### 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 | |

State | Published - Oct 28 2015 |

### Fingerprint

### 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

*Beitrage zur Algebra und Geometrie*,

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

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

Research output: Contribution to journal › Article

*Beitrage zur Algebra und Geometrie*, vol. 56, no. 2, pp. 473-477. https://doi.org/10.1007/s13366-014-0209-3

}

TY - JOUR

T1 - Aristotle’s problem

AU - Hulpke, Alexander

AU - Pambuccian, Victor

PY - 2015/10/28

Y1 - 2015/10/28

N2 - 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.).

AB - 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.).

KW - Constructible numbers

KW - Galois theory

KW - Hyperbolic geometry

KW - Squares with commensurable side and diagonal

UR - http://www.scopus.com/inward/record.url?scp=84940489543&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84940489543&partnerID=8YFLogxK

U2 - 10.1007/s13366-014-0209-3

DO - 10.1007/s13366-014-0209-3

M3 - Article

AN - SCOPUS:84940489543

VL - 56

SP - 473

EP - 477

JO - Beitrage zur Algebra und Geometrie

JF - Beitrage zur Algebra und Geometrie

SN - 0138-4821

IS - 2

ER -