Advanced Search

Query:

Fill in the form and click »Search«...

Format:

Display: entries per page entries

Zbl 1062.51013
Ungar, Abraham A.
The hyperbolic triangle defect. (English)
[A] Mladenov, Iva\"ilo 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. 225-236 (2004). ISBN 954-84952-8-7/pbk

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 (2001; Zbl 0972.83002)). A special kind of gyrovector spaces is used to describe the Poincaré ball model of hyperbolic geometry [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.
[Richard Bödi (Rüschlikon)]

MSC 2000:: *51M09 Elementary problems in hyperbolic and elliptic geometries

Keywords: hyperbolic trigonometry; triangle defect

Citations: Zbl 0972.83002; Zbl 0988.51017

Comment on this Item PDF MathML XML ASCII DVI PS BibTeX Online Ordering

	Scientific prize winners of the ICM 2010
	Overhang
	Lie groups, physics and geometry. An introduction for physicists, engineers and chemists.

Advanced Search

Zentralblatt MATH Berlin [Germany]