Advertisement

Discrete & Computational Geometry

, Volume 33, Issue 1, pp 143–155 | Cite as

Covering a Ball with Smaller Equal Balls in ℝn

  • Jean-Louis Verger-GaugryEmail author
Article

Abstract

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.

Keywords

Computational Mathematic Recent Result Asymptotic Estimate Equal Ball 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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