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Modelirovanie i Analiz Informatsionnykh Sistem, 2013, Volume 20, Number 6, Pages 149–161 (Mi mais352)  
This article is cited in 3 scientific papers (total in 3 papers)

Hyperbolic Tetrahedron: Volume Calculation with Application to the Proof of the Schläfli Formula

I. Kh. Sabitovab

a Lomonosov Moscow State University
b P. G. Demidov Yaroslavl State University, Sovetskaya str., 14, Yaroslavl, 150000, Russia
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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.
Keywords: Lobachevsky space, tetrahedron, volume, integral formula, Schläfli formula.
Received: 01.11.2013
Document Type: Article
UDC: 514.772.35
Language: Russian
Citation: I. Kh. Sabitov, “Hyperbolic Tetrahedron: Volume Calculation with Application to the Proof of the Schläfli Formula”, Model. Anal. Inform. Sist., 20:6 (2013), 149–161
Citation in format AMSBIB
\Bibitem{Sab13}
\by I.~Kh.~Sabitov
\paper Hyperbolic Tetrahedron: Volume Calculation with Application to the Proof of the Schl\"afli Formula
\jour Model. Anal. Inform. Sist.
\yr 2013
\vol 20
\issue 6
\pages 149--161
\mathnet{http://mi.mathnet.ru/mais352}
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    • This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Моделирование и анализ информационных систем
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