In which domains is pi better? And was there a discussion 2000 years ago that led to pi "winning"? (If so, it'd be really fun to read its reasoning.) [Both of these are honest questions; I'm not a mathematician.]
The Pi Manifesto has a few examples of pi beating tau (statistics, polygons, and complex numbers mainly), while also pointing out how silly and biased some of the tau examples are. However, the argument isn't very convincing from either side.
And as to your second question, I have no idea. I just know the idea has been settled for a long time now and I think this whole debate is needlessly distracting. Not that it isn't fun to watch or think about, but it confuses people who are just trying to learn and use math.
Their argument about the normal distribution is completely off though. There is completely no reason to group the two with the standard deviation.
Their biggest argument seems to be that the area of unit circle is exactly pi. Sadly, there is absolutely no need to work with fractions of areas of the unit circle, while if you're working with angles the unit circle is a most natural standardisation. The normal distribution has been a lot clearer to me since I've understood the two should be grouped with the pi.
Their argument about trigonometric functions is completely wrong and obviously so. Trigonometric functions work with angles and it's already shown (and pimanifesto readily admits) that tau shines there.
Their argument about Euler's identity is as inane as the tauists' is.
We can start with any domain where torque is a thing. Torque is a particularly bad thing to conflict with.
I've also seen arguments that it's better when dealing with triangles (all angles in a triangle add up to pi radians). I don't think I buy that one, since everyone uses degrees for that anyway.
