Convex sets of constant width and 3-diameter (Q2901918)
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scientific article; zbMATH DE number 6062415
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Convex sets of constant width and 3-diameter |
scientific article; zbMATH DE number 6062415 |
Statements
31 July 2012
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constant width
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3-diameter
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Reuleaux triangle
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Blaschke-Lebesgue theorem
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Convex sets of constant width and 3-diameter (English)
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The \(n\)-diameter of a set \(S\) is defined as the supremum of the geometric mean of all (Euclidean) distances among \(n\) points from \(E\). For \(n=2\) this is just the ordinary diameter of a set. In the paper under review the authors study the \(3\)-diameter of planar compact convex sets of constant width. Among others they prove that for this class of sets, disks have the smallest 3-diameter and Reuleaux triangles have the largest 3-diameter.
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