Can Equations Be Aesthetic Art?

[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!

 

[Orodruin]

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:
$$
\int_{M} d\omega = \oint_{\partial M} \omega
$$

 

[fresh_42]

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

 

[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.
$$\oint\frac{f(z)\;dz}{\left(z-z_{0}\right)^{n+1}}=\frac{2\pi i}{n!}f^{(n)}(z_{0})$$

 

[Mark44]

Here's one I like:

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

You might need to think about this one a bit ...

 

[NFuller]

Here's one I like:

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

You might need to think about this one a bit ...

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

 

[Orodruin]

Here's one I like:

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

You might need to think about this one a bit ...

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

 

[DS2C]

Here's one I like:

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

You might need to think about this one a bit ...

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

 

[OCR]

You might need to think about this one a bit ...

It looks difficult and unpleasant to me...

 

[martinbn]

It looks difficult and unpleasant to me...

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

 

[Ygggdrasil]

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

 

[Orodruin]

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

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

 

[Ygggdrasil]

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

Taking full advantage of rule #2

Spoiler

http://www.slate.com/blogs/browbeat...izard_of_evergreen_terrace_has_brilliant.html

 

[Orodruin]

Taking full advantage of rule #2

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.

 

[gmax137]

Spoiler

link

thanks Yggg, that is a great story

 

[ohwilleke]

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

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

 

[ohwilleke]

e^iπ + 1 = 0

 

[fresh_42]

e^iπ = -1

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 $1$ ...

 

[Buzz Bloom]

This was my mantra for a while.

e^iπ + 1 = 0

 

[PAllen]

Here's one I like:

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

You might need to think about this one a bit ...

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

 

[fresh_42]

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

$\int = S$

 

[OCR]

Only if you are very young and think that girls have cooties arithmetic bugs* [snip...]

It looks difficult and unpleasant to me...

You did see . → . right... ? .


*Definition of arithmetic bugs:

"They added to your troubles, subtracted from your pleasures, divided your attention, and multiplied like hell...!"

Lol...

 

[MarkFL]

This one's kinda purty:

$$1+\cfrac{1}{1+\cfrac{1}{1+\cfrac{1}{1+\cfrac{1}{1+\ddots}}}}=\sqrt{1+\sqrt{1+\sqrt{1+\sqrt{1+\cdots}}}}$$

 

[member 587159]

e^iπ + 1 = 0

You stole my profile picture (at least an equivalent form haha)

 

[Auto-Didact]

$$(\Box+\mu^2)\psi = 0$$

 

[aheight]

Extending Laurent's Theorem to algebraic functions:

$$
\begin{equation}
w_n(z)= \sum_{k=0}^{\infty} a_k (z^{1/n})^k+\sum_{k=1}^{\infty} \frac{b_k}{\left(z^{1/n}\right)^k} \\
a_k=\frac{1}{2n\pi i} \int\!\!\!\!\! 8 \frac{w_n(z)}{\left(z^{1/n}\right)^{k+n}} dz\\
b_k=\frac{1}{2n\pi i} \int\!\!\!\!\! 8 w_n(z)\left(z^{1/n}\right)^{k-n} dz
\end{equation}
$$

 

[TeethWhitener]

$$\frac{16}{64}\cdot\frac{26}{65}\cdot\frac{19}{95}\cdot\frac{49}{98} = \frac{1\!\!\!\not6}{\not64}\frac{\not2^{1}\!\!\!\not6}{\not65}\frac{1\!\!\!\not9}{\not95}\frac{\not4^{1}\!\!\!\not9}{\not9\!\!\!\not8_{\not21}}=\frac{1}{4\cdot5\cdot5}=\frac{1}{100}$$

 

[TeethWhitener]

I'm willing to ... admit I don't get it.

Neither do I, buddy. Neither do I.

 

[scottdave]

$$φ = 1 + \frac {1} {1 + {\frac {1} {1+{\frac {1} {1 + ...}}}}}$$

 

[Geometry_dude]

The vacuum Einstein equation:

$$\text{Ric} = 0 $$