Malfatti's problem on the hyperbolic plane

Details Malfatti's problem on the hyperbolic plane Malfatti's problem on the hyperbolic plane

2012-04-23

arxiv.org/abs/1204.5014v1

Mathematics

Metric Geometry

16 pages, 4 figures

Scientific paper

More than two centuries ago Malfatti raised and solved the following problem called by Malfatti's construction problem: In a triangle describe three small circles, each of them touching the other two, and also two sides of the triangle. Interesting fact that nobody investigated this problem on the hyperbolic plane, while the case of the sphere were solved at once. We now compensate for this shortage and solve the following exercise: Determine three cycles of the hyperbolic plane, each of them touching the two others, and also two of three given cycles of the hyperbolic plane. We also give a proof of the hyperbolic version of Malfatti's marble problem.

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