Tau is clearer in some domains and pi is better in others. The mental overhead from switching between the two is too much, so just pick one already. And let the rest of us know, so we can go back to having a clear standard and not requiring the mental overhead of switching while studying different authors.
Oh yeah, we went through that 2000 years ago and the winner was pi. I haven't seen any compelling reason to switch yet. (Says the guy who uses "j" for the imaginary constant. :P)
In which domains is pi better? And was there a discussion 2000 years ago that led to pi "winning"? (If so, it'd be really fun to read its reasoning.) [Both of these are honest questions; I'm not a mathematician.]
The Pi Manifesto has a few examples of pi beating tau (statistics, polygons, and complex numbers mainly), while also pointing out how silly and biased some of the tau examples are. However, the argument isn't very convincing from either side.
And as to your second question, I have no idea. I just know the idea has been settled for a long time now and I think this whole debate is needlessly distracting. Not that it isn't fun to watch or think about, but it confuses people who are just trying to learn and use math.
Their argument about the normal distribution is completely off though. There is completely no reason to group the two with the standard deviation.
Their biggest argument seems to be that the area of unit circle is exactly pi. Sadly, there is absolutely no need to work with fractions of areas of the unit circle, while if you're working with angles the unit circle is a most natural standardisation. The normal distribution has been a lot clearer to me since I've understood the two should be grouped with the pi.
Their argument about trigonometric functions is completely wrong and obviously so. Trigonometric functions work with angles and it's already shown (and pimanifesto readily admits) that tau shines there.
Their argument about Euler's identity is as inane as the tauists' is.
We can start with any domain where torque is a thing. Torque is a particularly bad thing to conflict with.
I've also seen arguments that it's better when dealing with triangles (all angles in a triangle add up to pi radians). I don't think I buy that one, since everyone uses degrees for that anyway.
After reading both the tau and pi manifestos I get the impression that it's quite an arbitrary choice: either the circumference is fundamental and angles are natural (tau), or the radius is fundamental and areas are natural (pi). It boils down to a trade-off and you can cherry-pick examples where either is "more natural", but in a mathematical sense it doesn't matter a single bit and that's why we should not waste time on this, it doesn't bring anything new to the table.
At uni, decades ago, I was told that whenever a "mathematician" appeared up on the telly, it was to present their new idea of definining a new constant equal to 2pi...
Not the same now, of course, with shows like Numb3rs and Big Bang Theory, and a greater public awareness of the importance of numeracy.
#define ONE 1
#define TWO 2
#define THREE 3
...
etc.
Then use the words in place of integers wherever you need them. Hell, mix and match. And tell me if you are just as productive as you would be sticking with the regular integers you know and love.
Sure. And in return, you can't use constants, but must instead type out 3.141592653... to whatever decimal place you deem important. Nor typedefs. Nor named flags (`FileRead | FileWrite` is just long-hand for `3`). At the end of the day we'll see who's pulling their hair more.
Then we'll go back in a couple weeks, and look at the same code again. Mine's wordy. Yours is cryptic, and requires looking up the use of everything.
Oh yeah, we went through that 2000 years ago and the winner was pi. I haven't seen any compelling reason to switch yet. (Says the guy who uses "j" for the imaginary constant. :P)