electric circuits - On this infinite grid of resistors, what's the equivalent resistance?

I searched and couldn't find it on the site, so here it is (quoted to the letter):

On this infinite grid of ideal one-ohm resistors, what's the equivalent resistance between the two marked nodes?

With a link to the source.

I'm not really sure if there is an answer for this question. However, given my lack of expertise with basic electronics, it could even be an easy one.

Answer

Nerd Sniping!

The answer is $\frac{4}{\pi} - \frac{1}{2}$.

Simple explanation:

Successive Approximation! I'll start with the simplest case (see image below) and add more and more resistors to try and approximate an infinite grid of resistors.

Mathematical derivation:

$$R_{m,m}=\frac 2\pi \left( 1 + \frac 13 + \frac 15 + \frac 17 + \dots + \frac 1 {2m-1} \right)$$