summation - Proof without words for $sum_{i=0}^infty(-1)^ifrac{1}{2i+1}$

$$\sum_{i=0}^\infty(-1)^i\frac{1}{2i+1}$$

$$1-\frac13+\frac15-\frac17+\frac19-\cdots=\frac\pi4$$

Does anyone know of a proof without words for this? I am not looking a for a just any proof, since I can prove it myself. What I am looking for is a elegant physical interpretation, or anything else that matches that kind of beauty.

Just to clear up, the proof I already know is

$$\int_0^1\left(1-x^2+x^4-x^6+x^8-\cdots\right)\,\mathrm{d}x = \int_0^1\frac{\mathrm{d}x}{1+x^2}$$

So I am intersted in anything that is not obviously related to this.