# Featured Contest: Equations as Art 2017

1. Sep 20, 2017

### Greg Bernhardt

The goal is to create the most beautiful or interesting equation aesthetically (pleasing to the eye).
This is not about it's mathematical significance. Get your inner designer on!

• Each member is allowed to post one equation
• The equation can be completely made up
• Must use LaTeX
• Be creative!

To vote for an equation simply click the "like" button. You can vote more than once. The contest will close next Wed Sep 27th.

The winner will receive a PF T-Shirt!

ps. do not try to register new usernames for more entries or for likes. It's painfully easy to figure these out.

Have fun! Go!

2. Sep 20, 2017

### Orodruin

Staff Emeritus
I find it difficult to disregard meaning when it comes to aesthetically judge an equation so I will go with Stokes’ theorem for integration of differential forms. Both for its aesthetics in terms of its integral signs, simplicity in the form of the $\omega$s appearing on both sides, and meaning:
$$\int_{M} d\omega = \oint_{\partial M} \omega$$

3. Sep 20, 2017

### Staff: Mentor

With the Fibonacci sequence $F_n$, the Lucas sequence $L_n$ and the Catalan sequence $C_n$
$$\sum_{n\in\mathbb{N}}\frac{1}{n}\cdot\frac{1}{n}\cdot \frac{1}{n+1} \cdot \frac{F_n \cdot L_n}{C_n} = \frac{(2\pi)^2}{\sqrt{5}^5}$$

Last edited: Sep 24, 2017
4. Sep 20, 2017

### NFuller

This is a fun thread! I agree with @Orodruin that much of the beauty comes from the meaning; so I will go with an extension of the Cauchy integral formula.
$$\oint\frac{f(z)\;dz}{\left(z-z_{0}\right)^{n+1}}=\frac{2\pi i}{n!}f^{(n)}(z_{0})$$

5. Sep 20, 2017

### Staff: Mentor

Here's one I like:

$$\int~e^x = f(u^n)$$

6. Sep 20, 2017

### NFuller

I think I saw this on a T-shirt once.

7. Sep 20, 2017

### Orodruin

Staff Emeritus
This is one of the few cases where the equality no longer holds if you actually perform the integral ...

8. Sep 20, 2017

### DS2C

Finally an equation that makes sense. Looks like I have a future in mathematics after all.

9. Sep 20, 2017

### OCR

It looks difficult and unpleasant to me...

10. Sep 21, 2017

### martinbn

Only if you are very young and think that girls have cooties, or very old and can remember the how but not the why.

11. Sep 21, 2017

### Ygggdrasil

$3987^{12} + 4365^{12} = 4472^{12}$

12. Sep 21, 2017

### Orodruin

Staff Emeritus
For some strange reason I don't buy it ...

13. Sep 21, 2017

### Ygggdrasil

Taking full advantage of rule #2

14. Sep 21, 2017

### Orodruin

Staff Emeritus
Which you are of course in your full right to do. Just saying I agree it is a valid contest entry, but not a valid actual equation.

15. Sep 21, 2017

### gmax137

thanks Yggg, that is a great story

16. Sep 21, 2017

### ohwilleke

Ha! Ha! Ha! (already familiar with the backstory).

17. Sep 21, 2017

### ohwilleke

e + 1 = 0

18. Sep 21, 2017

### Staff: Mentor

This one is the beauty in the contest and will always win, if mathematicians are honest with their votes, I think. I like the positive form $e^{i\pi}+1=0$ a little more, as there is also the $0$ involved: top of the pop, so to say. And I really have to fight myself, because I still have two other beauties in mind ... d... rule $1$ ...

19. Sep 21, 2017

### Buzz Bloom

This was my mantra for a while.

e + 1 = 0

20. Sep 21, 2017

### PAllen

I'm willing to be the idiot and admit I don't get it.