The pyjama problem

2 December 2013
Freddie Manners
The 'pyjama stripe' is the subset of the plane consisting of a vertical strip of width epsilon about every integer x-coordinate. The 'pyjama problem' asks whether finitely many rotations of the pyjama stripe about the origin can cover the plane. I'll attempt to outline a solution to this problem. Although not a lot of this is particularly representative of techniques frequently used in additive combinatorics, I'll try to flag up whenever this happens -- in particular ideas about 'limit objects'.
  • Junior Number Theory Seminar