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

Gülcan Balakan, Oğuzhan Demirel


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.


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

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Horvath, Akos G. Hyperbolic plane geometry revisited. J. Geom. 106 (2015), no. 2, 341-362.


Mednykh, A. D. Brahmagupta formula for cyclic quadrilaterials in the hyperbolic plane. Sib. lektron. Mat. Izv. 9 (2012), 247-255.

Baigonakova, G. A., Mednykh, A. D., On Bretschneider's formula for a hyperbolic quadrilateral, Mat. Zamet. YaGU, 19:2(2012), 12-19.

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


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


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.




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