Distribution of points on spheres and approximation by zonotopes
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It is proved that if we approximate the Euclidean ballBn in the Hausdorff distance up toɛ by a Minkowski sum ofN segments, then the smallest possibleN is equal (up to a possible logarithmic factor) toc(n)ε−2(n−1)/(n+2). A similar result is proved ifBn is replaced by a general zonoid inRn.
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