Packing rectangles into the unit square
type: Item
instance of: scholarly article
title: Packing rectangles into the unit square
zbMATH Open document ID: 0959.52013
DOI: 10.1023/A:1005263703808
author: Janusz Januszewski
published in: Geometriae Dedicata
publication date: 2001-05-06T00:00:00Z
review text: \textit{L. Moser} and \textit{J. W. Moon} [Colloq. Math. 17, 103-110 (1967; Zbl 0152.39502)] proved that every sequence of squares whose total area is not more than 1/2 can be packed (using isometries) into a unit square. Now Januszewski generalizes this to: a sequence of rectangles of side length at most 1 and total area at most 1/2 can be packed into a unit square. Furthermore the sides of the packed rectangles are parallel to the sides of the unit square. There is more, which makes this short paper packed with nice results about packings.
Mathematics Subject Classification ID: 52C15
zbMATH DE Number: 1505827
zbMATH Keywords: rectangles
zbMATH Keywords: unit square
zbMATH Keywords: packings
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1505827