TL;DR
This paper presents a non-elementary integral formula for calculating the volume of an orthosceme in hyperbolic space, avoiding the use of the Schl"afli differential formula and relying solely on edge lengths.
Contribution
It introduces a novel integral expression for hyperbolic orthosceme volume based only on edge lengths, simplifying volume calculations.
Findings
Derived a non-elementary integral formula for orthosceme volume
Avoided using the Schl"afli differential formula in volume computation
Provided a method relying solely on edge-length parameters
Abstract
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.
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Taxonomy
TopicsMathematics and Applications · Advanced Mathematical Theories · Computational Geometry and Mesh Generation