The theorems of Urquhart and Steiner-Lehmus in the Poincaré ball model of hyperbolic geometry (Q2853246)
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scientific article; zbMATH DE number 6217195
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | The theorems of Urquhart and Steiner-Lehmus in the Poincaré ball model of hyperbolic geometry |
scientific article; zbMATH DE number 6217195 |
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18 October 2013
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Möbius transformation
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gyrogroups
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gyrovector spaces
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hyperbolic trigonometry
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The theorems of Urquhart and Steiner-Lehmus in the Poincaré ball model of hyperbolic geometry (English)
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Results of \textit{A. A. Ungar} from [Comput. Math. Appl. 41, 135--147 (2001; Zbl 0988.51017)] are used in translating some theorems in Euclidean geometry to corresponding ones in hyperbolic geometry. Those are the Breusch's lemma, the Urquhart's theorem and the Steiner--Lehmus theorem. Since Ungar used Möbius gyrovector spaces for the introduction of the hyperbolic trigonometry, these theorems are presented in the Poincaré ball model of hyperbolic geometry.
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