The Pell Equation in the Pythagoreans, Theaetetus, and Hindu Mathematics

Stelios Negrepontis (), Vassiliki Farmaki () and Marina Brokou ()
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Stelios Negrepontis: Athens University, Department of Mathematics
Vassiliki Farmaki: Athens University, Department of Mathematics
Marina Brokou: Athens University, Department of Mathematics

A chapter in Handbook of the History and Philosophy of Mathematical Practice, 2024, pp 915-1021 from Springer

Abstract: Abstract The reinterpretation of Plato’s philosophy in terms of periodic anthyphairesis, in fact of palindromically periodic anthyphairesis in the Politicus, and the reading of Book X of Euclid’s Elements under the new light, reveal deep mathematical contributions by Theaetetus, including a proof of the general Pell equation. Fascinating similarities of Theaeteus’ reconstructed proofs with the Hindus’ solution of the problem of Pell are noted.

Keywords: Plato; Theaetetus; Book X of Euclid’s Elements; Palindromically periodic anthyphairesis; Pell equation; Cakravala (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/978-3-031-40846-5_72

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