# The most beautiful formula of all

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##

Greg Bernhardt

## Answers and Replies

d = 0

• ##E = m \cdot c^2##

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

member 587159, nasu, axmls and 3 others
strangerep
$$\text{What is the formula you regard as the most beautiful of all?}$$
Umm,... wasn't there a PF competition like this recently?

Mentor
Umm,... wasn't there a PF competition like this recently?
I might have missed it. Sure it was recently?

Mentor

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.

Last edited:
jim hardy
Gold Member
Dearly Missed
e i π + 1 = 0

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

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

George Jones
Staff Emeritus