Abstract
It is proved that forn ≥ 2 the Euclidean ballB n can be approximated up toɛ (in the Hausdorff distance) by a zonotope havingN summands of equal length withN ≤c(n)(ɛ −2|logɛ|)(n−1)/(n+2).
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Research supported in part by the U.S.-Israeli Binational Science Foundation. [Please see the Editors' note on the first page of the preceding paper.]
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Bourgain, J., Lindenstrauss, J. Approximating the ball by a minkowski sum of segments with equal length. Discrete Comput Geom 9, 131–144 (1993). https://doi.org/10.1007/BF02189313
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DOI: https://doi.org/10.1007/BF02189313