[scythe]

The Greek letter tau is already used to refer to the period of an oscillation, the time constant of a decay interval (these are intimately related), plus plenty of other stuff. There really aren't any Greek letters left that aren't used for a million things already. tau-as-time-constant is the standard use for the thing, and the confusion with torque and natural temperature is bad enough as it is.

Yes, pi shows up as the prime counting function, but there it's a function, which clears up the otherwise ambiguous notation. Furthermore these abuses of notation are generally considered a bad thing, something we try to avoid.

As for the intuitiveness of such deep results as Stirling's formula and the even values of the Riemann zeta: this is to concern oneself with the upholstery on the Space Shuttle.

If you want a new pi symbol, might I suggest the variant pi described here: http://en.wikipedia.org/wiki/Pi_%28letter%29 -- though I'm afraid this is all a waste of time and energy.

[ignifero]

Not to mention the tau neutrino. But the bigger question is why would one want to do that?

[scythe]

It is not an exercise worth ignoring: I had also once thought that pi should be replaced.

Slightly different motivation, though, as it seemed to me that pi/2 was really more interesting, and anyway it is really much easier to write multiplication than fractions when you run into a discrepancy. Here the roots of the sine are at even multiples and the roots of the cosine are at odd multiples, and e^(i pi/2) = i is more interesting than the previous incarnations of the Euler formula.

The thing is that the important parts of these formulae are the way they are derived and the structure they represent, not their appearance on a sheet of paper. If you can understand what relates the zeta function at even numbers to the ratio of a circle's radius and circumference, it really does not matter if you choose to represent this relation with a drawing of an elephant.

[ignifero]

You got a good case with pi/2, it's truly useful, as it represents the angle between 3d axes, the boundaries of the tangent and inverse trigonometric functions, the monotonic regions of cosine and sine etc. It will even make spherical coordinates easier to visualize mentally. (It will also make a two-digit number, 16, a common resident in lots of formulas). I vouch for it, and i call for a move to name it, confusingly, pi-bar

[Jach]

pi-bar? Nooooo, you'll make the Statistics community members' heads explode!

[ignifero]

not a big loss [smirk]

[bhousel]

All numbers are divisible by 2, in that sense..

[ignifero]

it was so embarrassing i had to remove it. what was i thinking