What your favorite variation of : Euler's Formula

[end3r7]

"What your favorite variation of" : Euler's Formula

I generally find that mathematicians always have a preferred way of writing an expression, whether be it because to them it's more aesthetic pleasing or easier to memorize. Few expressions, however, lend themselves to many forms as thus Euler's famous equation: e^{ix} = cos(x) + isin(x).

I've seen it written with pi, infinite series, limits, derivatives, etc.
Here is my personal favorite
\sqrt{e^{-\pi}} = i^i

You turn. =)

 

[Quantumduck]

I would have to stick with the classic:

e^(ipi) +1 = 0

It has multiplication, addition and exponents which are the three major operations, the multiplicative identity, the additive identity, equality, as well as two transcendental numbers and i, the imaginary unit.

I mean, after all, what more do you need that that? I think it is so beautiful I am going to have it tatooed on my ankle.

(yes, major geeky, but worth it.)

 

[Diffy]

how about:
e^{i\pi} = 1 + i\pi - \frac{\pi^2}{2!} - \frac{i\pi^3}{3!} + \frac{\pi^4}{4!} + \frac{i\pi^5}{5!}...