Most Beautiful Equation

[Ender]

What do you consider to be the most beautiful equation that you know?

For me, it would be one of these three:







Ignore the fact that the second one isn't an equation :P The second one is fun to prove btw. Oh, and check this out: here

[Camel]

My college's chant :P

[iago]

Teacher:  So y = r cubed over 3. And if you determine the rate of change in this curve correctly, I think you'll be pleasantly surprised.
[The class laughs except for Bart who appears confused.]
Teacher:  Don't you get it, Bart? Derivative dy = 3 r squared dr over 3, or r squared dr, or r dr r.

[Blaze]

Teacher:  So y = r cubed over 3. And if you determine the rate of change in this curve correctly, I think you'll be pleasantly surprised.
[The class laughs except for Bart who appears confused.]
Teacher:  Don't you get it, Bart? Derivative dy = 3 r squared dr over 3, or r squared dr, or r dr r.

I think we have a winner.

[Quik]

Teacher:  So y = r cubed over 3. And if you determine the rate of change in this curve correctly, I think you'll be pleasantly surprised.
[The class laughs except for Bart who appears confused.]
Teacher:  Don't you get it, Bart? Derivative dy = 3 r squared dr over 3, or r squared dr, or r dr r.

wtf?

[Rule]

Generalized Stokes' theorem:


From this clean looking expression comes almost every theorem in Calculus.

Since it is related to differential forms, however, I'm not sure if I'd call it the "most beautiful equation".  Possibly, but I'd need to think about it more. :P

[Joe]

Stokes is my girlfriend's nickname. Weird.

e = mc²

[Sidoh]

I'd have to be cliche and agree with you here.

[iago]

I'd have to be cliche and agree with you here.

Wouldn't this be simpler?

[Sidoh]

Wouldn't this be simpler?

I suppose, but the reason the other form is often viewed as beautiful is because it contains the five most fundamental constants in mathematics: pi, e, i, 1 and 0 (1 and 0 being identities for various groups... I just learned about groups yesterday.  Maybe there's another construct that makes more sense here?).

[Ender]

Wouldn't this be simpler?

I suppose, but the reason the other form is often viewed as beautiful is because it contains the five most fundamental constants in mathematics: pi, e, i, 1 and 0 (1 and 0 being identities for various groups... I just learned about groups yesterday.  Maybe there's another construct that makes more sense here?).

Yeah, and I also just find "e to the i pi plus one equals zero" to be more rhythmic.

Sidoh, group theory is really fun =) I bought a textbook recently and I'm doing an independent study of algebra.

[Sidoh]

Yeah, it seems like some pretty interesting stuff.  My friend is in some higher math courses (from my perspective, anyway.  I'm only in Calc 3) including cryptography, which he said has been abstract algebra as of late.

We're both doing an independent study with one of the professors who specializes in algorithms, so we meet a couple of times a week to talk about some of the material we've read in the book we got (there's another story there, but I won't bother going into it).  He's really enthusiastic when it comes to math, so when I showed interest when he started talking about groups, he went over some of the basics.  I really like advanced math that's outside calculus.  Don't get me wrong, I love calculus, but it's neat to see.

[Ergot]

[Rule]

Sidoh, group theory is really fun =)

How so? 

[Ender]

Sidoh, group theory is really fun =)

How so? 

I've only done a little with group theory, such as my friend's high school math team lectures and some library books, but I like what I've seen of it so far and I look forward to what is to come. While my class was doing SR my professor mentioned "yeah, and these Lorentz transformations form a group" and I was like, "yay!" It's also got to be really fun to solve a Rubik's cube with group theory, as well as the insolvability of order 5+ polynomials.

I can't wait to get started on my algebra textbook, but I'm first going to finish a good amount of homework due this week before that.