Should pi be replaced with tau in mathematics?

[Char. Limit]

And that for pi cannot derive that for pi/2 algebraically so there is not best equation whatsoever.

I don't think you get the meaning of the word "better". "Better" does not mean "best". "Less" does not mean "the least". I never said that e^(i pi) = -1 was the "best" equation. I said it was "better" and gave "more" information than e^(i tau) = 1, something that's undeniably true.

 

[dimension10]

I don't think you get the meaning of the word "better". "Better" does not mean "best". "Less" does not mean "the least". I never said that e^(i pi) = -1 was the "best" equation. I said it was "better" and gave "more" information than e^(i tau) = 1, something that's undeniably true.

Yup, but there are an infinite number of equations better than that.

\exp(i \frac{\pi}{2})=i

\exp(i \frac{\pi}{4})=\frac{i+1}{\sqrt{2}}

\exp(i \frac{\pi}{8})=\sqrt{\frac{i+1}{\sqrt{2}}}

 

[dimension10]

You can't derive Fermat's last theorem either, so what?

There does exist a proof for Fermat's last theorem. And here, I am saying that an infinite number of identities you cannot derive using {\exp}^{i}(\pi)=-1

 

[Char. Limit]

Yup, but there are an infinite number of equations better than that.

\exp(i \frac{\pi}{2})=i

\exp(i \frac{\pi}{4})=\frac{i+1}{\sqrt{2}}

\exp(i \frac{\pi}{8})=\sqrt{\frac{i+1}{\sqrt{2}}}

Okay, now I can see you're not even trying to dispute my argument. You're just making other arguments.

 

[dimension10]

There is also a suggestion for eta which is half pi.

http://www.youtube.com/watch?v=1qpVdwizdvI&feature=related

 

[FireStorm000]

I have to say I'm for using this; that said I wouldn't stop using pi, I'd use them together. In some cases it would be useful to define a constant that represents the ratio of radius to circumference, rather than diameter to circumference. In practice, it seem to me that radius is more fundamental than diameter: while we measure diameter, we use radius. I personally might start using that convention in my own work, as it keeps the constants from getting in the way. And it isn't like pi goes away, you just write that \tau = 2 \pi on your paper and everyone is on the same page as you. Also, I think 4\pi² occurs a lot in formulas I've seen, so that just becomes \tau². Also, if you integrated to get something squared, the constant should be 1/2. I'd rather use circumference = tau r and area = 1/2 tau r² because I can tie that into my knowledge of integration and remember it better. Also, the existence of tau would make using radians even easier than it is now, because you could convert from a fraction of a circle to radians very intuitively by simply memorizing a few places of tau; using 6.3 is fairly accurate, comparable to 3.14. Trigonometric functions are the same, as the input they take is in radians anyways. This would make trigonometry so radically simple.