The Formulas of Möbius-Bretschneider and Möbius-Cagnoli in the Poincaré Disc Model of Hyperbolic Geometry
DOI:
https://doi.org/10.23851/mjs.v32i1.932Keywords:
Hyperbolic triangle, hyperbolic quadrilateral, hyperbolic Bretschneider’s formula, hyperbolic Cagnoli’s formulaAbstract
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
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.
Downloads
Published
How to Cite
Issue
Section
License
The journal has no restrictions for the author to hold the copyrights of his articles. The journal does not allow authors to republish the same article in other journals or conferences that is published in one of its volumes.