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

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  • Hui Bao
  • Xingdi Chen

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.

Suggested Citation

  • Hui Bao & Xingdi Chen, 2014. "A New Hyperbolic Area Formula of a Hyperbolic Triangle and Its Applications," Journal of Mathematics, Hindawi, vol. 2014, pages 1-8, August.
    • Handle: RePEc:hin:jjmath:838497
    DOI: 10.1155/2014/838497
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