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A SPIKY BALL

Part of: Discrete geometry General convexity

Published online by Cambridge University Press:  17 February 2016

Márton Naszódi
Márton Naszódi*
Affiliation:
ELTE, Department of Geometry, Lorand Eötvös University, Pázmány Péter Sétány 1/C, Budapest 1117, Hungary email marton.naszodi@math.elte.hu
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Abstract

The illumination problem may be phrased as the problem of covering a convex body in Euclidean $n$-space by a minimum number of translates of its interior. By a probabilistic argument, we show that, arbitrarily close to the Euclidean ball, there is a centrally symmetric convex body of illumination number exponentially large in the dimension.

MSC classification

Primary: 52A22: Random convex sets and integral geometry 52C17: Packing and covering in $n$ dimensions
Type
Research Article
Information
Mathematika , Volume 62 , Issue 2 , 2016 , pp. 630 - 636
Copyright
Copyright © University College London 2016 

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