Art 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:

$$\text{Ric} = 0 $$

 

[fresh_42]

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

And you've stolen it from a blind man. ... What a bunch of thefts have I landed in ...

 

[Orodruin]

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 $1$ ...

It cannot win. It violates one of the competition rules:

• Must use LaTeX

 

[scottdave]

$\int = S$

Oh shoot! It is not about math. Ha... funny.

 

[fresh_42]

Oh shoot! It is not about math. Ha... funny.

We all must be cautious not to end up like me. Once in a not really crowded bar, the discussion at the table was boring and the music played "In the Army now" from Status Quo. At the far end was sitting a couple and well, the girl wore a t-shirt (not much "t" though) which uncovered more than it hid. Next I caught myself thinking about tangent spaces on named curved space and tried to imagine whether a certain point at the front is a real singularity or whether it's still differentiable ... Needless to say I didn't really try to figure it out by inspection.

 

[member 587159]

I like the wave equation:

$\Delta \vec Z - \frac{1}{v²}\frac{\partial² \vec Z}{\partial t²} = \vec 0$

 

[epenguin]

"... It only remained to write the book out... I worked at it from 10 to 12 hours a day for about eight months in the year, from 1907 to 1910" (the work having started about 1900) "..- the manuscript became more and more vast, and every time that I went out for a walk I used to be afraid that the House would catch fire and the manuscript get burnt up. It was not, of course, the sort of manuscript that could be typed, or even copied. When we finally took it to the University Press, it was so large that we had to hire an old four-wheeler for the purpose... The University Press estimated that there would be a loss of £600 on the book". After obtaining various generous contributions "the remaining £100 we had to find ourselves. We thus earned minus £50 each by ten years' work. This beats the record of Paradise Lost." (The Autobiography of Bertrand Russell 1872 to 1914)

However click theresultofthisivorytowerresearchhasfoundmanypractical applicationsandisevenusedbyeconomistsprovingyetagainthat contd. on p94(Edit I have now read the rules more carefully and see this creative selection and copying is not according to them, but maybe there are things some of you might like to know. These symbolic logic pages have an appearance different from ordinary math, very impressive when you don't know what they mean. But since the competition has to be in latex, and as I have just spent an hour failing to create two lines of latex, and they were only a modification of one line by someone else, I probably won't submit anything else.)

 

[martinbn]

$d^2=0$

 

[fresh_42]

$d^2=0$

Finally an equation which I exactly understand!

 

[QuantumQuest]

One of Euler's identities regarding the relationship between exponential and trigonometric functions

$\tan\theta = -i (\frac{e ^{i\theta} - e ^{-i\theta }}{e ^{i\theta} + e ^{-i\theta }})$

 

[Orodruin]

$d^2=0$

Earlier today I was wondering why nobody had put this already.

 

[fresh_42]

Earlier today I was wondering why nobody had put this already.

I would quote the "One cross each!" scene here, but some people might feel offended, so I don't insert the corresponding video clip.

 

[Orodruin]

I would quote the "One cross each!" scene here, but some people might feel offended, so I don't insert the corresponding video clip.

Who could be offended by classic Monty Python scenes? Oh, wait! There was that entire bout with the church over that one ...

 

[David Regen]

I attempted to submit an equation for the aesthetic-equation contest. Here's another try:

 

[rootone]

1=1

 

[ISamson]

π^π=π^π

 

[mfb]

If someone is offended by a Monty Python scene, it just means the scene is accurate.

 

[mfb]

My equation, in a separate post to allow unbiased voting:

$\nabla^2 = \Delta$

 

[stoomart]

$\overbrace{\smile}^{\theta\theta}$

 

[Buffu]

$$\int_{-1}^1\frac1x\sqrt{\frac{1+x}{1-x}}\ln\left(\frac{2\,x^2+2\,x+1}{2\,x^2-2\,x+1}\right)\ \mathrm dx = 4\pi \operatorname{arccot} \sqrt{\phi}$$.

Where $\phi = \dfrac{1+\sqrt{5}}{2},$ is our dear golden ratio.

 

[Buffu]

Not for contest :)

$$\int_{0}^{1}{x^{2} - 1 \over \ln{x}}\,d x =
\int_{0}^{1}\int_{0}^{1}{x^{t + 1} + x^{t}}\, dx \ dt$$