Plane Proof

[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.

[benorin]

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?