Minimal diameter of certain sets in the plane (Q1279661)
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scientific article; zbMATH DE number 1251153
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Minimal diameter of certain sets in the plane |
scientific article; zbMATH DE number 1251153 |
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Minimal diameter of certain sets in the plane (English)
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27 April 1999
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The authors deal with the following question. Of all sets of \(n\) points in the plane such that the mutual distances are at least 1 what set has the minimum diameter \(D(n)\)? The following theorem answers the question for \(n=8\): The minimal diameter \(D(8)\) is \((2\sin(\pi/14))^{-1} = 2.246\dots.\) The minimal diameter is attained only if the convex hull of the points is a regular heptagon of sidelength 1.
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geometrical extremum problem
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minimal diameter
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asymptotic behaviour
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convex hull
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