Rational Angled Hyperbolic Polygons
Metric Geometry
2014-12-15 v1 General Topology
Abstract
We prove that every rational angled hyperbolic triangle has transcendental side lengths and that every rational angled hyperbolic quadrilateral has at least one transcendental side length. Thus, there does not exist a rational angled hyperbolic triangle or quadrilateral with algebraic side lengths. We conjecture that there does not exist a rational angled hyperbolic polygon with algebraic side lengths.
Keywords
Cite
@article{arxiv.1412.3825,
title = {Rational Angled Hyperbolic Polygons},
author = {Jack S. Calcut},
journal= {arXiv preprint arXiv:1412.3825},
year = {2014}
}
Comments
9 pages, 6 figures