A la recherche de l'algèbre perdue: du côte de chez Gauss

Details A la recherche de l'algèbre perdue: du côte de chez Gauss A la recherche de l'algèbre perdue: du côte de chez Gauss

2008-04-28

arxiv.org/abs/0804.4357v1

Mat. Prosveschenie, 12 (2008), 127--144

Mathematics

General Mathematics

28 pages

Scientific paper

This paper is purely expositional. The statement of the Gauss criterion for constructibility of regular polygons is simple and well-known. We sketch an elementary proof of this criterion. We do not use the terms 'field extension', 'Galois group' and even 'group'. However, our presentation is a good way to learn (or recall) starting idea of the Galois theory. The paper is accessible for students familiar with elementary algebra (including complex numbers), and could be an interesting easy reading for mature mathematicians. The material is presented as a sequence of problems, which is peculiar not only to Zen monasteries but also to elite mathematical education (at least in Russia); most problems are presented with hints or solutions. An English version is followed by a more extended Russian version.

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