Asian Journal of Mathematics and Computer Research

THE AREA OF A GENERALIZED POLYGON WITHOUT PARABOLIC EDGES OF A HYPERBOLIC PLANE OF POSITIVE CURVATURE

LYUDMILA ROMAKINA *

Department of Geometry, Saratov State University, 83 Astrakhanskaya Street, 410012 Saratov, Russia.

*Author to whom correspondence should be addressed.

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Abstract

The geometry of a hyperbolic plane Ĥ of positive curvature can be realized on ideal domain of the Lobachevskii plane ∧². The planes Ĥ and ∧² are components of an extended hyperbolic plane H², i.e. the projective plane P₂ with the oval curve ϒ fixed on it. In this article the formula of expression of the area of the generalized polygon without parabolyc edges on the plane Ĥ through measures of its internal angles is proved.

Keywords: The hyperbolic plane Ĥ of positive curvature, a generalized polygon of the plane Ĥ, the area of a generalized polygon of the plane Ĥ

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