Geodesic
The theorems of Stewart and Steiner in the Poincaré disc model of hyperbolic geometry
Commentationes Mathematicae Universitatis Carolinae, Tome 50 (2009) no. 3, pp. 359-371 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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.
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.
Classification : 20N05, 30F45, 51B10, 51M10
Keywords: Möbius transformation; hyperbolic geometry; gyrogroups; gyrovector spaces and hyperbolic trigonometry 
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     author = {Demirel, O\u{g}uzhan},
     title = {The theorems of {Stewart} and {Steiner} in the {Poincar\'e} disc model of hyperbolic geometry},
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     zbl = {1212.51002},
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Demirel, Oğuzhan. The theorems of Stewart and Steiner in the Poincaré disc model of hyperbolic geometry. Commentationes Mathematicae Universitatis Carolinae, Tome 50 (2009) no. 3, pp. 359-371. http://geodesic.mathdoc.fr/item/CMUC_2009_50_3_a3/