Unit distances between vertices of a convex polygon (Q1199829)
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scientific article; zbMATH DE number 96050
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Unit distances between vertices of a convex polygon |
scientific article; zbMATH DE number 96050 |
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Unit distances between vertices of a convex polygon (English)
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17 January 1993
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The authors construct convex \(n\)-gons with the property: Their vertices are partitioned into sets \(A\) and \(B\) on opposite sides of a line such that each \(a\in A\) has distance 1 from three vertices in \(B\) and each \(b\in B\) has distance 1 from three vertices in \(A\). The smallest \(n\) for which this is possible is \(n=20\). [Cf. \textit{P. Erdős}, Colloq. Math. Soc. János Bolyai 48, 167-177 (1987; Zbl 0625.52008)].
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convex \(n\)-gons
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