The Pigeonhole Principle - Disk Coverings

In 1834, Johann Dirichlet noted that if there are five objects in four drawers then there is a drawer with two or more objects. The Schubfachprinzip, or drawer principle, got renamed as the pigeonhole principle, and became a powerful tool in mathematical proofs.

In this Demonstration, pigeons land in a park. If unit disks completely cover the park, then there must be a disk with two or more pigeons. These two pigeons must be within 2 units of each other. Move the disks to complete the proof.