Some strengthened versions of Klamkin's inequality and applications
type: Item
instance of: scholarly article
title: Some strengthened versions of Klamkin's inequality and applications
zbMATH Open document ID: 1468.51008
author: Quang Hung Tran
published in: Geometriae Dedicata
publication date: 2021-07-02T00:00:00Z
review text: Euler's inequality for a \(n\)-dimesional simplex in \(n\)-dimensional Euclidean space is \[R\geq nr,\] where \(R\) and \(r\) are the circumradius and the inradius of the simplex, respectively. \textit{M. S. Klamkin} [Math. Modelling 6, 49--64 (1985; Zbl 0573.49012)] obtained the improvement \[R^2\geq n^2r^2 + |OI|^2,\] where \(O\) and \(I\) are the circumcenter and the incenter of the simplex. As the title indicates, the author gives two sharpenings of the last inequality, from which Euler's inequality follows as an easy corollary.
reviewed by: Martin Lukarevski
Mathematics Subject Classification ID: 51M16
Mathematics Subject Classification ID: 51M04
zbMATH DE Number: 7367294
zbMATH Keywords: simplex
zbMATH Keywords: geometric inequalities
zbMATH Keywords: circumradius
zbMATH Keywords: inradius
MaRDI profile type: Publication
full work available at URL: s10711-020-00591-x
OpenAlex ID: W3119844532
cites work: The Circumradius-Inradius Inequality for a Simplex
cites work: An inequality for a simplex and its applications
cites work: Some geometric inequalities for a tangent point simplex
DOI: 10.1007/S10711-020-00591-X
description: scientific article; zbMATH DE number 7367294