[Jach]

Yes, it's one of my favorite proofs. (I think I like it more than Euler's formula, especially since many calc teachers will look at e^{-x^2} and say it's un-indefinite-integrable without a second thought at what else it can do.)

But I'm not quite sure how you seeing it as \sqrt{\tau/2} helps you see the proof more easily. Because if you see \tau (ignoring the 1/2) you think "It has to do with circles or polar form." as per my rule of thumb?

[drbaskin]

I'm sorry I wasn't more clear, but your interpretation is what I meant. Per your rule of thumb, seeing \tau should suggest that it has to do with circles or polar coordinates, and the square root points to how to get the polar coordinates.