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Formulas on hyperbolic volume

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Abstract

This paper collects some important formulas on hyperbolic volume. To determine concrete values of the volume function of polyhedra is a very hard question requiring the knowledge of various methods. Our goal is to give (in Sect. 3.3, Theorem 1) a new non-elementary integral on the volume of the orthoscheme (to obtain it without the Lobachevsky-Schläfli differential formula), using edge-lengths as the only parameters.

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Authors and Affiliations

  1. Department of Geometry, Budapest University of Technology and Economics, Budapest, 1521, Hungary

    Á. G. Horváth

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  1. Á. G. Horváth
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Correspondence to Á. G. Horváth.

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Dedicated to the memory of János Bolyai on the 150th anniversary of his death

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Horváth, Á.G. Formulas on hyperbolic volume. Aequat. Math. 83, 97–116 (2012). https://doi.org/10.1007/s00010-011-0100-3

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  • DOI: https://doi.org/10.1007/s00010-011-0100-3

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