A Spiky Ball

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.

7 pages, 1 figure

Cited by in corpus (2)

• Illumination of convex bodies with many symmetries
• On the illumination of centrally symmetric cap bodies in small dimensions