On the Delone triangulation numbers (Q5944138)
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scientific article; zbMATH DE number 1652664
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the Delone triangulation numbers |
scientific article; zbMATH DE number 1652664 |
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On the Delone triangulation numbers (English)
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17 July 2003
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Delone triangulation number
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asymptotic formula
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symmetric difference metric
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convex bodies
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0.92488986
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0.92488986
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0.9095811
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0.89041305
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0.8869833
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The Delone triangulation number \(\text{del}_{n-1}\) is a constant appearing in an asymptotic formula for the approximation (with respect to the symmetric difference metric) of smooth convex bodies in \(\mathbb{R}^n\) by polytopes with prescribed number of vertices. Here, the authors improve a previous estimate on \(\text{del}_{n-1}\) [J. Approximation Theory 107, No. 2, 268-280 (2000; Zbl 0974.52007)] and use this to show that NEWLINE\[NEWLINE\lim_{n \to \infty}{\text{del}_{n-1} \over n}={1\over 2\pi e}.NEWLINE\]
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