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Plane Proof

  1. Feb 11, 2007 #1
    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.
     
  2. jcsd
  3. Feb 12, 2007 #2

    benorin

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    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?
     
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