2 Pi or Not 2 Pi?

To my eye as a mathematician, the tau version I provided looks better.

e^i * tau = 1, has a much nicer geometric interperatation, of e^i * tau representing a full rotation (which is just the identity), whereas e^i * pi = -1 represents half a rotation, and it is not quite as immediately obvious that -1 is a 1/2 rotation (although this is not particularly opaque).

While I am on the subject, surely the equation you want to discuss is e^i * pi * x, = cos(pi * x)+isin(pi * x), which clearly represents a rotation of x/2 of a complete circle. Of course, viewing it this way, it seems even clearer why one would want to use tau.