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

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In Bharath Sriraman (ed.), Handbook of the History and Philosophy of Mathematical Practice. Cham: Springer. pp. 915-1021 (2024)
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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.

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10.1007/978-3-031-40846-5_72

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