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WetWired · 11:03 AM

WetWired said: [Goto]

Interesting. I don't think that was covered in any math class I've taken.

I do think it is the most beautiful equation I've ever seen. To me, if there is any evidence for a God in this universe, that is it.

It stems from

$\reverse e^{ix}=Cos(x)+iSin(x)$ .

This can be seen from a Taylor expansion about 0 of e^x, Cos(x) and Sin(x). It is very useful in complex variable theory, as one can now say

$\reverse A+Bi = \sqrt{ \|A^2\| + \|B^2\|}e^{i \theta}$

where theta is the angle a line from the origin to A+Bi makes with the positive real axis on the complex plane. Furthermore, if theta is made a variable that varies from 0 to 2*pi then

$\reverse e^{i \theta}$

is the unit circle.

I only created this thread with the intention of checking the functionality of LaTeX. But perhaps it is a subject that merits some discussion. Could someone move it to a more appropriate section, and title it "Most Beautiful Equation."