The most beautiful formula of all

[fresh_42]

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:

• $E = m \cdot c^2$

• $E^2 = m^2c^4 + p^2c^2$

• $e^{i\pi} + 1 = 0$

 

[cosmik debris]

d = 0

 

[micromass]

• $E = m \cdot c^2$

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

 

[strangerep]

$$\text{What is the formula you regard as the most beautiful of all?}$$

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

 

[fresh_42]

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

I might have missed it. Sure it was recently?

 

[strangerep]

I might have missed it. Sure it was recently?

https://www.physicsforums.com/threads/pf-contest-equations-as-art.863656/

My entry is at post #7. (The most interesting aspect of that thread is how some people seem unable to detect visual beauty/elegance, yet can perceive beauty-in-meaning quite deeply.)

 

[fresh_42]

https://www.physicsforums.com/threads/pf-contest-equations-as-art.863656/

My entry is at post #7. (The most interesting aspect of that thread is how some people seem unable to detect visual beauty/elegance, yet can perceive beauty-in-meaning quite deeply.)

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.

 

[jim hardy]

e ^{i π} + 1 = 0

 

[fresh_42]

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

 

[micromass]

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

Read the book by Hubbard to see the general form of that. http://matrixeditions.com/5thUnifiedApproach.html

 

[fresh_42]

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

 

[George Jones]

d = 0

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

 

[cosmik debris]

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

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

 

[mathwonk]

David Mumford, one of my heroes, likes this one because it is the only one he knows that includes the number 13:

https://news.dartmouth.edu/news/2015/01/art-equation-mathematical-formulas-exhibit