2.1.2013 13:04, firstname.lastname@example.org wrote: > The reason why Tau is a fundamental number is because it is the Identity Operator for Rotation. Pi is lacking in such fundamental utility. > > Tau is as fundamental to Rotation as Zero is to Addition and One is to Multiplication.Tonight I watched several YouTube videos about Tau and I didn't see anyone make mention of this fact. Bob Palais wrote an excellent article back in 2001. But the arguments that I've seen favoring Tau over Pi were basically a matter of style and taste. > > The reason why Tau is worthy of primacy over Pi is not because of any such artistic reasons, but because of this fundamental mathematical reason.
I agree that ideally tau should be used. Such things are important to cut away the complexity from formulas, and to bring out uniformity, something which in my experience always pays off, revealing structure and diminishing the amount of errors. Actually, I'd imagine, although I do not know, that the use of the tau has the symphathy of many mathematicians.
But there's also some conflict in that if I change to use tau in my papers, then the formulae will look odd to other readers, simply because they have been reading pi for all their life. I know that if I saw tau used in a Fourier transform, I would start looking for the meaning of tau as a variable. And perhaps a bit sadly, this need to be understood as well as possible may override ideality.
But I also think that this is one of those things which just need an initial push. After a critical mass of mathematicians/scientists adopt tau instead of pi, then the change happens naturally.