Can Equations Be Aesthetic Art?

[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 :)

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

 

[Buffu]

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

$\nabla^2 = \Delta$

That is clever, I like it.

 

[Orodruin]

$\nabla^2 = \Delta$

I always write $\nabla^2$ in order to avoid confusion with small but finite differences ... Does that make me weird?

 

[member 587159]

I regret that I didn't submit $\sum_{k=1}^{\infty} k = \frac{-1}{12}$

 

[dextercioby]

One of the most important results in mainstream physics:

$$\psi = e^{i\alpha} \phi \Rightarrow \hat{\psi} = \hat{\phi}$$

 

[fresh_42]

I regret that I didn't submit $\sum_{k=1}^{\infty} k = \frac{-1}{12}$

And I'm glad you didn't. This weird sum shows up on PF far too often already
I regret a little that I didn't take $2^n+7^n+8^n+18^n+19^n+24^n=3^n+4^n+12^n+14^n+22^n+23^n$, the best lesson on induction I've ever seen.

 

[mfb]

I guess you can solve that equation for possible values of n...

Here is a plot

 

[fresh_42]

I guess you can solve that equation for possible values of n...

Here is a plot

Yes, but the interesting point is behind the formula: who found that, how, and even more why? Did they use a mainframe and simply tried? And how much has someone to drink before he tackles such an undertaking. Strange.

 

[mfb]

A computer should find something like that quickly. Assign prefactors of -1 (left side), 0 (don't use) or 1 (right side) and find a set that fits for n from 0 to 5.

3²⁵ = 850 billion combinations if you use 1 to 25, but most of these combinations don't need to be considered.

 

[Baluncore]

I prefer a political statement; the flow of water is power. (Sorry, no LaTex here).

H₂O = m·c²

 

[robphy]

$$\left( \frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+\frac{1}{32}+\frac{1}{64}+\cdots\right)=1$$