A New Hyperbolic Area Formula of a Hyperbolic Triangle and Its Applications

Hui Bao and Xingdi Chen

Journal of Mathematics, 2014, vol. 2014, 1-8

Abstract:

We study some characterizations of hyperbolic geometry in the Poincaré disk. We first obtain the hyperbolic area and length formula of Euclidean disk and a circle represented by its Euclidean center and radius. Replacing interior angles with vertices coordinates, we also obtain a new hyperbolic area formula of a hyperbolic triangle. As its application, we give the hyperbolic area of a Lambert quadrilateral and some geometric characterizations of Lambert quadrilaterals and Saccheri quadrilaterals.

Date: 2014
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jjmath:838497

DOI: 10.1155/2014/838497

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