Hyperbolic Tetrahedron: Volume Calculation with Application to the Proof of the Schläfli Formula
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 func...
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| Format: | Article |
| Language: | English |
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Yaroslavl State University
2013-12-01
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| Series: | Моделирование и анализ информационных систем |
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| Online Access: | https://www.mais-journal.ru/jour/article/view/167 |
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| author | I. Kh. Sabitov |
| author_facet | I. Kh. Sabitov |
| author_sort | I. Kh. Sabitov |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-3a0ea0b47c6f40d68a5cab26f5ac5895 |
| institution | Kabale University |
| issn | 1818-1015 2313-5417 |
| language | English |
| publishDate | 2013-12-01 |
| publisher | Yaroslavl State University |
| record_format | Article |
| series | Моделирование и анализ информационных систем |
| spelling | doaj-art-3a0ea0b47c6f40d68a5cab26f5ac58952025-08-20T04:00:26ZengYaroslavl State UniversityМоделирование и анализ информационных систем1818-10152313-54172013-12-0120614916110.18255/1818-1015-2013-6-149-161161Hyperbolic Tetrahedron: Volume Calculation with Application to the Proof of the Schläfli FormulaI. Kh. Sabitov0Lomonosov Moscow State University; P.G. Demidov Yaroslavl State UniversityWe 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.https://www.mais-journal.ru/jour/article/view/167lobachevsky spacetetrahedronvolumeintegral formulaschläfli formula |
| spellingShingle | I. Kh. Sabitov Hyperbolic Tetrahedron: Volume Calculation with Application to the Proof of the Schläfli Formula Моделирование и анализ информационных систем lobachevsky space tetrahedron volume integral formula schläfli formula |
| title | 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_short | 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 schlafli formula |
| topic | lobachevsky space tetrahedron volume integral formula schläfli formula |
| url | https://www.mais-journal.ru/jour/article/view/167 |
| work_keys_str_mv | AT ikhsabitov hyperbolictetrahedronvolumecalculationwithapplicationtotheproofoftheschlafliformula |