Mladenov, Ivaïlo M. (ed.) et al., Proceedings of the 5th international conference on geometry, integrability and quantization, Sts. Constantine and Elena, Bulgaria, June 5--12, 2003. Sofia: Bulgarian Academy of Sciences (ISBN 954-84952-8-7/pbk). 225-236 (2004).
The author introduces hyperbolic trigonometry by means of gyrovector spaces (for a comprehensive introduction into the theory of gyrogroups and gyrovector spaces see the author’s book [Beyond the Einstein addition law and its gyroscopic Thomas precession. The theory of gyrogroups and gyrovector spaces. Dordrecht: Kluwer (2001; Zbl 0972.83002
)]). A special kind of gyrovector spaces is used to describe the Poincaré ball model of hyperbolic geometry [the author, Comput. Math. Appl. 41, No. 1--2, 135--147 (2001; Zbl 0988.51017
)]. Within this setting the author derives formulae for the hyperbolic law of sines and cosines, the Pythagorean Theorem, and the angular defect of a hyperbolic triangle. For the entire collection see [Zbl 1048.53002
|51M09||Elementary problems in hyperbolic and elliptic geometries|