Can Equations Be Aesthetic Art?

[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]

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

 

[chimay]

$$\arctan \frac{1}{x}=\frac{\pi}{2}-\arctan x$$

 

[MexChemE]

The ideal gas law
$$PV=nRT$$

 

[Laurie K]

$$\frac {\lambda}{2 \pi}=\frac {\hbar}{mc}\\$$

 

[Charles Link]

I like the Planck blackbody function: $\\$ $L(\lambda,T)=\frac{2 h c^2}{\lambda^5 (e^{\frac{hc}{\lambda k_b T}}-1)}$.

 

[diogenesNY]

$E=IR$

Clean lines. Beautiful simplicity, yet breathtakingly utilitarian.
Like a cold beer on a hot day!

submitted for your approval,
diogenesNY

(I previously cited Ohm's law in a similar thread some years ago... my opinion remains unchanged... although I did have to figure out how to use latex for this one)

 

[scottdave]

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

Ha. Actually pretty easy to disprove.

 

[Charles Link]

Ha. Actually pretty easy to disprove.

A numerical computation of it shows it doesn't miss by much. Fermat's last theorem says that it can't be equal, but it's much closer than I expected.

 

[mfb]

3987 and 4365 are divisible by 3, therefore their 12th powers are divisible by 3, same for the sum. 4472 is not divisible by 3, and taking the 12th power doesn't change that.

 

[Baluncore]

A numerical computation of it shows it doesn't miss by much. Fermat's last theorem says that it can't be equal, but it's much closer than I expected.

 3987^12 = x = 16134474609751291283496491970515151715346481.
 4365^12 = y = 47842181739947321332739738982639336181640625.
       x + y = 63976656349698612616236230953154487896987106.
 4472^12 = z = 63976656348486725806862358322168575784124416.
   x + y - z =  error =  1211886809373872630985912112862690.

So, it is not out by much, only by about 1.2 x 10^33.

 

[scottdave]

$E=IR$

Clean lines. Beautiful simplicity, yet breathtakingly utilitarian.
Like a cold beer on a hot day!

submitted for your approval,
diogenesNY

(I previously cited Ohm's law in a similar thread some years ago... my opinion remains unchanged... although I did have to figure out how to use latex for this one)

I like to see it with the E above, and the I and R below that.