# The most beautiful formulae in maths & science

1. Mar 5, 2008

### rohanprabhu

I just though i'd make up a list of a few of the really beautiful formulas in mathematics.

One in my list is:

$$e^{i\pi} + 1 = 0$$

and definately, the Pythagoras theorem... as for physics.. the energy-mass equivalence is another beautiful formula:

$$E = mc^{2}$$

and.. the Bohr's formula for quantized angular momentum:

$$L = \frac{nh}{2\pi}$$

I also think that the Dirac equation is a beautiful result as it predicted the existence of a positron before it's actual discovery..

any others u can think of??

2. Mar 5, 2008

3. Mar 5, 2008

### lisab

Staff Emeritus
You already have my favorite- Euler's.

There's a lot of ugly ones, too .

4. Mar 5, 2008

### Jimmy Snyder

No object is so beautiful that, under certain conditions, it will not look ugly. - Oscar Wilde.

5. Mar 5, 2008

### lisab

Staff Emeritus
:rofl:

6. Mar 5, 2008

### George Jones

Staff Emeritus
There's a sign mistake for the term a third of the way through the line that's a quarter of the way down.

Dark matter found!

7. Mar 5, 2008

### lisab

Staff Emeritus
"...sans gravity..."!

Well duh...wouldn't want to complicate it! :rofl:

8. Mar 5, 2008

### Werg22

A formula doesn't strike beautiful, an idea does though.

9. Mar 5, 2008

### tacosareveryyum

What book is that from? You've got me interested now.

10. Mar 5, 2008

### Mk

Probably a joke, note the "Excercise #1.1.1.1.1.1.a"

11. Mar 5, 2008

### robphy

12. Mar 5, 2008

### Kurdt

Staff Emeritus
The Schrödinger equation is pretty nice.

13. Mar 5, 2008

### Schrodinger's Dog

For sheer actual physical good looks, and usefulness I'd say the Laplacian looks quite nice.

$$\displaystyle \Delta = \frac{\partial^2 f}{\partial x^2} + \frac{\partial^2 f}{\partial y^2} + \frac{\partial^2 f}{\partial z^2}$$

14. Mar 5, 2008

### humanino

Well, if I were a genius indian mathematician I'd say $$\sum_{n=1}^{\infty }n=-\frac{1}{12}$$

15. Mar 5, 2008

### gravenewworld

Maybe my eyes are just bad, but that isn't an equation, it is meaningless.

one of my favs.-

Last edited: Mar 5, 2008
16. Mar 5, 2008

### Pythagorean

shouldn't it be turned around, squared, and acting on something on the left side?

17. Mar 5, 2008

### gravenewworld

This one also helped the US win WWII and also has been called one of the most important advances in science in the 20th centurty

N2 + 3H2---------> 2NH3 (Fe/K2O/Al2O3/250 atm/500 C)

18. Mar 5, 2008

### CaptainQuasar

I've always been partial to the Leibnitz formula for pi:

$$\huge \mathbf{\pi} = 4 \sum_{n=0}^\infty \frac{(-1)^n}{2n + 1}$$​

19. Mar 5, 2008

### humanino

:rofl:
They were telling the same to Fourier.

Probably one of the most important and beautiful mathematical object is the Riemann zeta function.
Since you like to copy equations from wikipedia, maybe you can check it out for real from time to time. It is instructive.

EDIT BTW, I was refering to Ramanujan who was maybe one of the most prolific for genuinely beautiful formulae

Last edited: Mar 5, 2008
20. Mar 5, 2008

### gravenewworld

No, I said it because what was posted did not contain any equal sign, and hence it is impossible for it to be an equation. At least the riemann zeta function has an equal sign.