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Einstein’s velocity addition law and its hyperbolic geometry. (English) Zbl 1132.83301

Summary: Following a brief review of the history of the link between Einstein’s velocity addition law of special relativity and the hyperbolic geometry of Bolyai and Lobachevski, we employ the binary operation of Einstein’s velocity addition to introduce into hyperbolic geometry the concepts of vectors, angles and trigonometry. In full analogy with Euclidean geometry, we show in this article that the introduction of these concepts into hyperbolic geometry leads to hyperbolic vector spaces. The latter, in turn, form the setting for hyperbolic geometry just as vector spaces form the setting for Euclidean geometry.

MSC:

83A05 Special relativity
53Z05 Applications of differential geometry to physics
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