Polygons in hyperbolic geometry 1: Rigidity and inversion of the n-inequality

Details Polygons in hyperbolic geometry 1: Rigidity and inversion of the n-inequality Polygons in hyperbolic geometry 1: Rigidity and inversion of the n-inequality

2010-08-19

arxiv.org/abs/1008.3404v1

Mathematics

Metric Geometry

34 pages, 2 figures

Scientific paper

Certain topics on polygons are extended from Euclidean to hyperbolic geometry. This first part deals with uniqueness and existence of cocyclic polygons with prescribed sidelengths. The non-Euclidean versions are more difficult due to the existence of three different types of circles in the hyperbolic plane. The second part will be concerned with the problem of maximizing the area of polygons with fixed sidelengths. By the metric character of these problems it is necessary to dispense to a certain extent with classical hyperbolic trigonometry because angles must be replaced by length quantities. So this first part also takes regard of this technical aspect.

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