The Formulas of Möbius-Bretschneider and Möbius-Cagnoli in the Poincaré Disc Model of Hyperbolic Geometry

Authors

  • Gülcan Balakan Department of Mathematics, Faculty of Science and Literature, University of Afyon Kocatepe, TURKEY
  • Oğuzhan Demirel Department of Mathematics, Faculty of Science and Literature, University of Afyon Kocatepe, TURKEY

DOI:

https://doi.org/10.23851/mjs.v32i1.932

Keywords:

Hyperbolic triangle, hyperbolic quadrilateral, hyperbolic Bretschneider’s formula, hyperbolic Cagnoli’s formula

Abstract

In this paper, we present two gyroarea formulas (Möbius-Bretschneider’s formula and Möbius-Cagnoli’s formula) for Möbius gyroquadrilaterals in the Poincaré disc model of hyperbolic geometry.

References

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Ungar, Abraham A., Analytic hyperbolic geometry. Mathematical foundations and applications. World Scientific Publishing Co. Pte. Ltd., Hackensack, NJ, 2005.

CrossRef

Ungar, Abraham A., Barycentric calculus in Euclidean and hyperbolic geometry. A comparative introduction. World Scientific Publishing Co. Pte. Ltd., Hackensack, NJ, 2010.

CrossRef

Frenkel, Elena; Su, Weixu. The area formula for hyperbolic triangles. Eighteen essays in non-Euclidean geometry, IRMA Lect. Math. Theor. Phys., 29, Eur. Math. Soc., Zrich, 2019 27-46.

CrossRef

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Published

2021-02-24

How to Cite

[1]
G. Balakan and O. Demirel, “The Formulas of Möbius-Bretschneider and Möbius-Cagnoli in the Poincaré Disc Model of Hyperbolic Geometry”, MJS, vol. 32, no. 1, pp. 31–38, Feb. 2021.

Issue

Section

Mathematics