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Nonlinear Analysis pp 721–770Cite as

Möbius Transformation and Einstein Velocity Addition in the Hyperbolic Geometry of Bolyai and Lobachevsky

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Part of the book series: Springer Optimization and Its Applications ((SOIA,volume 68))

Abstract

In this chapter, dedicated to the 60th Anniversary of Themistocles M. Rassias, Möbius transformation and Einstein velocity addition meet in the hyperbolic geometry of Bolyai and Lobachevsky. It turns out that Möbius addition that is extracted from Möbius transformation of the complex disc and Einstein addition from his special theory of relativity enable the introduction of Cartesian coordinates and vector algebra as novel tools in the study of hyperbolic geometry.

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Authors and Affiliations

  1. Department of Mathematics, North Dakota State University, Fargo, ND, 58108, USA

    Abraham Albert Ungar

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  1. Abraham Albert Ungar
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Correspondence to Abraham Albert Ungar .

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  1. , Department of Industrial & Systems Engin, University of Florida, Weil Hall 401, Gainesville, 32611, Florida, USA

    Panos M. Pardalos

  2. Center for Applied Optimization, Dept. Industrial & Systems, University of Florida, Weil Hall 303, Gainesville, 32611-6595, Florida, USA

    Pando G. Georgiev

  3. , Department of Mathematics & Statistics, University of Victoria, Finnerty Road 3800, Victoria, V8W 3R4, British Columbia, Canada

    Hari M. Srivastava

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Dedicated to Professor Themistocles M. Rassias on the occasion of his 60th birthday.

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Ungar, A.A. (2012). Möbius Transformation and Einstein Velocity Addition in the Hyperbolic Geometry of Bolyai and Lobachevsky. In: Pardalos, P., Georgiev, P., Srivastava, H. (eds) Nonlinear Analysis. Springer Optimization and Its Applications, vol 68. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-3498-6_41

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