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

Gülcan Balakan; Oğuzhan Demirel

doi:10.23851/mjs.v32i1.932

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.

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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.

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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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Key Dates

Published

24-02-2021

Issue

Vol. 32 No. 1 (2021)

Section

Original Article

License

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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”, Al-Mustansiriyah Journal of Science, vol. 32, no. 1, pp. 31–38, Feb. 2021, doi: 10.23851/mjs.v32i1.932.