After conferring with some fellow mathematicians, nobody had heard of the "tau movement", and nobody cares. Tau is for people who want to feel like they're taking stances on things that matter in math without actually putting in any of the work to do math.
I think tau is really just motivated by people who like things to be "clean". You see them in all walks, wishing programming language syntax, math notation, spelling, grammar, etc, had been chosen to be cleaner or make more sense from the beginning.
I don't have a strong opinion, but from what I've seen I think tau makes the most sense. These things are fun to think about, because it requires that you think about how pi is used in mathematics and contemplate how we organize and use the concepts related to pi. It's a good brain exercise.
But how much cleaner is using tau, beyond grade-school geometry? Euler's equation is arguably the most beautiful relationship in mathematics: e^(ipi)= -1. I'm afraid tau would dirty it up.
Not only that. If you think about multiplying any number z by e^(ia), where a is a real number, as rotating z by a radians in the complex plane, then i think the tau version of the Euler's equation conveys a more fundamental meaning: rotating any complex number by a whole turn yields that same number, it's the same as multiplying it by the multiplicative identity (i.e. doing nothing).
e^(iτ) = 1
And, as rotating something by one whole turn is the same as rotating it by any number of whole turns, you can get a nice intuitive series of equivalences that are not as pretty if you where to use pi:
Can people really not separate out a factor of 2? There's weirdness in every language. If I started SUDDENLY speaking English with a more uhh... orthogonal grammar, people would maybe get what I was thinking, but also deem me a self-righteous asshole. This is EXACTLY how mathematicians see tau. Math is no more flexible than any other widely spoken language.
Yes, once you have learnt the basics, factoring out a 2 is trivial. But that doesn't make it right to make children that still haven't learnt that wonder "what's the angle of 3/4 turns?". One and half pi? Why? It's 3/4 tau. It should be trivial. There shouldn't need to be any conversion by a factor of 2, especially for people that are starting with that stuff (angles and trigonometry is where lots of kids get lost at maths).
I think it's not too much about doing maths, but instead about teaching maths. It's much easier to explain to a kid that the angle of a slice of pizza is tau/8 (that is, if you cut your pizzas in 8 slices), and a quarter of a pizza has a tau/4 angle, and so on, instead of their pi equivalents. The idea that 1 tau = 1 turn is very powerful and simple.
anecdote, N=1: I was explaining some basic trig to a child and while I was at it also explained the concept of tau. The kid said he liked tau better :) (I was careful to also explain that his schoolteachers probably didn't know about tau so he needed to know 2pi as well)
I can see the utility in programming, since defining Tau to be 2 * pi potentially saves a lot of multiplication operations (although a good compiler would optimize these away anyway).
But I agree that it's a distraction, and I don't think the radial relationship is that important. I got over my annoyance of typing 2 * pi by thinking about it as the ratio of the diameter to the circumference.
I neither know nor care. It doesn't make geometry any more difficult to conceive of it that way, so I've been happy to do so. I do a lot of compass & straightedge type geometry for fun so it wasn't hard to adapt.
I disagree, but setting aside the radius/diameter debate, consider the simple equation: area=pir^2. How is it not more difficult to think of the constant in terms of diameter, when the rest of your equation is in terms of the radius. Unless you use area = 1/4pi*d^2, which I have never seen.
I'm not telling you what to do, I'm telling you what I like to do. Yes, I do sometimes use (pi * d^2)/4. It's not more efficient, and I didn't claim it was (though if I were concerned with efficiency I could argue that pi * d is a pleasingly simple way to calculate circumference).
I'm sorry that my personal idiosyncrasy bothers you so much.
I use tau every time I do something that would typically involve pi. It is simply cleaner. I view the tau movement more as a symbol of cleaning up math, and pi/tau is simply low hanging fruit.
