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Non-Euclidean Geometries pp 487–506Cite as

Placing the Hyperbolic Geometry of Bolyai and Lobachevsky Centrally in Special Relativity Theory: An Idea Whose Time has Returned

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Part of the book series: Mathematics and Its Applications ((MAIA,volume 581))

Abstract

We show that Einstein addition of relativistically admissible velocities is regulated by the hyperbolic geometry of Bolyai and Lobachevski just as Newtonian velocity addition is regulated by Euclidean geometry. Hence, the time to study special relativity in terms of its underlying hyperbolic geometry has returned.

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Author information

Authors and Affiliations

  1. Department of Mathematics, North Dakota State University, Fargo, ND, 58105, USA

    Abraham A. Ungar

Authors
  1. Abraham A. Ungar
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Editor information

Editors and Affiliations

  1. Rutgers Center for Operations Research, Piscataway, New Jersey, USA

    András Prékopa

  2. Budapest University of Technology and Economics, Hungary

    Emil Molnár

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Ungar, A.A. (2006). Placing the Hyperbolic Geometry of Bolyai and Lobachevsky Centrally in Special Relativity Theory: An Idea Whose Time has Returned. In: Prékopa, A., Molnár, E. (eds) Non-Euclidean Geometries. Mathematics and Its Applications, vol 581. Springer, Boston, MA. https://doi.org/10.1007/0-387-29555-0_24

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