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

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

## Abstract

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.

## Information

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