Discrete & Computational Geometry

, Volume 62, Issue 4, pp 781–787 | Cite as

Covering a Ball by Smaller Balls

  • Alexey GlazyrinEmail author


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.


Euclidean ball Sphere covering Covering by homothets 

Mathematics Subject Classification

05B40 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.


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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.School of Mathematical & Statistical SciencesThe University of Texas Rio Grande ValleyBrownsvilleUSA

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