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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.
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
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.
I think your favorite equation should be E^2=m^2c^4+p^2c^2.
Nah?
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.
There are 11 types of people:
Those who understand binary
Those that don't
And those that think they do.
Someone hates these cans.
There are 10 kinds of people: those who understand binary and those who don't.
Dyslexics have more fnu.
It's actually E^2 = (m^2 * c^4) + (p^2 * c^2)
More like: E^2 = (m0^2 * c^4) + (p^2 * c^2)
m0 is defined as the mass at rest (v = 0). If you substitute m = m0 / sqrt(1 - v^2/c^2), you can rework that to E = mc^2. And, if v = 0, you get E0 = m0c^2, the "energy at rest" of an object.
I agree with the original poster, the full version is much more useful than the E = mc^2 form. The short form hides one of the most important conclusions of relativity theory: that mass is a function of speed.
WWTTD?
Of special importance to slashdot:
garbage in = garbage out
Jolyon
Please read my Canon EOS tech blog at http://www.everyothershot.com
Apropos to the current discussion was this response:
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.
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."
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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