Hyperbolic plane geometry revisited
\'Akos G.Horv\'ath
TL;DR
This paper revisits hyperbolic plane geometry by applying Vörös's method to derive new results on triangles and circles, including a model-independent solution to Malfatti's problem and novel trigonometric formulas.
Contribution
It introduces a model-independent construction for Malfatti's problem and new trigonometric formulas, advancing the understanding of hyperbolic geometry.
Findings
Model-independent construction for Malfatti's problem
New trigonometric formulas for hyperbolic triangles
Results related to hyperbolic triangles and circles
Abstract
Using the method of C. V\"or\"os, we establish results in hyperbolic plane geometry, related to triangles and circles. We present a model independent construction for Malfatti's problem and several trigonometric formulas for triangles.
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Taxonomy
TopicsMathematics and Applications · History and Theory of Mathematics · graph theory and CDMA systems