Which Equation Deserves the Title of the World's Most Beautiful?

[lisab]

pi=3.0

 

[Pinčiukas]

1782¹²+1841¹²=1922¹²

 

[Dembadon]

pi=3.0

Upisoft hits R for 9000 damage (.14159 Overkill)
R dies

 

[G037H3]

Upisoft hits R for 9000 damage (.14159 Overkill)
R dies

not over 9K, notice

 

[Upisoft]

Upisoft hits R for 9000 damage (.14159 Overkill)
R dies

They will fix it in the next version...

 

[xeniosm]

the very simple (and suppressed!) standard model lagrangian

 

[chaoseverlasting]

$$f(x)=\frac{a_0}{2} + \sum_{n=1}^\infty \, [a_n \cos(nx) + b_n \sin(nx)]$$

I'm surprised no one has put this one up yet!

 

[elfboy]

my identity

a single equation? i don't know too many to think of

 

[micromass]

The most beautiful "equation" is

$$\langle a,b~\vert~o(a)=2, o(b)=3, o(ab)=29, o((ab)^4(abb)^2)=50, o(a((ab)^4(abb)^2)^{25})=5, o(ab^{abababababb})=34\rangle$$

Extra points for anybody who says what I've written down here

 

[Containment]

Ohm's law gets my vote.

 

[Pengwuino]

$$G_{\mu \nu} = 8T_{\mu \nu}$$

Where I have set $$c = G = \pi = 1$$

 

[FtlIsAwesome]

I'd say: 1 = 0. From this one, you can derive everything

What about i>u ?

 

[Pattonias]

I find derivatives beautiful even though I also hate them.

 

[Pythagorean]

Math:

Euler's Equation
$$e^{\pm i \theta} = \cos(\theta) + i \sin(\theta)$$

because it demonstrates the meaning of i as a transform/operator, rather than sqrt(-1)

Physics:

Continuity Equation (for conserved $$\phi$$):
$$\frac{\delta \phi}{\delta t} + \nabla \cdot f = 0$$

because it relates the physical meaning of the partial derivative to that of the total derivative.

Biology:

$$\Delta G = -n F \Delta E$$

Energy for work is the number of moles of stored energy from electric charge.