Lower Bounds for Pinning Lines by Balls

Details Lower Bounds for Pinning Lines by Balls Lower Bounds for Pinning Lines by Balls

2009-06-16

arxiv.org/abs/0906.2924v1

Computer Science

Computational Geometry

Scientific paper

A line L is a transversal to a family F of convex objects in R^d if it intersects every member of F. In this paper we show that for every integer d>2 there exists a family of 2d-1 pairwise disjoint unit balls in R^d with the property that every subfamily of size 2d-2 admits a transversal, yet any line misses at least one member of the family. This answers a question of Danzer from 1957.

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