Axiomatizations of Euclidean geometry in terms of points, equilateral triangles or squares, and incidence

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Abstract

Dimension-free Euclidean geometry over Euclidean ordered fields can be axiomatized in a two-sorted first-order language, with points and regular n-gons (with n = 3 or 4) as variables, and with a binary predicate standing for the incidence of a point and a regular n-gon as the only primitive notions.

Original languageEnglish (US)
Pages (from-to)413-417
Number of pages5
JournalIndagationes Mathematicae
Volume15
Issue number3
DOIs
StatePublished - Sep 27 2004

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ASJC Scopus subject areas

  • Mathematics(all)

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