Covering a Ball by Smaller Balls

Covering a Ball by Smaller Balls

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.

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Veröffentlicht in:Discrete & computational geometry 2019-12, Vol.62 (4), p.781-787
1. Verfasser: Glazyrin, Alexey
Format: Artikel
Sprache:eng
Schlagworte:
Combinatorics
Computational Mathematics and Numerical Analysis
Euclidean geometry
Mathematics
Mathematics and Statistics
Upper bounds
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Beschreibung
Zusammenfassung: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.
ISSN:0179-5376
1432-0444
DOI:10.1007/s00454-018-0010-4