Apollonian circles and hyperbolic geometry

Details Apollonian circles and hyperbolic geometry Apollonian circles and hyperbolic geometry

2010-10-13

arxiv.org/abs/1010.2630v4

Mathematics

Metric Geometry

20 pages, 4 figures

Scientific paper

The goal of this paper is to study two basic problems of hyperbolic geometry.
The first problem is to compare the hyperbolic and Euclidean distances. The
second problem is to find hyperbolic counterparts of some basic geometric
constructions such as the construction of the middle point of a hyperbolic
geodesic segment. Apollonian circles have a key role in this study.

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