Packing rectangles into a rectangle
type: Item
instance of: scholarly article
title: Packing rectangles into a rectangle
zbMATH Open document ID: 1060.52010
author: Liping Yuan
author: Changqing Xu
author: Ren Ding
published in: Southeast Asian Bulletin of Mathematics
publication date: 2004-11-25T00:00:00Z
review text: In the sequel, it is assumed that the sides of the geometrical objects considered are parallel. \textit{J. Januszewski} [Geom. Dedicata 81, 13--18 (2000; Zbl 0959.52013)] proved that any sequence of rectangles of side lengths at most 1 and whose total area is at most \(\frac{1}{2}\) can be packed into a unit square. This result is here extended by showing that any sequence of rectangles of side lengths at most \(a\) and whose total area is at most \(\frac{ab}{2}\) can be packed into an \(a\times b\) rectangle, where \(a \leq b\). The bound in the result cannot be tightened: for any \(\varepsilon >0\), three squares of side \(1+\varepsilon\) cannot be packed into a \(2\times 3\) rectangle.
Mathematics Subject Classification ID: 52C15
zbMATH DE Number: 2119035
zbMATH Keywords: packing
zbMATH Keywords: rectangle
reviewed by: Patric R. J. Östergård
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 2119035