# The Most Beautiful Equation?

1. Nov 19, 2008

### Or Entity?

Lets elect World's most beautiful equation!

Two categories:

1.Mathematics
2.Physics

My personal favourites would be:

1. e$$^{i\pi}$$+1=0 (Do i need to give an argument?)

2. E=mc$$^{2}$$ (I know its mainstream.. but i doesent get much more simple and general than this!)

Last edited: Nov 19, 2008
2. Nov 19, 2008

### Ed Aboud

$$i\hbar\frac{\partial\Psi}{\partial t} = \frac{\hbar^2}{2m}\frac{\partial^2\Psi}{\partial x^2} + V\Psi$$

3. Nov 20, 2008

### vanesch

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

4. Nov 20, 2008

### saman

Maxwell's equations of EM?

$$\nabla \cdot D= \rho$$
$$\nabla \cdot B=0$$
$$\nabla \times E=- \partial B/ \partial t$$
$$\nabla \times H=J+ \partial D/ \partial t$$

5. Nov 20, 2008

### andrewm

$$p = \frac{h}{\lambda}$$

6. Nov 21, 2008

### robphy

I think you are missing a minus sign.

7. Nov 21, 2008

### joeyar

1/. cos²(x) + sin²(x) = 1
2/. ω² = k/m

8. Nov 21, 2008

### Staff: Mentor

Isn't it only an approximation?

9. Nov 21, 2008

### redargon

FD=½ρv2ACD

Some engineering fudgeamatics

Last edited: Nov 21, 2008
10. Nov 21, 2008

### Binhjuventus™

For me, it's:
i2=-1

11. Nov 21, 2008

### joeyar

12. Nov 21, 2008

### Staff: Mentor

As far as I remember mc2 is only a first term of the power series. Next terms are smaller by at least c2 factor (or even c4, my memory fails me here), so they can be safely ignored, but E=mc2 is still only an approximation.

13. Nov 21, 2008

### carapauzinho

I think you refer this equation:

E2=m2c4+p2c2

14. Nov 21, 2008

### Staff: Mentor

15. Nov 21, 2008

### robphy

You may referring to the Taylor expansion (with respect to the velocity) for the relativistic energy:
http://en.wikipedia.org/wiki/Kinetic_energy
expressed as
$$E_{rel}=m_{rel}c^2=m_0c^2 \frac{1}{\sqrt{1-(v/c)^2}}=m_0c^2\bigg(1+\frac{1}{2}(v/c)^2+\frac{3}{8}(v/c)^4+\ldots\bigg) \approx m_0c^2 \bigg( 1+\frac{1}{2}(v/c)^2 \bigg)\mbox{[for small (v/c)]}$$

The rest energy $$E_0=m_0c^2$$ is a Lorentz invariant, and $$E_{rel}$$ and $$m_{rel}$$ are observer-dependent quantities.

From a special-relativistic viewpoint, these are exact relations.

From a Newtonian-physics viewpoint, one often refers to some of these terms as "relativistic corrections".

16. Nov 21, 2008

### Naty1

E= ir !

17. Nov 22, 2008

### Ed Aboud

$$i\hbar\frac{\partial\Psi}{\partial t} = - \frac{\hbar^2}{2m}\frac{\partial^2\Psi}{\partial x^2} + V\Psi$$

18. Nov 22, 2008

### Friesiangirl

Well, it may be hard to say. I am a junior in high school, so my physics knowledge is limited, however, I am fond of

i^2 = -1

Imaginary x Imaginary = Real. Seems silly but awesome.

Hayley

19. Nov 22, 2008

### M Grandin

Maxwell`s velocity distribution formula

f(v) = 4 $$\pi$$ [ m / 2 $$\pi$$ k T ]^(3/2) v^2 e^(-m v^2 / 2 k T )

The elegance because he derived this formula just by logical reasoning
almost without calculus or any kind of information. Intellectual wizardy.

Last edited: Nov 22, 2008
20. Nov 22, 2008

### Loren Booda

zeta(s)=1+(2^-s)+(3^-s)+(4^-s)+...

- the zeta function from which the Riemann hypothesis derives.