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.
Information
Published: 1 January 2017
First available in Project Euclid: 4 October 2018
zbMATH: 07272052
MathSciNet: MR3728500
Digital Object Identifier: 10.2969/aspm/07310225
Subjects:
Primary:
53A35
Secondary:
53A05
Keywords:
Ceva theorem
,
Euler Theorem
,
hyperbolic geometry
,
Lambert theorem
,
Lexell Theorem
,
Menelaus Theorem
,
spherical geometry
Rights: Copyright © 2017 Mathematical Society of Japan
