Densest packing of translates of a domain (Q1063879)
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scientific article; zbMATH DE number 3917143
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Densest packing of translates of a domain |
scientific article; zbMATH DE number 3917143 |
Statements
Densest packing of translates of a domain (English)
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1985
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Let s be an open set of points in the Euclidean plane. Let d(s) be the density of the densest packing of translates of s, and let \(d^*(s)\) be the density of the densest lattice-packing of translates of s. It is shown that, if s is a limited semi-convex domain, then \(d(s)=d^*(s)\). This generalises a result for convex domains by \textit{C. A. Rogers} [Acta Math. 86, 309-321 (1951; Zbl 0044.192)].
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density
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lattice-packing of translates
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convex domains
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