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

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

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<p>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...

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Main Author: I. Kh. Sabitov
Format: Article
Language:English
Published: Yaroslavl State University 2013-01-01
Series:Modelirovanie i Analiz Informacionnyh Sistem
Subjects:
пространство Лобачевского
тетраэдр
объем
интегральная формула
формула Шлефли
Online Access:http://mais-journal.ru/jour/article/view/167
id doaj-7e1bc927fecd4beabd43ae8c052a4363
record_format Article
spelling doaj-7e1bc927fecd4beabd43ae8c052a43632020-11-25T01:59:02ZengYaroslavl State UniversityModelirovanie i Analiz Informacionnyh Sistem1818-10152313-54172013-01-01206149161161Hyperbolic Tetrahedron: Volume Calculation with Application to the Proof of the Schläfli FormulaI. Kh. Sabitov0Московский государственный университет им. М.В. Ломоносова; Ярославский государственный университет им. П.Г. Демидова<p>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.</p>http://mais-journal.ru/jour/article/view/167пространство Лобачевскоготетраэдробъеминтегральная формулаформула Шлефли
collection DOAJ
language English
format Article
sources DOAJ
author I. Kh. Sabitov
spellingShingle I. Kh. Sabitov
Hyperbolic Tetrahedron: Volume Calculation with Application to the Proof of the Schläfli Formula
Modelirovanie i Analiz Informacionnyh Sistem
пространство Лобачевского
тетраэдр
объем
интегральная формула
формула Шлефли
author_facet I. Kh. Sabitov
author_sort I. Kh. Sabitov
title Hyperbolic Tetrahedron: Volume Calculation with Application to the Proof of the Schläfli Formula
title_short Hyperbolic Tetrahedron: Volume Calculation with Application to the Proof of the Schläfli Formula
title_full Hyperbolic Tetrahedron: Volume Calculation with Application to the Proof of the Schläfli Formula
title_fullStr Hyperbolic Tetrahedron: Volume Calculation with Application to the Proof of the Schläfli Formula
title_full_unstemmed Hyperbolic Tetrahedron: Volume Calculation with Application to the Proof of the Schläfli Formula
title_sort hyperbolic tetrahedron: volume calculation with application to the proof of the schläfli formula
publisher Yaroslavl State University
series Modelirovanie i Analiz Informacionnyh Sistem
issn 1818-1015
2313-5417
publishDate 2013-01-01
description <p>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.</p>
topic пространство Лобачевского
тетраэдр
объем
интегральная формула
формула Шлефли
url http://mais-journal.ru/jour/article/view/167
work_keys_str_mv AT ikhsabitov hyperbolictetrahedronvolumecalculationwithapplicationtotheproofoftheschlafliformula
_version_ 1724966344524300288

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