I like the compromise of using Tau and its fractions when it makes sense and using a single Pi when it's not so intuitively-connected with a circle. e.g. \int_{-\infty}^{\infty} e^{−x^2} dx = \sqrt{\pi}.
Plus Tau Day's a fun excuse to eat two pies.
Plus Tau Day's a fun excuse to eat two pies.
How to derive the value of the integral: Square the integral to make it an integral in two variables, introduce polar coordinates, then change variables.
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?
One could always celebrate 2\pi day. ;)