Favorite Mathematical Equation

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vanyali
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Favorite Mathematical Equation

Postby vanyali » Thu Sep 27, 2007 12:44 am UTC

What's your favorite mathematical equation/inequality/formula/proof/etc?

My favorite equation is definitely

Image

It's beautiful, relatively simple, and its proof is not trivial yet not horribly complex.

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Postby Sana » Thu Sep 27, 2007 1:29 am UTC

Probably
Image

Not sure why. It's just interesting I guess.

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Postby scowdich » Thu Sep 27, 2007 2:03 am UTC

Now you're just fucking with me.

Personally, I'm a fan of Maxwell's Equation's. They just look so simple and compact in delta-notation form...

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Postby ICDB » Thu Sep 27, 2007 2:15 am UTC

The Maclaurin/Taylor (dunno which one is correct) series for e^x
Image
... sexy
Edit: fixed some noob forumfu

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Postby ATCG » Thu Sep 27, 2007 2:34 am UTC

A favorite of electrical engineers, fans of AC circuit theory, and wave mechanics aficionados: Euler's formula.
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Postby Marbas » Thu Sep 27, 2007 2:53 am UTC

ATCG wrote:A favorite of electrical engineers, fans of AC circuit theory, and wave mechanics aficionados: Euler's formula.


Hooray for phasors!


I've always liked Laplace transforms and Fourier Series and transforms.

I don't know why.
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Postby CodeLabMaster » Thu Sep 27, 2007 2:59 am UTC

I always found this to be a cooler one:

Image

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Postby shill » Thu Sep 27, 2007 4:01 am UTC

All of Ramanujan's, really.

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Postby mountaingoat » Thu Sep 27, 2007 4:03 am UTC

Image
lawlnoob.

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Postby ATCG » Thu Sep 27, 2007 5:36 am UTC

Marbas wrote:Hooray for phasors!

Amen to that.

Marbas wrote:I've always liked Laplace transforms and Fourier Series and transforms.

I don't know why.

I'm going to go out on a limb here and guess that you have yet to take a course in control theory or communication theory. If/when you do so, the ability to take problems that would be soul crushing in the time domain and graphically whip out solutions in the frequency domain will lead you to sing hosannas to Pierre-Simon Laplace and Joseph Fourier.
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Postby Marbas » Thu Sep 27, 2007 5:45 am UTC

ATCG wrote:
Marbas wrote:Hooray for phasors!

Amen to that.

Marbas wrote:I've always liked Laplace transforms and Fourier Series and transforms.

I don't know why.

I'm going to go out on a limb here and guess that you have yet to take a course in control theory or communication theory. If/when you do so, the ability to take problems that would be soul crushing in the time domain and graphically whip out solutions in the frequency domain will lead you to sing hosannas to Pierre-Simon Laplace and Joseph Fourier.


You would be correct. I am still in high school so that would be kind of odd. Most of what I know is what I've taught myself, but my short attention span prevents me from actually building and designing circuits, so I just end up with a lot of theory and blackboard work done. Which is kind of bad, because building circuits is very different from blackboard work. :oops:
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Postby ATCG » Thu Sep 27, 2007 7:32 am UTC

Marbas wrote:
ATCG wrote:I'm going to go out on a limb here and guess that you have yet to take a course in control theory or communication theory. If/when you do so, the ability to take problems that would be soul crushing in the time domain and graphically whip out solutions in the frequency domain will lead you to sing hosannas to Pierre-Simon Laplace and Joseph Fourier.


You would be correct. I am still in high school so that would be kind of odd. Most of what I know is what I've taught myself, but my short attention span prevents me from actually building and designing circuits, so I just end up with a lot of theory and blackboard work done. Which is kind of bad, because building circuits is very different from blackboard work. :oops:

I'm impressed. You're well ahead of where I would expect even an AP calculus student to be. I don't know if you've had any exposure to linear differential equations (which phasors largely allow you to sidestep, anyway), but it sounds like you've amassed most or all the math you'd need for DC and AC circuit analysis and design, and that would get you well down the road for the rest of an EE curriculum as well.

I'm going to crawl a little further out on that limb I'm on and assume that you might be interested in pursuing EE. If so, I'd like to encourage you; it's a discipline that welcomes bright, capable people. As far as your "short attention span", it certainly hasn't hindered your mathematical development any. And as far as actually having built (or not) real, live circuits, that should be the least of your concerns. The guys with all the electronic construction experience who started the EE program along with me were at no advantage whatsoever. It was the guys who could absorb and master the theory that thrived. Better that you be more comfortable holding a piece of chalk than a soldering iron. To me it sounds like you've got the goods to be successful in electrical engineering, if such were your goal.
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Postby brodieboy255 » Thu Sep 27, 2007 7:42 am UTC

dunno if it counts as a formula, seeing as its more of a property, but i love that d/dx(e^x) = e^x

Euler's formula is also cool. I love the way it merges trig, e, and imaginary numbers.

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Postby Torn Apart By Dingos » Thu Sep 27, 2007 9:02 am UTC

Cauchy's integral formula is rad:
Image

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Re:

Postby Rilian » Thu Sep 27, 2007 1:29 pm UTC

Sana wrote:Probably
Image

Not sure why. It's just interesting I guess.


Uh... do I know you? I was gonna say that I know this person who's in love with this equation....
And I'm -2.

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Re:

Postby aguacate » Thu Sep 27, 2007 2:35 pm UTC

Sana wrote:Probably
Image

Not sure why. It's just interesting I guess.


Yes this one is a classic, although I think

e^(i*pi) + 1 = 0

is better.
Image

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Re: Re:

Postby Yakk » Thu Sep 27, 2007 2:54 pm UTC

aguacate wrote:
Sana wrote:Probably
Image

Not sure why. It's just interesting I guess.


Yes this one is a classic, although I think

e^(i*pi) + 1 = 0

is better.


Agreed -- it contains the 4 most important constants in mathematics, as opposed to just 3 of them. :)
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Re: Favorite Mathematical Equation

Postby Mathmagic » Thu Sep 27, 2007 3:02 pm UTC

I'm going to have to n'th the vote for Euler's Formula. I just recently discovered how handy it is when deriving just about any trig identity. :)
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Re: Re:

Postby GBog » Thu Sep 27, 2007 3:06 pm UTC

Yakk wrote:
aguacate wrote:
Sana wrote:Probably
Image

Not sure why. It's just interesting I guess.


Yes this one is a classic, although I think

e^(i*pi) + 1 = 0

is better.


Agreed -- it contains the 4 most important constants in mathematics, as opposed to just 3 of them. :)


4? I count 5.

And (n+1)'th. Or maybe I like e^(ix) = cos x + i sin x slightly better, I can't decide.

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Re: Favorite Mathematical Equation

Postby Mathmagic » Thu Sep 27, 2007 3:15 pm UTC

GBog wrote:Or maybe I like e^(ix) = cos x + i sin x slightly better, I can't decide.

That's the form that I was referring to with my n'th vote. The two forms are really the same thing anyway. :)
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Re:

Postby MoonBuggy » Thu Sep 27, 2007 8:52 pm UTC

Sana wrote:Probably
Image

Not sure why. It's just interesting I guess.


Does anyone have a link/explanation that can tell me why that occurs? I wouldn't really know what to Google for in order to find it :?

And hopefully the act of asking hasn't inadvertently betrayed a startling lack of mathematical ability...
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Re: Favorite Mathematical Equation

Postby CodeLabMaster » Thu Sep 27, 2007 8:56 pm UTC


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Re: Re:

Postby Buttons » Thu Sep 27, 2007 8:57 pm UTC

MoonBuggy wrote:Does anyone have a link/explanation that can tell me why that occurs? I wouldn't really know what to Google for in order to find it :?

Darn, he beat me to the link.

(Also, you're not the same MoonBuggy who used to play KoL, are you?)

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Re: Favorite Mathematical Equation

Postby MoonBuggy » Thu Sep 27, 2007 9:08 pm UTC

Thanks, and nope, not the same person, sorry :)
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Re: Re:

Postby Sana » Thu Sep 27, 2007 9:45 pm UTC

Rilian wrote:
Sana wrote:Probably
Image

Not sure why. It's just interesting I guess.


Uh... do I know you? I was gonna say that I know this person who's in love with this equation....


Nah. I guess I just like this one because I learned it at a young age.

GBog wrote:
Yakk wrote:
aguacate wrote:Yes this one is a classic, although I think

e^(i*pi) + 1 = 0

is better.


Agreed -- it contains the 4 most important constants in mathematics, as opposed to just 3 of them. :)


4? I count 5.

And (n+1)'th. Or maybe I like e^(ix) = cos x + i sin x slightly better, I can't decide.


I like it in the form I posted because that's how I learned it originally. But I suppose you guys have a point. Or points. You guys have points. Pointy.

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Re: Re:

Postby Number » Thu Sep 27, 2007 11:51 pm UTC

Yakk wrote:
aguacate wrote:
Yes this one is a classic, although I think

e^(i*pi) + 1 = 0

is better.

Agreed -- it contains the 4 most important constants in mathematics, as opposed to just 3 of them. :)

e^(i*pi) + 1 = 0 * 17. That's the 6 most important. Hah!

I happen to like (out of the routinely used) Heron' forumula, K = sqrt[s(s-a)(s-b)(s-c)] = sr, which doesn't stand up to the Quartic formula.
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Re:

Postby jeff_attack » Fri Sep 28, 2007 12:47 am UTC

brodieboy255 wrote:dunno if it counts as a formula, seeing as its more of a property, but i love that d/dx(e^x) = e^x

Euler's formula is also cool. I love the way it merges trig, e, and imaginary numbers.


Isn't e^x the greatest? It was like Christmas when you got an e^x question on a test. Just knowing that its integral and its derivative are the same function, it's kinda strangely beautiful when you think about it. I hate myself for using those words, but I don't know how else to describe it.
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Re: Favorite Mathematical Equation

Postby Korandder » Fri Sep 28, 2007 12:50 am UTC

I have to say Eular's.
Image

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Re: Favorite Mathematical Equation

Postby 22/7 » Fri Sep 28, 2007 3:59 am UTC

I'm a fan of Bernoulli's, though I'm not sure if this is actually a "math" equation. But I quite enjoy it.
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Re: Favorite Mathematical Equation

Postby Ended » Fri Sep 28, 2007 6:46 am UTC

I like the general form of Stokes' theorem. (I don't actually understand it, I just think it looks elegant, and I like the way it generalizes so many results)

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Re: Favorite Mathematical Equation

Postby Fat Kat » Fri Sep 28, 2007 7:15 am UTC

It has to be the golden ratio equation: x^2 - x - 1 = 0 (or φ or ψ depending on preference and context), because it's a thing of (natural) beauty, and it's everywhere!
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Re: Favorite Mathematical Equation

Postby Macbi » Fri Sep 28, 2007 11:33 am UTC

(1+2+3+...+n)^2=1^3+2^3+3^3...+n^3
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Re: Favorite Mathematical Equation

Postby evilbeanfiend » Fri Sep 28, 2007 11:39 am UTC

0.9... = 1 ?

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Re:

Postby jack » Fri Sep 28, 2007 12:33 pm UTC

CodeLabMaster wrote:I always found this to be a cooler one:

Image


That is my new favourite. What an Earth is it?

It looks familiar, is it something to do with the Riemann hypothesis and Ramanujan?

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Re: Favorite Mathematical Equation

Postby BioTronic » Fri Sep 28, 2007 7:05 pm UTC

Time to introduce myself. Norwegian math lover (we seem to be a rare kind, even here). Felt I should show off this one:

Integral z squared dz
from one to the cube root of three
times the cosine
of three pi over nine
equals log of the cube root of e.

Image

Though I instantly fell in love with OP's equation. Sat awake for hours just thinking it was pretty.

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Re: Favorite Mathematical Equation

Postby Pesto » Fri Sep 28, 2007 7:16 pm UTC

Wouldn't that just be 1/3?

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Re: Favorite Mathematical Equation

Postby skeptical scientist » Fri Sep 28, 2007 7:19 pm UTC

Pesto wrote:Wouldn't that just be 1/3?

Yes, but that neither rhymes nor scans.
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Re: Favorite Mathematical Equation

Postby Mathmagic » Fri Sep 28, 2007 8:05 pm UTC

skeptical scientist wrote:
Pesto wrote:Wouldn't that just be 1/3?

Yes, but that neither rhymes nor scans.

Although, you could write it as:

Integral z squared dz
from one to the cube root of three
times the cosine
of three pi over nine
equals the rational one over three
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Re: Favorite Mathematical Equation

Postby Pesto » Fri Sep 28, 2007 8:07 pm UTC

Oh... words. I can't be bothered with words.

*slinks away*

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Re: Favorite Mathematical Equation

Postby Sana » Sat Sep 29, 2007 5:10 pm UTC

evilbeanfiend wrote:0.9... = 1 ?

i'll get my coat.


Oh, thread over. How could I forget this one?
Image
I actually enjoy debating with the people who don't understand that the equation is verified by the definition of infinite.

Oh, and I apologize for the tilde syntax.


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