Covering a plane convex body with five smaller homothetical copies (Q1089614)
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scientific article; zbMATH DE number 4005046
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Covering a plane convex body with five smaller homothetical copies |
scientific article; zbMATH DE number 4005046 |
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Covering a plane convex body with five smaller homothetical copies (English)
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1987
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A conjecture of Marek Lassak (1986) concerning Hadwiger's covering problem is solved: For a convex body C in the Euclidean plane, let \(h_ k(C)\) be the smallest positive ratio of k homothetical copies of C whose union covers C. Define \(h_ k=\inf \{h_ k(C): C\) is a plane convex body\(\}\). Then \(h_ 5=1/2\). Lassak also formulated the conjecture that \(h_ 6=1/2\), but this is still unsolved.
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Hadwiger's covering problem
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convex body
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Euclidean plane
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homothetical copies
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0.9191486
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0.91149616
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0.8973557
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0.89703935
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0.8932926
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