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.

THINGS TO TRY

SNAPSHOTS

  • [Snapshot]
  • [Snapshot]
  • [Snapshot]

DETAILS

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

Embed Interactive Demonstration New!

Just copy and paste this snippet of JavaScript code into your website or blog to put the live Demonstration on your site. More details »

Files require Wolfram CDF Player or Mathematica.







Related Curriculum Standards

US Common Core State Standards, Mathematics