The view-obstruction problem for spheres in \(\mathbb{R}^ 5\) (Q1921388)
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scientific article; zbMATH DE number 920728
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | The view-obstruction problem for spheres in \(\mathbb{R}^ 5\) |
scientific article; zbMATH DE number 920728 |
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The view-obstruction problem for spheres in \(\mathbb{R}^ 5\) (English)
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28 October 1996
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In the view-obstruction problem, congruent convex bodies centered at the points \(({1\over2},\dots, {1\over2})+\mathbb{Z}^n\) are expanded until they block all rays from the origin to the open positive cone. The first problem of this type for the cube were posed and partially solved in 1967 [the reviewer, Monatsh. Math. 71, 263-269 (1967; Zbl 0148.27505)]. These problems are closely related to Kronecker's approximation theorem. Later Cusick generalized the problem to other convex bodies and baptized these problems `view-obstruction problems'. The authors solve the difficult case of 5-spheres.
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view-obstruction problem for spheres
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diophantine approximation
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sphere packings
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convex bodies
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Kronecker's approximation theorem
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0.8504989147186279
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0.8489143252372742
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