On some classical constructions extended to hyperbolic geometry

Details On some classical constructions extended to hyperbolic geometry On some classical constructions extended to hyperbolic geometry

2011-05-11

arxiv.org/abs/1105.2153v1

Matematicheskoe prosveshenie. Tret'ya seriya, 2009, N. 13 pp. 155-170 (in Russian)

Mathematics

Metric Geometry

12 pages, 6 figures

Scientific paper

We consider some constructions in hyperbolic geometry that are analogous to
classical constructions in Euclidean geometry. We show that both Monge's
theorem and the theorem on the concurrence of the common chords of three
circles also hold in absolute geometry. We proffer analogues of the Euler line
and the Euler nine-point circle and also extend Feuerbach's famous theorem.

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