully a satisfactory) explanation of Pythagorean's approximation method, i.e. of their so-called side and diagonal (or diameter) numbers.

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