On the existence of a equilateral triangle in \(H\)-planes
type: Item
instance of: scholarly article
title: On the existence of a equilateral triangle in \(H\)-planes
zbMATH Open document ID: 0931.51006
DOI: 10.1007/BF01221245
published in: Journal of Geometry
publication date: 2000-02-20T00:00:00Z
review text: This interesting paper contains a proof for the existence of an equilateral triangle in absolute planes (satisfying Hilbert's axioms I 1-3, II, III). In particular, it is shown how to construct such a triangle with ruler and gauge. However, it is in general not possible to find an equilateral triangle with a given base, even if the plane is satisfying Bachmann's ``Lotschnittaxiom'' or the Archimedian axiom. The non--existence is shown for an absolute plane over the Pythagorean hull of \({\mathbb Q}(t)\) (with the usual ordering) and an absolute plane over a super-Pythagorean field (allowing exactly two orderings), respectively.
Mathematics Subject Classification ID: 51F05
zbMATH DE Number: 1268140
zbMATH Keywords: absolute plane
zbMATH Keywords: equilateral triangle
zbMATH Keywords: Pythagorean field
author: Victor V. Pambuccian
reviewed by: Hans Havlicek
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf01221245
OpenAlex ID: W2000110758
description: scientific article; zbMATH DE number 1268140