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On Trigonometry in Beltrami–Klein Model of Hyperbolic Geometry

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Abstract

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.

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  1. Department of Mathematical Sciences, Isfahan University of Technology, 84156-83111, Isfahan, Iran

    Mahfouz Rostamzadeh & Sayed-Ghahreman Taherian

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  1. Mahfouz Rostamzadeh
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  2. Sayed-Ghahreman Taherian
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Correspondence to Sayed-Ghahreman Taherian.

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Rostamzadeh, M., Taherian, SG. On Trigonometry in Beltrami–Klein Model of Hyperbolic Geometry. Results. Math. 65, 361–369 (2014). https://doi.org/10.1007/s00025-013-0350-6

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  • DOI: https://doi.org/10.1007/s00025-013-0350-6

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