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

Source
Proceedings of the Fifth International Conference on Geometry, Integrability and Quantization, Ivaïlo M. Mladenov and Allen C. Hirshfeld, eds. (Sofia: Softex, 2004), 225-236

Dates
First available in Project Euclid: 12 June 2015

Permanent link to this document
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


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