On hyperbolic analogues of some classical theorems in spherical geometry

Abstract : We provide hyperbolic analogues of some classical theorems in spherical geometry due to Menelaus, Euler, Lexell, Ceva and Lambert. Some of the spherical results are also made more precise. Our goal is to go through the works of some of the eminent mathematicians from the past and to include them in a modern perspective. Putting together results in the three constant-curvature geometries and highlighting the analogies between them is mathematically as well as aesthetically very appealing.
Type de document :
Chapitre d'ouvrage
Hyperbolic geometry and geometric group theory (ed. K. Fujiwara, K. Ohshika and S. Kojima), Advanced Studies of Pure Mathematics, No. 73, Mathematical Society of Japan, Tokyo, 2017, p. 225-253 , 2017, 978-4-86497-042-6
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https://hal.archives-ouvertes.fr/hal-01630212
Contributeur : Athanase Papadopoulos <>
Soumis le : mardi 7 novembre 2017 - 12:24:31
Dernière modification le : mercredi 8 novembre 2017 - 01:03:51

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  • HAL Id : hal-01630212, version 1

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Athanase Papadopoulos, Weixu Su. On hyperbolic analogues of some classical theorems in spherical geometry. Hyperbolic geometry and geometric group theory (ed. K. Fujiwara, K. Ohshika and S. Kojima), Advanced Studies of Pure Mathematics, No. 73, Mathematical Society of Japan, Tokyo, 2017, p. 225-253 , 2017, 978-4-86497-042-6. 〈hal-01630212〉

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