Covering a Ball by Smaller Balls
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We prove that, for any covering of a unit d-dimensional Euclidean ball by smaller balls, the sum of radii of the balls from the covering is greater than d. We also investigate the problem of finding lower and upper bounds for the sum of powers of radii of the balls covering a unit ball.
KeywordsEuclidean ball Sphere covering Covering by homothets
Mathematics Subject Classification05B40 52C17
The author would like to thank Arseniy Akopyan and Alexandr Polyanskii for bringing this problem to his attention and for invaluable discussions. The author was supported in part by NSF Grant DMS-1400876.
- 1.Böröczky Jr., K., Wintsche, G.: Covering the sphere by equal spherical balls. In: Aronov, B., et al. (eds.) Discrete and Computational Geometry. Algorithms and Combinatorics, vol. 25, pp. 235–251. Springer, Berlin (2003)Google Scholar