Aristotle’s problem

Alexander Hulpke, Victor Pambuccian

Research output: Contribution to journalArticlepeer-review


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
Issue number2
StatePublished - Oct 28 2015


  • 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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