Two new approaches to obtaining estimates in the Danzer-Grünbaum problem (Q1957082)
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scientific article; zbMATH DE number 5791078
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Two new approaches to obtaining estimates in the Danzer-Grünbaum problem |
scientific article; zbMATH DE number 5791078 |
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Two new approaches to obtaining estimates in the Danzer-Grünbaum problem (English)
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24 September 2010
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This paper deals with estimation of \(a(n)=\max|S|\), where \(S\) is an arbitrary subset of \(\mathbb{R}^n\), such that any three points of \(S\) form acute angle. The author proves \[ a(n)\leq\frac23\left[\sqrt2\left(\frac2{\sqrt3}\right)^n\right] \] using probabilistic method.
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Danzer-Grünbaum problem
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sets forming only acute angles
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