Open Access
VOL. 5 | 2004 The Hyperbolic Triangle Defect
Abraham A. Ungar

Editor(s) Ivaïlo M. Mladenov, Allen C. Hirshfeld

Geom. Integrability & Quantization, 2004: 225-236 (2004) DOI: 10.7546/giq-5-2004-225-236


The hyperbolic trigonometry, fully analogous to the common Euclidean trigonometry, is presented and employed to calculate the hyperbolic triangle defect in the Poincaré ball model of $n$-dimensional hyperbolic geometry. It is shown that hyperbolic trigonometry allows the hyperbolic triangle defect to be expressed in terms of the triangle hyperbolic side lengths by a remarkably elegant identity.


Published: 1 January 2004
First available in Project Euclid: 12 June 2015

zbMATH: 1062.51013
MathSciNet: MR2082308

Digital Object Identifier: 10.7546/giq-5-2004-225-236

Rights: Copyright © 2004 Institute of Biophysics and Biomedical Engineering, Bulgarian Academy of Sciences


Back to Top