So to save confusion over a mere factor of two, you're proposing devoting an entire new Greek letter to just double a constant, and requiring students to understand pi anyway to make sense of hundreds of years of mathematical and scientific corpus?
It's just like that xkcd comic about introducing a new standard and now having N+1 standards. Except in this case the new standard offers only a factor of two.
Look, it's more about saying that the area of a right triangle is naturally represented (and explained) as half that of a rectangle sharing the height and width - but being divided in two equal halves by the hypotenuse.
You can argue that you're so used to right triangles that it's the square and the rectangle that should be considered special, and "twice the area" - but I don't think that makes much sense.
Pi is a useful constant, but it's chief role is in cycles/frequencies and circles. Not half-circles. It is perfectly ok to disagree - but I'm one of those people to find the concepts behind pi start making much more sense when thinking of tau as the constant, and half-tau (pi) as the special case.
Maybe it's because I always hate having logic and math concepts waved away as "that's the way it is" when there obviously is some pattern or explanation that's being hidden or lost. I'm no good at rote calculation, and with tau a lot of things that just look odd and "special" unify quite nicely.
It may very well be that for higher dimensions than two (or three) tau doesn't make much more sense than pi - but I found the "tau manifesto" examples plenty convincing.
It was easier for me to grasp, and I believe it would be a lot easier to teach.
Ha, yeah I know. On rereading my comment, it does come across as somewhat defensive but I definitely wasn't meaning it to be that way. Actually I was smiling as I wrote it.
See my other comments on this thread about sigma, for instance.
It's just like that xkcd comic about introducing a new standard and now having N+1 standards. Except in this case the new standard offers only a factor of two.