Aristotle’s problem

Alexander Hulpke, Victor Pambuccian

Research output: Contribution to journalArticle

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 languageEnglish (US)
Pages (from-to)473-477
Number of pages5
JournalBeitrage zur Algebra und Geometrie
Volume56
Issue number2
DOIs
StatePublished - Oct 28 2015

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Hypotenuse
Isosceles triangle
Right-angled triangle
Ruler
Hyperbolic Plane
Constructible
Triangle

Keywords

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

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Geometry and Topology

Cite this

Aristotle’s problem. / Hulpke, Alexander; Pambuccian, Victor.

In: Beitrage zur Algebra und Geometrie, Vol. 56, No. 2, 28.10.2015, p. 473-477.

Research output: Contribution to journalArticle

Hulpke, Alexander ; Pambuccian, Victor. / Aristotle’s problem. In: Beitrage zur Algebra und Geometrie. 2015 ; Vol. 56, No. 2. pp. 473-477.
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