Covering planar sets of constant width by three sets of smaller diameters (Q1205422)
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scientific article; zbMATH DE number 147283
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Covering planar sets of constant width by three sets of smaller diameters |
scientific article; zbMATH DE number 147283 |
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Covering planar sets of constant width by three sets of smaller diameters (English)
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1 April 1993
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Using an element separation property of triples of boundary points from a plane set \(K\) of constant width \(w\), the author proves the following theorem: If \(\{B_ 1,B_ 2,B_ 3\}\) is a cover of \(K\) with \(d(B_ i)\) denoting the diameter of \(B_ i\) and \(d(B_ i)<w\) for \(i=1,2,3\), then \[ d(B_ 1)+d(B_ 2)+d(B_ 3)>2w. \]
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constant width
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separation theorems
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Reuleaux triangle
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0.9339982
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0.9003508
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0.89768314
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0.8828765
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0.8684038
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