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arXiv · 1510.00782

A Spiky Ball

Márton Naszódi
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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.

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Márton Naszódi. 2015-10-03. A Spiky Ball. https://doi.org/10.1112/s0025579315000406

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