Israel Journal of Mathematics

, Volume 64, Issue 1, pp 25–31

Distribution of points on spheres and approximation by zonotopes

  • J. Bourgain
  • J. Lindenstrauss

DOI: 10.1007/BF02767366

Cite this article as:
Bourgain, J. & Lindenstrauss, J. Israel J. Math. (1988) 64: 25. doi:10.1007/BF02767366


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.

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