Lemme restate my solution:
Use them when they are more useful.
You (JWinslow) described numerous formulae with 2π and, yes, you admitted that although not all formulae use it, most do.
I think tau should be taught/used where it is more efficient/makes more sense logically, and pi used where is would be more efficient/makes more sense.
There are 2 ways such a solution could go
A) Students learn about how the circle constants relate to their maths more clearly, and are able to see why sometimes one is preferred over the other.
B) Students try to memorize which one to use in which scenario rather than thinking of what it means, and end up getting them mixed up and being thoroughly confused.
Well, I kinda disagree with the "simple conversion" thing. Sure, at first, the fact that there needs to be a conversion, however simple, from pi to tau is unavoidable. However, my own goal with this is for the correct convention (which I believe is tau) to be collectively set in the minds of students, teachers, mathematicians, and the like. This is only possible if there are people that are willing to go the extra mile with this idea, e.g. using it in a high-profile mathematical paper, or teaching a class with it. Tau isn't only reserved to a passing mention in any class.
It took quite a long time even for the convention of pi to be used and accepted by many. Some people used pi, but some people used pi/delta, some used p, some used c, and some even used a weird curly symbol to express the same quantity, C/D. And even after pi became standard, people still used 2pi as a separate symbol (i.e. always writing 2pi/4 instead of pi/2). Pi has been around for about 300 years, and only now is it as famous and popular as it is today, so I wouldn't hold my breath that we'd change immediately, of course. But the great thing is, it doesn't need to happen all at once.
My algebra teacher introduced it as an alternative.
(And I showed him it
Also, weren't there several petitions to make pi equal to exactly 3 in some areas
"And he [Hiram] made a molten sea, ten cubits from the one rim to the other it was round all about, and...a line of thirty cubits did compass it round about....And it was an hand breadth thick...." — First Kings, chapter 7, verses 23 and 26
One of my all time favorite passage from teh bibble
Happy Tau Day, everyone! I hope you all take the time to read The Tau Manifesto
today! It might convince some of the unconvinced here
Apparently there are other examples of pi being equal to three to the ancients.