Can Equations Be Purely Aesthetic?

[epenguin]

As any fule no

 

[samalkhaiat]

You still seem to be thinking in terms of beauty-in-meaning, rather than visual beauty.

Actually, it's fascinating how high powered mathematicians like yourself and A. Neumaier (to name just 2 among others in this thread) perceive beauty-in-meaning where others do not, yet have trouble perceiving the visual beauty that others can. Other types of people (e.g., conventional artists) suffer the reverse -- they create beautiful pictures yet cannot even understand how basic percentages work.

“Beauty” is in “Usefulness” and “Simplicity”. Imagine you are working on extremely important problem with limited time scale, and suddenly the following difficult integral pops up in your face
$$\int_{0}^{\infty} dx \ e^{-(x^{2} + \frac{1}{x^2})} .$$
Do you waste precious time trying to evaluate the integral, which is not easy, or use the following “simple” and “extremely useful” inequality to guess correctly its value?
$$x + \frac{1}{x} \geq 2 .$$
By the way, the inequality I posted in #4 follows from the above beautiful inequality

 

[Kevin McHugh]

Now you have to show that it is either generally true in some way or defines something meaningful.

No I don't. The rule was it has to be ascetically pleasing.

 

[Kevin McHugh]

I think most people would consider it true. I just don't get why this forum allows it...

Whatsamattta U? What's not to allow?

 

[micromass]

No I don't. The rule was it has to be ascetically pleasing.

This is the rule:

• The equation must be valid and true.

Yours isn't.

 

[Greg Bernhardt]

Yours isn't.

It is literally true, but not mathematically. I didn't really specify

 

[micromass]

It is literally true, but not mathematically. I didn't really specify

I don't think it's true for everybody though...

 

[Kevin McHugh]

This is the rule:
Yours isn't.

Lighten up Francis

 

[Kevin McHugh]

I don't think it's true for everybody though...

Good God man!

 

[micromass]

Lighten up Francis

I got to admit I'm pretty upset because you missed the $dx$...

 

[Kevin McHugh]

I got to admit I'm pretty upset because you missed the $dx$...

OK, now there's a response I can wrap my head around

 

[Ssnow]

... and the domain of integration must be the union of intervalls $C\cup O \cup N \cup D \cup O \cup M$

 

[strangerep]

[...] Naturwissenschaften box (I love how this word tickles my tongue!

That picture reminds me of a joke that circulated during my high school German class: "In dieser Box ist viele Ratschidt gemixt."

 

[strangerep]

It seems most of the people actually feel the same as micromass about the equations but they either don't know it or don't want to admit it!

Don't get me wrong. I, too, can perceive beauty-in-meaning. Indeed, I'm sure I'd enjoy a brief Insights article explaining Micromass's entry more extensively.

But this contest is about visual beauty, as Greg already explained.

 

[strangerep]

“Beauty” is in “Usefulness” and “Simplicity”.

Heh, I see you are from the "Marie Curie" school of beauty and deportment. (IIRC, Einstein said that MC "never smelt the roses".)

But I think you (and several others) misunderstand me. I can also perceive beauty in usefulness and simplicity. My point is that it's not the same thing as visual beauty.

 

[Patrick_Hutecker]

A⊥=-(PG)/3*R
P=M/V
R: radius
An equation written by Leonard Susskind in his lessons which not only shows how to calculate the force of a gravitational field onto an object but is shows the mystery and challenge of gravity an unknown divergence.

 

[TeethWhitener]

Wow, I leave town for a few days and come back to a whole bunch of love from PF. I guess the lesson is that I need to go on vacation more often.

Since no one specified that the equation had to be a math equation, have a chemical equation:

I actually considered something along these lines myself. Maybe Ru-catalyzed olefin metathesis, or Pd-catalyzed cross coupling. Something about those catalytic cycles reminds me of the factory scenes in Looney Tunes (plus, the metallacycles formed within the catalytic cycles strike me as sort of a chemical epicycle). I also find the syntheses of molecules like dodecahedrane and cubane to be quite beautiful.

 

[Sophia]

Don't get me wrong. I, too, can perceive beauty-in-meaning. Indeed, I'm sure I'd enjoy a brief Insights article explaining Micromass's entry more extensively.

But this contest is about visual beauty, as Greg already explained.

Well, one must understand the meaning of the equation to see the beauty.
I personally don't see absolutely anything in these equations. In fact, the way most of them are written looks ugly and scary to me. That's because I have absolutely no idea what they mean.
I could only like pythagoran theorem and one explained by collinsmark because the meaning of it seemed beautiful to me.
I was once forced by a teacher to draw a picture using equations for homework. Well my tutor gave me so many hints and explained everything for so long that he finally made me draw a simple picture of a Chinese man in a hat using equations. It was interesting but I still didn't see the beauty of it as I never really understood what the heck those equations are about.
To me, equations are like beautiful poetry written in hieroglyphs. You can't appreciate it without first understanding the language.

 

[Ygggdrasil]

I actually considered something along these lines myself. Maybe Ru-catalyzed olefin metathesis, or Pd-catalyzed cross coupling. Something about those catalytic cycles reminds me of the factory scenes in Looney Tunes (plus, the metallacycles formed within the catalytic cycles strike me as sort of a chemical epicycle). I also find the syntheses of molecules like dodecahedrane and cubane to be quite beautiful.

I would also agree that those would be good examples of beautiful chemical equations.

 

[diogenesNY]

E=IR

Simple. Classic. Clean lines. Gracefully applicable, yet ruggedly utilitarian, like a Brannock Device or a Mongol 482 pencil.

Also, just always a personal favorite equation. I always 'just liked it'.

I can imagine that it's personal soundtrack is _Joy_ by Apollo 100.

--diogenesNY

 

[Greg Bernhardt]

Congrats to @TeethWhitener who's equation won with 26 votes!

Well, if it's just aesthetics and not significance, then how about this:
$$1+\frac{1}{1+\frac{1}{1+\frac{1}{1+\cdots}}} = \sqrt{1+\sqrt{1+\sqrt{1+\sqrt{1+\cdots}}}}$$