Aristotle’s problem

Alexander Hulpke; Victor Pambuccian

doi:10.1007/s13366-014-0209-3

Aristotle’s problem

Research output: Contribution to journal › Article › peer-review

Abstract

We ask if there is any right isosceles triangle in the hyperbolic plane, constructible with ruler and compass, for which the ratio of the hypotenuse to the side is rational. Although the question remains open, we determine that there are no such triangles with ratio (Formula presented.), with (Formula presented.).

Original language	English (US)
Pages (from-to)	473-477
Number of pages	5
Journal	Beitrage zur Algebra und Geometrie
Volume	56
Issue number	2
DOIs	https://doi.org/10.1007/s13366-014-0209-3
State	Published - Oct 28 2015

Keywords

Constructible numbers
Galois theory
Hyperbolic geometry
Squares with commensurable side and diagonal

ASJC Scopus subject areas

Algebra and Number Theory
Geometry and Topology

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10.1007/s13366-014-0209-3

Cite this

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Aristotle’s problem

Abstract

Keywords

ASJC Scopus subject areas

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