# The most beautiful formula of all

1. Jul 24, 2016

### Staff: Mentor

I like to do a little survey and ask all who are interested:
$$\text{What is the formula you regard as the most beautiful of all?}$$
In order to avoid everybody answer the same, please don't post one of the following:
• $E = m \cdot c^2$

• $E^2 = m^2c^4 + p^2c^2$

• $e^{i\pi} + 1 = 0$

2. Jul 24, 2016

### cosmik debris

d = 0

3. Jul 24, 2016

### micromass

Staff Emeritus
$E = m\cdot (a^2 + b^2)$

4. Jul 24, 2016

### strangerep

Umm,... wasn't there a PF competition like this recently?

5. Jul 24, 2016

### Staff: Mentor

I might have missed it. Sure it was recently?

6. Jul 24, 2016

### strangerep

7. Jul 24, 2016

### Staff: Mentor

Ok, but that's slightly different. I don't mean beauty as a concept of art but in the way the excluded formulas indicate. I admit that in your case it fulfills both criteria. I had to exclude the above because especially Euler's equation is widely seen as to be the most beautiful. The popular version $E=mc^2$ certainly comes in close. I wonder whether there are others of comparable beauty.

Last edited: Jul 24, 2016
8. Jul 25, 2016

### jim hardy

e i π + 1 = 0

9. Jul 25, 2016

### Staff: Mentor

I've found a beautiful one today
$$grad \; f = \lim_{V \rightarrow 0} \frac{\oint_{\partial \mathcal{V}} f d \vec{A}}{V}$$

10. Jul 25, 2016

### micromass

Staff Emeritus
11. Jul 25, 2016

### Staff: Mentor

Thank you. I appreciate references (from certain people I know I can rely on).

12. Jul 27, 2016

### George Jones

Staff Emeritus
$d^2 = 0$ is nice, too.

13. Jul 27, 2016

### cosmik debris

I can see now that there are a whole family of them :-) You're a man after my own heart George.

14. Jul 28, 2016