M\"obius Transformation and Einsten Velocity Addition in the Hyperbolic Geometry of Bolyai and Lobachevsky
Abstract
In this chapter, dedicated to the 60th Anniversary of Themistocles M. Rassias, M\"obius transformation and Einstein velocity addition meet in the hyperbolic geometry of Bolyai and Lobachevsky. It turns out that M\"obius addition that is extracted from M\"obius transformation of the complex disc and Einstein addition from his special theory of relativity are isomorphic in the sense of gyrovector spaces.
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