Favorite Equation: Quadratic Formula - Solving for X

[djosey]

e^{i\theta}=\cos\theta + i \sin\theta

This has already been mentioned but I thought it was the coolest thing ever when using series to show it.

For all of you talking about Euler's formula, i'd recommend looking at:
http://betterexplained.com/articles/intuitive-understanding-of-eulers-formula/

Which gives what to me is a very good explanation, kinda breaks the wonder in a way but deepens the understanding.

I don't have a favorite formula, though the one posted by yayness is very interesting!

 

[MorallyObtuse]

Polar Inertial Momentum Inequality

 

[Yayness]

I don't have a favorite formula, though the one posted by yayness is very interesting!

It is, but it's not recommended if you want to calculate really large amounts of decimals in π. Even though it goes quickly towards π, you need to calculate a lot more decimals in \sqrt 2 than what the number of correct decimals in π will be.
Let's say you calculate k decimals in \sqrt 2, then you'll have k/2 correct decimals in \sqrt{2+\sqrt 2} and k/4 correct decimals in \sqrt{2+\sqrt{2+\sqrt 2}}, and then k/8, k/16 and so on. I still like the formula though. It is simple and easy to remember.

 

[RichardParker]

n! \approx\sqrt{2 \pi n}(\frac{n}{e})^{n}

Stirling's Approximation. Haha.

 

[micromass]

My favorite equation is

e^\pi-\pi=20

It's a good way to check whether your computer is experiencing rounding errors

http://xkcd.com/217/

 

[eddybob123]

my favourite equation actually, is 1=1, cause it holds the fabric of math together

 

[Char. Limit]

my favourite equation actually, is 1=1, cause it holds the fabric of math together

But that's not true.

 

[eddybob123]

im not talking about beauty, I am talkingg about my favourite equation

 

[Char. Limit]

The equation 1=1, it's not true.

 

[TylerH]

Explain.

 

[Jabberwocky]

Euler's equation is beautiful, but I think my favorite is Stokes' Theorem:

Given a k-chain, M in \mathbb{R}^n and a k-1 form, \omega \in \Omega^{k-1}\mathbb{R}^n,
\int_{M}d\omega=\int_{\partial M}\omega.

All the classical theorems of div, grad, and curl, follow from this one elegant equation.