## Proceedings of the International Conference on Geometry, Integrability and Quantization

### The Hyperbolic Triangle Defect

Abraham A. Ungar

#### 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.

#### Article information

Dates
First available in Project Euclid: 12 June 2015

https://projecteuclid.org/ euclid.pgiq/1434147930

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

Mathematical Reviews number (MathSciNet)
MR2082308

Zentralblatt MATH identifier
1062.51013

#### Citation

Ungar, Abraham A. The Hyperbolic Triangle Defect. Proceedings of the Fifth International Conference on Geometry, Integrability and Quantization, 225--236, Softex, Sofia, Bulgaria, 2004. doi:10.7546/giq-5-2004-225-236. https://projecteuclid.org/euclid.pgiq/1434147930