A Note on the Size of the Largest Ball Inside a Convex Polytope
Period. Math. Hungar. Vol. 51, No. 2 (2005), pp. 15-18 Let $m>1$ be an integer, $B_m$ the set of all unit vectors of $\Bbb R^m$ pointing in the direction of a nonzero integer vector of the cube $[-1, 1]^m$. Denote by $s_m$ the radius of the largest ball contained in the convex hull of $B_m$. We d...
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| Zusammenfassung: | Period. Math. Hungar. Vol. 51, No. 2 (2005), pp. 15-18 Let $m>1$ be an integer, $B_m$ the set of all unit vectors of $\Bbb R^m$
pointing in the direction of a nonzero integer vector of the cube $[-1, 1]^m$.
Denote by $s_m$ the radius of the largest ball contained in the convex hull of
$B_m$. We determine the exact value of $s_m$ and obtain the asymptotic equality
$s_m\sim\frac{2}{\sqrt{\log m}}$. |
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| DOI: | 10.48550/arxiv.math/0505301 |