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Greatest Equations Ever
sgant writes "What is your favorite equation? This was the question asked by Physics World in a recent poll. This is also covered in a New York Times article about the same poll. Some of the equations mentioned were the simplistic 1+1=2 and Euler's equation, ei + 1 = 0. What are some of your favorite equations?"
Euler's equation is actually Exp[i*Pi] + 1 = 0 not Exp[i*n] +1 = 0 (unless they say n = Pi, which they don't). I'd have to say this is the most elegant equation of all time. It combines the 5 most important numbers in all of mathematics into a single formula. This formula also has tremendous applications in many fields of engineering and other areas of applied mathematics. If it wasn't for this equation, your cell phone wouldn't work.
Scott
a^3+b^3 = (a+b)(a^2-ab+b^2)
first proof, that i'd seen at least, of the existance of negative numbers.
GENERATION 26: The first time you see this, copy it into your sig on any forum and add 1 to the generation.
Gotta Love V=IR. Works pretty well, I use it daily, well that and P=VI.
Take a look at the username, and take a guess at mine :o)
So.. it has come to this
In my opinion, the most important equations are those that brought together Algebric representation of Geometry -- that has been the single most fundamental basis for today's advancement in mathematics and physics.
B*u*pi * integral of e^x
Hint: Try writing it in mathematical notation.
Happiness = Food x Friends x Fun
From Woz.
It's the most important and beautiful equation I've ever seen.
First we state that women require time and money:
Women = Time X Money
And as we all know "time is money"
Time = Money
Therefore by substituting Money for Time we get:
Women = Money X Money
Women = (Money)2
And because "money is the root of all evil" we therefore can state:
Money = (Evil)1/2
And Since
(Money)2 = Women
Then (Money)2 = Evil
And we are forced to conclude by substituting "women" for "(money)2" from above that:
Women = Evil
** "It's not my job to stand between the people talking to me, and the ones listening to me." -- Pego the Jerk
My favorite is the thinkgeek tshirt that says "2+2=5 for extremely large values of 2".
It is not just funny... if you consider the numbers not as integers, but as any float value with that integer as the first number, it is true.
ih/2Pi dPhi/dt = hc/2iPi (A1 dPhi/dx1 + A2 dPhi/dx2 + A3 dPhi/dx3) + A4 mc(squared)Phi
Said by Hotson to be the Equation of Everything. First part, second part. Worth a read IMO.
Maybe we deserve this world ?
My favorite is 0 = 0, because it's the one that most often indicates you're done with the math exercise. :-)
Please correct me if I got my facts wrong.
"What is your favorite equation? ..."
Shashdot has already covered this in a poll! We all already know that E=mc^2 is the overall favorite, closely followed by F=ma.
http://slashdot.org/pollBooth.pl?qid=804
Anyway, just thought I'd share that because E=m^2c^4 + p^2c^2 is my favorite equation and most people think it looks a little familiar but wouldn't know what it was without a little additional explanation.
When things get complex, multiply by the complex conjugate.
The integral of a differential form on the boundry of a manifold is equal to the integral of the exterior derivative on the manifold itself.
S_{dM)w=S_(M)dw
An important special case is the fundamental theorem of calculus. Not only is this a beautiful looking theorem, but important too.
Other special cases are the classical forms of green's theorem, stoke's theorem, and the divergence theorem.
I dunno if its my favorite equation, but its up there.
Everything = 42
If it wasn't for this equation, your cell phone wouldn't work.
If it wasn't for the laws of nature things wouldn't work. The mathematical formulas are our way of expressing them.
Really, I know what I'm doing...Ohhhh, look at the shiny buttons!
I always liked this one that my calc teacher says he saw once on a students paper
Sin x / n = 6
The logic of this was that the n on the bottom cancelled out the n on the top so the result was Six. Oh well I laughed when I was shown it.
No, everybody is correct.
The only thing is that schematix (grandparent) misread the Pi as a 'n', which look very similar, indeed (on my screen anyway).
There are 11 types of people:
Those who understand binary
Those that don't
And those that think they do.
Someone hates these cans.
If you don't have a math tool handy, you can use the Google calculator to check some of the equations mentioned here. For instance:
sqr(-1)
e^(i.pi)+1
1+1
That is, if you're suspicious...
The problem with Slashdot memes is that YOU INSENSITIVE CLOD!
There are 10 kinds of people: those who understand binary and those who don't.
Dyslexics have more fnu.
Of special importance to slashdot:
garbage in = garbage out
Jolyon
Please read my Canon EOS tech blog at http://www.everyothershot.com
0.999999... is just another way of symbolising the value 1. Its the same value, just two ways to write it.
this is not my signature.
I use this in day-to-day life probably more than anything else. Helpful for calculating my home theater projector screen sizes when I need to one-up friedns that get new televisions.
Apropos to the current discussion was this response:
I submitted it the equation to /. wrong...(thanks for calling me stupid btw, very helpfull)
But the equation IS e^(i*pi)+1 = 0
That's Eurler's equation. That's it. You're simply writing it in a different way.
Hell you can even plug in e^(i*pi)+1 into Google and it will spit out zero. Go ahead, give it a try.
Also, I won't call you stupid for making this mistake....I'll let it slide.
"Leo Fender was in a 'state of grace' when he designed the Stratocaster." -- Paul Reed Smith
us {all,your,base}
Of course if sets aren't your thing...
#hostfile 0.0.0.0 primidi.com 0.0.0.0 www.primidi.com 0.0.0.0 radio.weblogs.com
I would have to say, at the moment, my favorite equation would have to be the one giving the coefficients of the generalized Fourier series involving a set of eigenfunctions {p_n}, ie., c_n = <f, p_n>/||p_n||^2.
Simple stuff, but incredibly cool, considering that Fourier series don't always have to involve just sines and cosines, and you get similar sorts of behaviour.
Come on, folks? The Schrödinger equation!
H*Psi = E*Psi
(note: H is an operator folks, not a number)
Perhaps not as famous as E=mc^2.. or as exact as the Dirac equation (relativistic version of the S.E.),
but.. in terms of practical benefit to mankind, I think this one has done more than any other equation during the last century.
Atoms. Molecules. Semiconductors. Lasers.
The number of things explained and modelled by the Schrödinger equation are just uncountable. You can explain almost* all of chemistry with that thing.
Relativity is nice, but it hasn't had the technical uses quantum physics has.
(*Relativistic effects are important in heavy elements. For instance the yellow color of gold is a relativistic effect.)
The answer is simple. The most beautiful equations, hands down, are those from which all of mathematics can be derived. These are the axioms of ZFC set theory. What could possibly be more beautiful or more important than that? And it's a shame so few people know about them. See Zermelo-Fraenkel Axioms and Metamath Proof Explorer.
Comment removed based on user account deletion
George Bush still doesn't know if Bin Laden is alive! After numerous rounds of "We don't even know if Osama is still alive", Osama himself decided to send George Bush a message in his own handwriting to let him know that he was still in the game.
Bush opened the letter and it appeared to contain a coded message:
370HSSV-0773H
Bush was baffled, so he typed it out and e-mailed it to Colin Powell. Colin and his aides had no clue either so they sent it to the CIA. No one could solve it, so it went to the NSA and then to MIT and NASA and the Secret Service.
Eventually they asked Britain's M I6 for help. They cabled the White House: "Tell the President he is looking at the message upside down."
A classic misquote. The verse actually runs, "The love of money is the root of all evil," but this joke wouldn't be as funny that way.
It's still funny--you just have to change the punchline to "The love of money is the root of all women."
What part of "shall not be infringed" is so hard to understand?
Here's my favorite:
First we state that women require time and money:
Women = Time x Money
And as we all know "time is money"
Time = Money
Therefore by substituting Money for Time we get:
Women = Money x Money
Women = (Money)^2
And because "money is the root of all evil" we therefore can state:
Money = (Evil)^1/2
And Since
(Money)^2 = Women
Then (Money)^2 = Evil
And we are forced to conclude by substituting "women" for "(money)^2" from above that:
Women = Evil
Can't argue with mathematical proof!
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77 77 77 2e 6d 65 6c 76 69 6e 73 2e 63 6f 6d
A^2+B^2=C^2
This is the only equation that will give you the quickest way from here to there in an airplane.
Aah, change is good. -- Rafiki
Yeah, but it ain't easy. -- Simba