Apollonian circles and hyperbolic geometry
Metric Geometry
2013-01-14 v4
Abstract
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.
Keywords
Cite
@article{arxiv.1010.2630,
title = {Apollonian circles and hyperbolic geometry},
author = {Riku Klén and Matti Vuorinen},
journal= {arXiv preprint arXiv:1010.2630},
year = {2013}
}
Comments
20 pages, 4 figures