Your favorite equations.

(Yay! Nerdiest thread evar!)

My personal fav. is Minkowski's "c = i".  I.e. the speed of light is equal to \sqrt{1} as a dimensioned constant.

De Morgan's laws:

>>1
That's a rare/antiquated view of special relativity.  Nowadays, people prefer pseudoriemannian manifolds over complex riemannian manifolds.  ie instead of making time imaginary, one just has a metric that is not positive definite.  I can't think of any other reason why one would want c to equal i.

>>3
'Cuz it's fucking cool, that's why.

0.999... = 1

And that's all there is to it.

lets get some e^{\pi i} + 1 = up in this mofo....

>>6
You must mean
e^{\pi i}-1 = 0
I must say, it is one of the most elegant equations I know.

>>7
Best be trollin' nigger.

>>8
Please don't bring this /b/ crap in here.

>>9

>>7 is /b/ crap.

quadratic.  everyone has a special bond with the quadratic equation, just because it's probably the first one they've ever really had to wrap their minds around.

P = NP ?

>>7
yeah, stupid fucking 4chan fucked up my latex. stupid shit.

>>11
Seconding this. My true favorite, though, is the general solution to the quartic.

I thought about this a bit and figured e, i, pi, and all that would automatically be covered, so...

One of my very favorites is a simple result of calculus 1: the integral from zero to pi of the sine of x, is equal to two.  This blew my mind at the time; that a function, with a graph, having a relatively complex definition, resulting in a nice curved shape, should have a natural number's worth of area in each of its humps.  It was a thing that I earnestly worried over in high school before learning calculus, and I was deeply gratified to learn the answer.

>>15
PROTIP: If you graph abs(sin(x)), it looks like boobies! :D

(.)(.)

The generalized Stokes theorem is a beautiful, simple and powerful statement.

>>12
Can you prove this?

C^2 = A^2 + B^2
i proved it with LEGO when i was little, then discovered Pythagoras had done it a shitton years before ;_;