Spherical distribution of 5 points with maximal distance sum (Q542388)
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scientific article; zbMATH DE number 5906695
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Spherical distribution of 5 points with maximal distance sum |
scientific article; zbMATH DE number 5906695 |
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Spherical distribution of 5 points with maximal distance sum (English)
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10 June 2011
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The paper shows that on a sphere, the sum of distances among 5 points is (uniquely) maximized, if two points are placed at antipodal ``poles'' and the remaining three are placed equidistantly on the ``equator''. The proof is computer assisted and is based on interval analysis. It is worth noting that this configuration is also known as a spherical 1-design [\textit{R. H. Hardin} and \textit{N. J. A. Sloane}, Spherical designs, \url{http://www2.research.att.com/~njas/sphdesigns/}].
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spherical distribution
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interval analysis
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computer-assisted proof
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spherical 1-design
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0.8446202
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0.83197904
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0.83051187
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0.8262251
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