So there's this big debate in math whether or not we should use tau or pi for all of our calculations. What do you think? What should we use?
Heh I meant whether or not we should use tau instead of pi :P. Sorry for any confusion caused xD
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Interesting question...
look at two of the basic formulas... circumference of a circle
C=2pi*r or pi*d
or
C=tau*r or (d/2)*tau
area of a circle
A=pi*r^2 or pi*(d/2)^2
A=tau*r^2/2 or tau*d^2/8
pi here still seems easier from a computational point of view.
but as soon as you witch to trig, tau is the clear winner since one full revolution is tau radians instead of 2*pi radians. It would make angles a little more instinctive and much easier to compare.
I don't think pi will go away any time soon (it's firmly entrenched throughout math and science) but incorporate tau in places where it can make things simpler.
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Abstractly, my money's on tau. It seems more natural in more situations, eg. Fourier transforms; radian measurement; normal distribution scale factor; values of the zeta function at even integers; Stirling's approximation; Cauchy's integral formula. Each of these is super important. Usually when I see a formula that seems nicer with pi, there's another more natural interpretation with tau. For instance, the integral of e^(-x^2) from -infty to infty is sqrt(pi). This might at first seem nicer than sqrt(tau/2), but I think I prefer the latter, since you're taking both the geometric and algebraic means--i.e. you're using 1/2 in both reasonable ways, as an exponent and as a multiplicative factor--which to me is somehow pleasingly symmetric.
Practically, I teach pi and nothing else since that's what the crushing majority of the world uses and has used throughout history, and almost all of my students are there to use math as a tool. Still, I should try out tau on a class and see what they think.
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Neither is right or wrong, they are only more convenient for a given purpose. Tau is frankly much easier to use and is more intutive; especially for radians. Pi has been used for a long time so it's not going anywhere, but tau greatly simplifies things without sacrificing accuracy -- since they are really the same thing. I would liken it to: Is it easier to use 4 or 2(2)? They're the same thing, one is just a more complicated expression of that thing.
James
I'm thinking the question is meant to suggest tau or phi, not pi.
I can't imagine any math organization suggesting using the letter pi to represent anything other than what it does today. Nonsense from people with too much time and too little understanding.
Rita the dog
Coxeter used tau for (1+sqrt(5)) / 2. What are you using tau for?