Two problems concerning the area-perimeter ratio of lattice-point-free regions in the plane
type: Item
instance of: scholarly article
title: Two problems concerning the area-perimeter ratio of lattice-point-free regions in the plane
zbMATH Open document ID: 0873.52017
author: Salvador Segura Gomis
author: Uwe Schnell
published in: Beiträge zur Algebra und Geometrie
publication date: 1996-09-18T00:00:00Z
full work available at URL: https://eudml.org/doc/225492
full work available at URL: no.1
review text: The authors consider the integer lattice in the euclidean plane and prove that for a lattice-point-free simple connection (i.e. not necessarily convex) region \(M\) with area \(A(M)\) and perimeter \(P(M)\) holds: \(A(M)<\gamma P(M)\), where \(\gamma=0.58\dots\) is the solution of a transcendental equation. In particular the inequality is tight. As a consequence they prove a tight Dido-type for simple connected regions.
Mathematics Subject Classification ID: 52C05
Mathematics Subject Classification ID: 52A40
zbMATH DE Number: 928003
zbMATH Keywords: inequalities
zbMATH Keywords: convex bodies
zbMATH Keywords: lattice
zbMATH Keywords: euclidean plane
reviewed by: Jörg M. Wills
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 928003