Irrationality of the square root of 2: the early Pythagorean proof, Theodorus's and Theaetetus's generalizations
type: Item
instance of: scholarly article
title: Irrationality of the square root of 2: the early Pythagorean proof, Theodorus's and Theaetetus's generalizations
zbMATH Open document ID: 1331.01005
author: Zoran Lučić
published in: The Mathematical Intelligencer
publication date: 2016-01-29T00:00:00Z
review text: This is a lucid presentation of the existing explanations for the possible proof methods by which the early Pythagoreans, Theodorus and later Theaetetus, arrived at the realization that square roots of non-square integers cannot be ratios of integers. One finds the explanation based on a pure theory of the even and the odd, going back to the early Pythagoreans (one reads that it is ``more probable that Pythagoras, and not Hippasus, could have been the author of the the doctrine of irrational and incommensurable quantities and of the [\(\ldots\)] proof'' (p.\ 30) of the irrationality of \(\sqrt{2}\)), which works for all non-squares that are not of the form \(8k+1\), and which helps explain why Theodorus, according to Plato's \textit{Theaetetus}, stopped proving the irrationality of square roots when he reached \(\sqrt{17}\), the significance of the geometric passage in Plato's \textit{Meno}, and an explanation of the way in which Euclid deals with the irrationality of square roots in his \textit{Elements}, primarily in VIII.14.
Mathematics Subject Classification ID: 01A20
Mathematics Subject Classification ID: 11-03
Mathematics Subject Classification ID: 11J72
zbMATH DE Number: 6536979
zbMATH Keywords: Pythagoras
zbMATH Keywords: Theodorus
zbMATH Keywords: Theaetetus
zbMATH Keywords: Euclid
reviewed by: Victor V. Pambuccian
MaRDI profile type: Publication
full work available at URL: s00283-014-9521-x
OpenAlex ID: W230001204
Wikidata QID: Q114230183
cites work: Q5764005
cites work: Extreme proofs. I: The irrationality of \(\sqrt 2\)
cites work: Q3234138
cites work: Q5726619
cites work: Q4135445
cites work: Q5828997
cites work: Pythagoras and the Early Pythagoreans
DOI: 10.1007/S00283-014-9521-X
description: scientific article; zbMATH DE number 6536979