On application of contemporary proof of the Sforza formula to computation of volumes of hyperbolic tetrahedra of special kind
type: Item
instance of: scholarly article
title: On application of contemporary proof of the Sforza formula to computation of volumes of hyperbolic tetrahedra of special kind
author: Yanyan Li
published in: Journal of Mathematical Sciences (New York)
publication date: 2022-10-10T00:00:00Z
review text: The research for volume formulas for hyperbolic tetrahedra began with the discovery of hyperbolic geometry, and many researchers have been making partial refinements of the formulas until now. The volume of a hyperbolic polyhedron determines its shape in hyperbolic geometry, and it is one of the crucial formulas in low-dimensional topology. Since it is a natural occurrence that volume formulas are formulated in terms of integral formulas, it is essential from the viewpoint of application to be able to obtain simple formulas under certain conditions. In this paper, from an old theorem known as Sforza's formula, a relatively simple integral formula by a dihedral angle is derived for the case of tetrahedra with some special conditions (orthoschemes and tetrahedra with the symmetry group \(S^4\)).
reviewed by: Kazushi Ahara
Mathematics Subject Classification ID: 51M25
Mathematics Subject Classification ID: 51M10
zbMATH DE Number: 7599124
zbMATH Keywords: volume formula
zbMATH Keywords: Sforza formula
zbMATH Keywords: hyperbolic volume of tetrahedron
Wikidata QID: Q114225118
MaRDI profile type: Publication
full work available at URL: s10958-022-06085-3
OpenAlex ID: W4295942364
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DOI: 10.1007/S10958-022-06085-3
description: scientific article; zbMATH DE number 7599124