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The Pigeonhole Principle - Disk Coverings

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number of pigeons
4
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,
n
pigeons land in a park. If
n-1
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.
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