Plane Proof

  • #1

Homework Statement


A plane is colored blue and red in any way . Prove that there exists a rectangle with vertices of the same color


Homework Equations



Its obviously true.

The Attempt at a Solution



I was thinking proofy by pig hole, but havent quite figured it out.
 

Answers and Replies

  • #2
benorin
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It is called the pigeon hole principle: if there are more pigeons than pigeon holes, then there is at least one pigeon hole containing more than one pigeon.

In the infinite sense (useful for this problem): if there are infinitely many pigeons and finitely many pigeon holes, then there is at least one pigeon hole containing infinitely many pigeons.

In this problem, what are the pigeon holes?
 

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