On the area of a polygon in the hyperbolic plane.
Kántor, Sándor (1998)
Beiträge zur Algebra und Geometrie
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Kántor, Sándor (1998)
Beiträge zur Algebra und Geometrie
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Jarosław Kosiorek, Andrzej Matraś (2004)
Bulletin of the Polish Academy of Sciences. Mathematics
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The model of the Minkowski plane in the projective plane with a fixed conic sheds a new light on the connection between the Minkowski and hyperbolic geometries. The construction of the Minkowski plane in a hyperbolic plane over a Euclidean field is given. It is also proved that the geometry in an orthogonal bundle of circles is hyperbolic in a natural way.
Ilija Knezević, Radmila Sazdanović, Srdjan Vukmirović (2002)
Visual Mathematics
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Nicolas Curien, Wendelin Werner (2013)
Journal of the European Mathematical Society
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We construct and study the unique random tiling of the hyperbolic plane into ideal hyperbolic triangles (with the three corners located on the boundary) that is invariant (in law) with respect to Möbius transformations, and possesses a natural spatial Markov property that can be roughly described as the conditional independence of the two parts of the triangulation on the two sides of the edge of one of its triangles.
Günaltılı, İ., Akça, Z., Olgun, Ş. (2006)
APPS. Applied Sciences
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Oğuzhan Demirel (2009)
Commentationes Mathematicae Universitatis Carolinae
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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.
Demirel, Oğuzhan, Soytürk, Emine (2008)
Novi Sad Journal of Mathematics
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R. Krasnodębski (1970)
Colloquium Mathematicae
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Baker, R.D., Ebert, G.L., Wantz, K.L. (2001)
Advances in Geometry
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Pambuccian, Victor (2004)
Mathematica Pannonica
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Jan Mycielski, Grzegorz Tomkowicz (2013)
Fundamenta Mathematicae
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The second author found a gap in the proof of the main theorem in [J. Mycielski, Fund. Math. 132 (1989), 143-149]. Here we fill that gap and add some remarks about the geometry of the hyperbolic plane ℍ².