Results in Mathematics

, Volume 65, Issue 3–4, pp 361–369 | Cite as

On Trigonometry in Beltrami–Klein Model of Hyperbolic Geometry



Ungar (Math. Appl. 49:187–221, 2005) employed the binary operation of Einsteins velocity addition to introduce into hyperbolic geometry the concepts of vectors, angles and trigonometry in full analogy with Euclidean geometry. We use the isomorphism between \({(\mathbb R,+,\cdot)}\) and \({((-1,1),\oplus,\otimes)}\) in Beltrami–Klein model of hyperbolic geometry for similar results.

Mathematics Subject Classification (2000)

Primary 51A25 Secondary 20N05 


Trigonometry in hyperbolic geometry K-loop gyrogroup Beltrami–Klein model special relativity 


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Copyright information

© Springer Basel 2013

Authors and Affiliations

  1. 1.Department of Mathematical SciencesIsfahan University of TechnologyIsfahanIran

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