Open AccessApplication of Contemporary Proof of the Sforza Formula to Computation of Volumes of Hyperbolic Tetrahedra of Special Kind
Author(s) -
V. A. Krasnov,
V. A. Krasnov
Publication year - 2019
Publication title -
sovremennaâ matematika. fundamentalʹnye napravleniâ
Language(s) - English
Resource type - Journals
eISSN - 2949-0618
pISSN - 2413-3639
DOI - 10.22363/2413-3639-2019-65-4-623-634
Subject(s) - tetrahedron , euclidean geometry , mathematics , computation , symmetry (geometry) , tetrahedral symmetry , dihedral angle , pure mathematics , geometry , physics , algorithm , quantum mechanics , rotational symmetry , hydrogen bond , molecule
In this paper, we use the contemporary proof (by Abrosimov and Mednykh) of the Sforza formula for volume of an arbitrary non-Euclidean tetrahedron to derive new formulas that express volumes of hyperbolic tetrahedra of special kind (orthoschemes and tetrahedra with the symmetry group S 4) via dihedral angles.