1. Feb 11, 2007 #1

   DaveElliott

   

   1. The problem statement, all variables and given/known data
   A plane is colored blue and red in any way . Prove that there exists a rectangle with vertices of the same color
   
   
   2. Relevant equations
   
   Its obviously true.
   
   3. The attempt at a solution
   
   I was thinking proofy by pig hole, but havent quite figured it out.

    

   DaveElliott, Feb 11, 2007
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3. Feb 12, 2007 #2

   benorin

   

   Homework Helper

   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?

    

   benorin, Feb 12, 2007

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