Compactness Theorems for Geometric Packings
| dc.creator | Martin, Greg | |
| dc.date | 2000-05-05 | |
| dc.date.accessioned | 2026-07-07T04:35:02Z | |
| dc.date.available | 2026-07-07T04:35:02Z | |
| dc.description | Moser asked whether the collection of rectangles of dimensions 1 x 1/2, 1/2 x 1/3, 1/3 x 1/4, ..., whose total area equals 1, can be packed into the unit square without overlap, and whether the collection of squares of side lengths 1/2, 1/3, 1/4, ... can be packed without overlap into a rectangle of area pi^2/6-1. Computational investigations have been made into packing these collections into squares of side length 1+epsilon and rectangles of area pi^2/6-1+epsilon, respectively, and one can consider the apparently weaker question whether such packings are possible for every positive number epsilon. In this paper we establish a general theorem on sequences of geometrical packings that implies in particular that the ``for every epsilon'' versions of these two problems are actually equivalent to the original tiling problems. | |
| dc.description | 10 pages | |
| dc.identifier | https://arxiv.org/abs/math/0005054 | |
| dc.identifier | http://arxiv.org/abs/math/0005054 | |
| dc.identifier | J. Combin. Theory Ser. A 97 (2002), 225-238. | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/59132 | |
| dc.subject | Metric Geometry | |
| dc.subject | Combinatorics | |
| dc.subject | General Topology | |
| dc.subject | 52C17 (52C15, 54H99) | |
| dc.title | Compactness Theorems for Geometric Packings | |
| dc.type | text |