Acta Math. Acad. Paed. Nyíregyháziensis
15 (1999), 1-7

Pythagorean side and diagonal numbers

László Filep



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 effect 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.


Mathematics Subject Classification. 01A20.

Key words and phrases. Incommensurability, approximation, Pythagoreans.

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