Displaying similar documents to “On the area of a polygon in the hyperbolic plane.”

Some Connections between Minkowski and Hyperbolic Planes

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.

The Markovian hyperbolic triangulation

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.

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

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.

Boundaries of right-angled hyperbolic buildings

Jan Dymara, Damian Osajda (2007)

Fundamenta Mathematicae

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We prove that the boundary of a right-angled hyperbolic building is a universal Menger space. As a consequence, the 3-dimensional universal Menger space is the boundary of some Gromov-hyperbolic group.