Inequalities involving the inradii of simplexes
type: Item
instance of: scholarly article
title: Inequalities involving the inradii of simplexes
zbMATH Open document ID: 0851.51012
DOI: 10.1007/BF01223042
author: Huaming Su
published in: Journal of Geometry
publication date: 1996-06-13T00:00:00Z
review text: Let \(r\) be the inradius of an \(n\)-simplex \(A = A_1 A_2 \dots A_{n+1}\) in \(E^n\) \((n \geq 3)\), and \(r_i\) the inradius of the \((n-1)\)-simplex \(F_i = A_1 \dots A_{i-1} A_{i+1} \dots A_{n+1}\). The author proves that \(\sum^{n+1}_{j=1} r^{-2}_j \leq (n-1)r^{-2}\), with equality if and only if \(A\) is regular. He also proves an inequality concerning the inradii of \(k\)-simplexes and \(\ell\)-simplexes \((3 \leq k < \ell \leq n)\) whose vertices lie in a finite set of points in \(E^n\).
reviewed by: E. J. F. Primrose
Mathematics Subject Classification ID: 51M16
Mathematics Subject Classification ID: 52B05
zbMATH DE Number: 872724
zbMATH Keywords: \(n\)-simplex
zbMATH Keywords: inequality
zbMATH Keywords: inradii
MaRDI profile type: Publication
cites work: Q3310513
description: scientific article; zbMATH DE number 872724