I read that a while ago and I thought i made a lot of sense. And the really good part is: It's backwards compatible. just write, at the top of each calculation def: tau = 2*pi
So of course I then started doing my math with tau instead of pi. Turns out we actually tend to have pi without a factor of two quite a lot. In my case it was the fact that -1 = e^(i*pi) that made everything messy.
Suddenly I got a lot of fractions where I beforehand had none. And really, fractions are way more messy than multiplications. I prefer having a lot of 2*pi than even a few extra tau/2.
If anything, it might be a good idea to have the constant be for a quarter of a circle rather than a half. That would probably simplify complex calculations a lot. Since 1, i, -1, -i could all be described in polar notation without any fractions.
TL;DR: Tau is better in theory. Pi is simpler in practice. A constant for Pi/2 might be a good idea.
Do you suffer painful illumination? -- Isaac Newton, "Optics"