Hyperbolic Tetrahedron: Volume Calculation with Application to the Proof of the Schläfli Formula
https://doi.org/10.18255/1818-1015-2013-6-149-161
Abstract
We propose a new approach to the problem of calculations of volumes in the Lobachevsky space, and we apply this method to tetrahedra. Using some integral formulas, we present an explicit formula for the volume of a tetrahedron in the function of the coordinates of its vertices as well as in the function of its edge lengths. Finally, we give a direct analitic proof of the famous Schläfli formula for tetrahedra.
About the Author
I. Kh. Sabitov
Lomonosov Moscow State University;
P.G. Demidov Yaroslavl State University
Russian Federation
Russian Federation
профессор;
ведущий научный сотрудник,
Sovetskaya str., 14, Yaroslavl, 150000, Russia
References
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Review
For citations:
Sabitov I.Kh. Hyperbolic Tetrahedron: Volume Calculation with Application to the Proof of the Schläfli Formula. Modeling and Analysis of Information Systems. 2013;20(6):149-161. (In Russ.) https://doi.org/10.18255/1818-1015-2013-6-149-161
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