The Pigeonhole Principle - Disk Coverings

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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.

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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.

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Contributed by: Ed Pegg Jr (March 2011)
Open content licensed under CC BY-NC-SA


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Based in part on Erich's Packing Center: Covering http://www.stetson.edu/~efriedma/packing.html.



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