Can somebody explain this to me?

Question

anonymous · Answer

I'm currently in Calculus 2, and I'm assuming I shouldn't know this yet, but I've seen it over the interwebz and it sounds interesting.

$$e^{i \Pi} + 1 = 0$$

parthkohli · Answer

Yeah, this is Euler's Identity.

parthkohli · Answer

In general, Euler says that,$$e^{i\pi} =-1$$Why is this beautiful? It is because we are operating on two transcendental and an imaginary number, where the result yields a simple and cute integer.

parthkohli · Answer

Arguably, this is the most beautiful equation, apart from the Batman Equation which was discovered recently.

parthkohli · Answer

I assume that you already know the following:$$i = \sqrt{-1}$$$$\pi = {C \over d}$$$$e = \lim_{x \to \infty } {\left( 1 + {1 \over n}\right)^n}$$

anonymous · Answer

Yes I understand those three ideas.

parthkohli · Answer

Very well, so did you understand Euler's Identity?

parthkohli · Answer

It takes a lifetime, literally, to derive it.

anonymous · Answer

I don't understand how this all comes together though...it sounds extremely interesting.

anonymous · Answer

What level of mathematics is this necessarily under where I would learn it in a college setting?

anonymous · Answer

do u know about$$e^{i\theta}=\cos \theta+i \sin \theta$$???

anonymous · Answer

No, I have no prior knowledge of these ideas.

anonymous · Answer

ok :)