Abstract

Dark Directions of Circle Packings

Joszef Beck
Wed Sep. 29 at 11:30am in the Graduate Student Lounge

I discuss a plane geometry problem that is very easy to understand, but not so easy to solve. Consider a Circle Packing (pairwise disjoint congruent circles) with positive upper density. Is it true that there is always a Dark Direction (i.e., a direction such that every parallel line hits a circle)? How large is the set of Dark Directions?
How about those Circle Packings for which every direction is dark? Is it possible that all directions are `equally dark" ?