### 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) |
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Pages (from-to) | 473-477 |

Number of pages | 5 |

Journal | Beitrage zur Algebra und Geometrie |

Volume | 56 |

Issue number | 2 |

DOIs | |

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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## Cite this

Hulpke, A., & Pambuccian, V. (2015). Aristotle’s problem.

*Beitrage zur Algebra und Geometrie*,*56*(2), 473-477. https://doi.org/10.1007/s13366-014-0209-3