A bound on the ratio between the packing and covering densities of a convex body (Q1972306)
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scientific article; zbMATH DE number 1436016
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A bound on the ratio between the packing and covering densities of a convex body |
scientific article; zbMATH DE number 1436016 |
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A bound on the ratio between the packing and covering densities of a convex body (English)
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3 January 2001
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A convex body is a compact convex set having a nonempty interior. The author considers packings and coverings with centrally symmetric convex bodies. It is proved that for any such body, the ratio between the density of its thinnest lattice covering of Euclidean 3-space and the density of its tightest lattice packing in Euclidean 3-space is less than or equal to 4.
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convex body
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density
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Euclidean 3-space
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lattice covering
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lattice packing
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0.9587941
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0.95481884
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0.9336418
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0.92582583
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0.9138057
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0.9112377
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