Some inequalities for planar convex figures
type: Item
instance of: scholarly article
title: Some inequalities for planar convex figures
zbMATH Open document ID: 0839.52006
author: Martin Henk
author: George A. Tsintsifas
published in: Elemente der Mathematik
publication date: 1994-12-01T00:00:00Z
full work available at URL: https://eudml.org/doc/141565
review text: The paper concerns inequalities for compact convex subsets of the Euclidean plane. Let \({\mathcal K}^2\) be the class of such sets. For every \(K \in {\mathcal K}^2\) let \(A(K)\), \(D(K)\), and \(r(K)\) be the area, the diameter, and the inradius of \(K\). The authors prove the following. Theorem 1.1. For every \(K \in {\mathcal K}^2\) \(A(K) \leq 2D (K) \cdot r(K)\). The equality holds if and only if \(\text{int} K = \emptyset\). The term ``width'' is used here in a sense different than usually. It is understood as thickness, i.e. the infimum of widths in all directions.
reviewed by: Maria Moszyńska
Mathematics Subject Classification ID: 52A40
Mathematics Subject Classification ID: 52A38
Mathematics Subject Classification ID: 52A10
zbMATH DE Number: 698834
zbMATH Keywords: area
zbMATH Keywords: diameter
zbMATH Keywords: inradius
zbMATH Keywords: circumradius
zbMATH Keywords: planar convex figure
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 698834