The generalized sine theorem and inequalities for simplices
type: Item
instance of: scholarly article
title: The generalized sine theorem and inequalities for simplices
zbMATH Open document ID: 0937.51013
DOI: 10.1016/S0024-3795(97)10096-9
author: Yao Zhang
author: Gangsong Leng
published in: Linear Algebra and its Applications
publication date: 1999-10-28T00:00:00Z
review text: The authors establish a generalized sine theorem for the Euclidean \(n\)-simplex \(S\), i.e., they extend the known \(n\)-dimensional sine theorem (given in terms of the volume, the facet areas and vertex angles of \(S)\) to \(k\)-order vertex angles (e.g., for \(k=2\) yielding a corresponding theorem about dihedral angles). They apply this generalized theorem by deriving some inequalities in terms of the \(k\)-order vertex angles of \(S\), these inequalities also yielding several characterizations of regular \(n\)-simplices. For proving these results, they use informations about the inverse matrix of the metric matrix of an \(n\)-parallelotope.
reviewed by: Horst Martini
Mathematics Subject Classification ID: 51M16
zbMATH DE Number: 1354781
zbMATH Keywords: \(n\)-parallelotope
zbMATH Keywords: \(n\)-simplex
zbMATH Keywords: dihedral angle
zbMATH Keywords: regular simplex
zbMATH Keywords: determinant
zbMATH Keywords: sine theorem
zbMATH Keywords: vertex angles
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1354781