Discrete & Computational Geometry

, Volume 33, Issue 1, pp 143–155

Covering a Ball with Smaller Equal Balls in ℝn


DOI: 10.1007/s00454-004-2916-2

Cite this article as:
Verger-Gaugry, JL. Discrete Comput Geom (2005) 33: 143. doi:10.1007/s00454-004-2916-2


We give an explicit upper bound of the minimal number νT,n of balls of radius 1/2 which form a covering of a ball of radius T > 1/2 in ℝn, n \geq 2. The asymptotic estimates of νT,n we deduce when n is large are improved further by recent results of Böröczky, Jr. and Wintsche on the asymptotic estimates of the minimal numberof equal balls of ℝn covering the sphere Sn-1. The optimality of the asymptotic estimates is discussed.

Copyright information

© Springer-Verlag 2004

Authors and Affiliations

  1. 1.Institut Fourier, University of Grenoble I, UMR5582 (UJF-CNRS), BP 74, 38402 St. Martin d’Hères CedexFrance

Personalised recommendations