Abstract
It is proved that if we approximate the Euclidean ballB n 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 ifB n is replaced by a general zonoid inR n.
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Bourgain, J., Lindenstrauss, J. Distribution of points on spheres and approximation by zonotopes. Israel J. Math. 64, 25–31 (1988). https://doi.org/10.1007/BF02767366
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DOI: https://doi.org/10.1007/BF02767366