Rectangle with vertices of the same color in a two-colored plane

[DaveElliott]

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 haven't 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?