An estimate for the problem of illumination of the boundary of a convex body in \(E^3\) (Q1301606)
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scientific article; zbMATH DE number 1334360
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | An estimate for the problem of illumination of the boundary of a convex body in \(E^3\) |
scientific article; zbMATH DE number 1334360 |
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An estimate for the problem of illumination of the boundary of a convex body in \(E^3\) (English)
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31 July 2000
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Let \(A\) be a convex body in Euclidean space \(\mathbb E^n.\) Let \(H(A)\) be the smallest number of homothetic ``reduced copies'' of \(A\) by which it is possible to cover the whole of \(A.\) The conjecture of Hadwiger is \(H(A) \leqslant 2^n\) [\textit{H.~Hadwiger}, Ungelöste Probleme. 20, Elem. Math. 12, 121 (1957)]. The author proves that \(H(A) \leqslant 16,\) for \(n=3.\)
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convex body
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Euclidean space
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conjecture of Hadwiger
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covering convex body by smaller homothetic copies
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tiling problem
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0.91414195
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0.8978318
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0.88694704
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0.88591576
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0.8852862
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0.8746834
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