Oğuzhan Demirel
The theorems of Stewart and Steiner in the Poincaré disc model of hyperbolic geometry

Comment.Math.Univ.Carolinae 50,3 (2009) 359-371.

Abstract:In [Comput.\ Math.\ Appl.\ {\bf 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 Poincar\'{e} disc model of hyperbolic geometry.

Keywords: Möbius transformation, hyperbolic geometry, gyrogroups, gyrovector spaces and hyperbolic trigonometry
AMS Subject Classification: 51B10 51M10 30F45 20N05

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