Israel Journal of Mathematics

, Volume 64, Issue 1, pp 25–31 | Cite as

Distribution of points on spheres and approximation by zonotopes

  • J. Bourgain
  • J. Lindenstrauss


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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Copyright information

© Hebrew University 1988

Authors and Affiliations

  • J. Bourgain
    • 1
  • J. Lindenstrauss
    • 2
  1. 1.IHESBures-sur-YvetteFrance
  2. 2.The Hebrew University of JerusalemJerusalemIsrael

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