This paper collects some important formulas on hyperbolic volume. To
determine concrete values of volume function is a very hard question requiring
the knowledge of various methods. Our goal to give a non-elementary integral on
the volume of the orthosceme (obtain it without using the Schl\"afli
differential formula), using edge-lengthes as the only parameters.Comment: 7 figure

Horváth, Á. G.

English

arXiv

This paper collects some important formulas on hyperbolic volume. To determine con-crete values of volume function of polyhedra is a very hard question requiring the knowledge of various methods. Our goal is to give (in Section 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-lengthes as the only parameters. MSC(2000): 51F10, 52B1

Formulas on hyperbolic volume

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