An alternate proof of Gerretsen's inequalities
type: Item
instance of: scholarly article
title: An alternate proof of Gerretsen's inequalities
zbMATH Open document ID: 1364.51009
DOI: 10.4171/EM/317
author: Martin Lukarevski
published in: Elemente der Mathematik
publication date: 2017-03-13T00:00:00Z
review text: The author proves the \(16Rr-5r^2\leq s^2\) part of Gerretsen's inequality by using Schur's inequality and the \(s^2\leq 4R^2+4Rr+3r^2\) part by using an inequality that holds for any three real numbers together with an identity involving \(\cos A \cos B \cos C\). He then considers equivalent forms and shows that Ono's inequality for acute triangles (\(27(-a^2+b^2+c^2)^2(a^2-b^2+c^2)^2(a^2+b^2-c^2)^2\leq (4A)^6\)), Blundon's inequality (\(s\leq 2R+ (3\sqrt{3}-4)r\)), and the Hadwiger-Finsler inequality can be deduced from Gerretsen's inequality.
reviewed by: Victor V. Pambuccian
Mathematics Subject Classification ID: 51M16
zbMATH DE Number: 6694041
zbMATH Keywords: Gerretsen inequality, Ono inequality
zbMATH Keywords: Hadwiger-Finsler inequality
zbMATH Keywords: Schur inequality
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.4171/em/317
OpenAlex ID: W2570493790
description: scientific article; zbMATH DE number 6694041