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Aristotle’s problem
- Source :
- Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry. 56:473-477
- Publication Year :
- 2014
- Publisher :
- Springer Science and Business Media LLC, 2014.
-
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 $$1+\frac{m}{n}$$ , with $$n\le 12$$ .
- Subjects :
- Algebra and Number Theory
business.product_category
Mathematics::General Mathematics
Hyperbolic geometry
Mathematics::History and Overview
Galois theory
Constructible number
Algebraic geometry
Computer Science::Computational Geometry
Combinatorics
Ruler
Hypotenuse
Isosceles triangle
Geometry and Topology
Algebra over a field
business
Mathematics
Subjects
Details
- ISSN :
- 21910383 and 01384821
- Volume :
- 56
- Database :
- OpenAIRE
- Journal :
- Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry
- Accession number :
- edsair.doi...........2fc6fe1ff498ad3f69ffa587774577da
- Full Text :
- https://doi.org/10.1007/s13366-014-0209-3