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Keywords:
Möbius transformation; hyperbolic geometry; gyrogroups; gyrovector spaces and hyperbolic trigonometry
Möbius transformation; hyperbolic geometry; gyrogroups; gyrovector spaces and hyperbolic trigonometry
Summary:
In [Comput. Math. Appl. 41 (2001), 135--147], A. A. Ungar employs the Möbius gyrovector spaces for the introduction of the hyperbolic trigonometry. This Ungar's work plays a major role in translating some theorems from Euclidean geometry to corresponding theorems in hyperbolic geometry. In this paper we explore the theorems of Stewart and Steiner in the Poincaré disc model of hyperbolic geometry.
References:
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