On hyperbolic analogues of some classical theorems in spherical geometry

Athanase Papadopoulos (1, 2) , Weixu Su (3)

1 IRMA - Institut de Recherche Mathématique Avancée
2 Department of Mathematics and Statistics [Hunter College]
3 Fudan University

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.

Mots clés: Hyperbolic geometry; spherical geometry; Menelaus Theorem; Euler Theorem; Lexell Theorem; Ceva theorem; Lambert theorem

Domaines: Topologie géométrique [math.GT]; Géométrie différentielle [math.DG]

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⟩