Tau-ists aren't saying formulas using 2pi should continue using 2pi. 2pi should always be replaced with tau. However, some formulas may look nicer when you replace 1/2tau with pi, so you could do that if you'd wish. You know how on some calculators you've got a [SHIFT] key? I think Pi should be [SHIFT] [Tau]. However, tau is the more fundamental thing. It isn't all about whether tau or pi is more useful or makes formulas look nicer. Math should be as simple, fundamental and elegant as possible. In that aspect, to me, tau takes the cake.

Honestly, pi and tau would both work. But it isn't about which one works. That's where math and physics differ. In physics, using 9.81 as g in the formula y=gt would work, as the time isn't defined exactly. However, in Maths you often give exact answers:

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x^2 = 2

x = sqrt(2)

Sure, in a practical sense, using 1.414 for sqrt(2) would work just fine. But that wouldn't be mathematics, now, would it?

Pro-Pi people often use practical examples to support pi, e.g.

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A=pi*r^2 looks nicer and is easier than A=1/2*tau*r^2

However, as I just explained, that's not the point.

You said you're trying to picture tau as the solution to a problem. The thing is: there is no real

*problem*. Tau and pi both work. It's about which one is more fundamental, beautiful and elegant.

Quote from: Blizzard on November 14, 2012, 04:03:20 pm

Pi is fundamental in many formulas while in some formulas 2 Pi is used because of its connection.

Pi is fundamental in some formulas? Pi is either fundamental or not fundamental. It's like saying: "In some formulas, the kinetic energy is fundamental." The kinetic energy can, however, be more fundamental than a function using the kinetic energy in a more complicated manner. Maybe it's not the best analogy, as I just explained physics is not like mathematics, but you get the point.