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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.
1 + 1 = 11
I was impressed by the technical background of it.
Take a look at the username, and take a guess at mine :o)
So.. it has come to this
Nothing from nothing leaves nothing!
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.
but my personal favorite :)
GENERATION 26: The first time you see this, copy it into your sig on any forum and add 1 to the generation.
e^in + 1 = 0
I read about this two weeks ago in a local newspaper. Didn't the article mean e^(i*\pi)+1=0 ?
Anyway, it could be my fonts confusing me.
Quantum hacker.
Happiness = Food x Friends x Fun
From Woz.
It's the most important and beautiful equation I've ever seen.
Projectile equations of motion, very useful in FPS games.
Due to lack of disk space this user has been discontinued
C^2=A^2+B^2 or or Volume = 4/3 * pi r^3
"You win again Gravity!" -Futurama (Zapp)
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.
Drugs+Money=Chicks
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.
I() means integral in the proper space I(div(F)dV) = I(Fda) That's damn useful.
Gotta love motorcycles. Mmmwwhahahaaaa.
Deleted
1 + 1 = 3
For large values of 1 (and small values of 3)
"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
To paraphrase one of my math professors:
"These sums may look incredibly ugly to you. But I got my tenure by working on them, so they're beautiful to me."
C^2 = 1 /(0*0)
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.
Beauty * Brains = Constant
I guess that the list of greatest equations would be completely different if polled in a mathematical community, instead of the physics community polled in the referred article. Some of the equations that are in this list, and universal to mathematics and physics (like 1+1=2 and e^i*pi+1=0) would definitely pop up in the mathematics list too, but many other differences will be easy to spot (e.g. mathematicians wouldn't have maxwell's, general relativity, gas laws and the such in their list)
--- Sigmentation Fault - Comments Dumped
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.
Comment removed based on user account deletion
Everything = 42
Taylor series expansions
Schrodinger's Equation
Heisenberg Uncertainty Principle
Normal Distribution Curve
Einstein's Time Dilation and relativistic equations
Newtons three laws and law of universal gravitation
Fourier's transformation(s)
thank you sir. for those still doubtful, check out my sig. Specifically, this section.
GENERATION 26: The first time you see this, copy it into your sig on any forum and add 1 to the generation.
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!
b4i (square root)u ru/16
Life, The Universe & Everything = 42
I have a first class with honours degree in electronics sytems and I modelled for a short time in my youth!
i like that equation best when it comes to music (nomeansno)
Sample this!
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.
Though its more famously attributed to in words, it works in math too:
Intelligence * WorldPopulation = Constant
this topic reminds me of a poster i have
3600/sec. per part*length of part/12000*MFT=lbs/hr
Some beautiful equations of mathematical physics
Banu
Karma: -2147483648 (Mostly affected by integer overflow)
Somehow manages to take the beauty of a quadractic curve and turns it into a grunge problem.
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).
From the Simpsons episode, "Bart the Genius"...
Teacher at gifted school:
So y = r^3/3 and if you determine the rate of change in this curve correctly, I think you will be pleasantly surprised.
[The Class laughs. Bart looks confused.]
Teacher:
Don't you get it, Bart?
Derivative dy = 3r^2 dr/3, or r^2 dr, or r dr r. Har-de-har-har!
Get it?
what no S = k.ln(W) ?
That's my favorite.
I used to even use "exp(pi^2/12ln2)" as my name in Quakeworld.
Oh sorry, I only RTFA... the submitter (sgant) was the one misreading the pi.
= 1/0! + x/1! + x^2/2! + x^3/3! + x^4/$! + ...
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!
It's OK to use HTML on a website, you know. I suggest:
... which will work nicely in most browsers.
I have discovered a truly remarkable
x / 0 = math sucks
... You are the Equation of the week. ( I wish I could find the Achewood cartoon this is from, so here's link to the T-Shirt instead. )
One god, one market, one truth, one consumer.
this equation holds if n belongs to the integears set.
I'd have E=0.5mv^2 rebated into every car steering wheel in the land. And maybe a nice E display on the dashboard.
There are 10 kinds of people: those who understand binary and those who don't.
Dyslexics have more fnu.
Point nine recurring equals one.
qntm.org
1 + 1 = A window ;-)
OCT 31 = DEC 25.
That's why geeks always confuse Halloween and Christmas.
Wokka wokka wokka!
1-1/2+1/3-1/4+1/5-...= ln(2)
s html/ for a couple examples)
1-1/3+1/5-1/7+1/9-...=Pi/4
These can be gotten from plugging x=1 in the taylor series for ln(1+x) or arctan(x), but require a fair bit of proof that the series actually converge to what you think they do. It's amazing that series that look so alike can get you pi on one hand and logs on the other!
On the other hand, for sheer drop-your-jaw-in-awe-ness it's hard to beat some of the formulas from Ramanujan's notebooks (see example #5 at http://www.cut-the-knot.org/do_you_know/fraction.
Two words: Bayes' Theorem.
Link goes to an excruciatingly gentle introduction to what this whole Bayesian thing is about, and why your friends seem to think it's so important... but I'll go ahead and spoil the ending, and say that Bayes' Theorem is, in a sense, the underlying equation of science itself; it tells you what constitutes "rational evidence" and exactly how much evidence it is, in which direction.
F=MA is a beautiful equation, don't get me wrong - but can it compare to the equation that describes how scientific theories are confirmed or falsified?
Planetary death rate: 150,000 lives per day. End the slaughter
You PL/1 coder you! Pah, bitstrings...
In High School, a buddy of mine wrote on the blackboard:
1 apple + 2 oranges = 4 orpples
Yeah, I don't get it either.
How could I say to men: "Speak louder, shout! For I am deaf!"? -Ludwig van Beethoven
divide by banana error
reload "UNIVERSE"
RESTART Y/N ?
Bacardi + slashdot = negative karma.
E=mc^2
and i'm afraid one that affect most of us (Norwegian Blues: taste is inversely proportional to lust with a factor of sex. But then again it might just be me *sigh*
Becuase when written like this it holds for relativistic (crotch)rockets. Weeee! (If you look really hard you can even see Hawking.)
my stupid one would be : lim( sqrt(8) , 8->9) = 3 :)
Imposition of Order = Escalation of Chaos
d/dx [e^x] = e^x
Fellow nerds dont you know that 1+1=10 ;)
Join us now and the help make the internet a better place to live in.ATAOTW (Anti-troll association of the world)
it's simple and though the basis of all logic.
cb
PV=nRT
Karma = Mensa + Harvard
But, seriously. My favourite equation is (EURval/USDval)=EURperUSDrate, where EURperUSDrate is the current EUR per USD rate. Why? Because every time I use it, it means that I have some money.
Sincerely,
Pan Tarhei Hosé, PhD.
"Homo sum et cogito ergo odi profanum vulgus et libido."
It means the math exercise is done with you! ...seriously, having a 0=0 result for a systems of equations, more often than not means you did something wrong.
Working in the realm of web design and art, one of my favorite 'mathematical concepts' has always been the golden ratio. Now, I realize that this is really more a number than it is an equation, but at any rate it is truly amazing to experiment in the world of design with how shapes adhering to the golden ration often bring about more pleasing and content looking designs as well as playing with the inexpressible startling feel of a design with say, one aspect out of touch with the golden ratio whereas everything else adheres.
I once found a remarkable proof of this fact, and wanted to share it with the world, but there was not enough space in the signatures on Slashdot to write it.
One I always remember from schooldays.
General solution for a quadratic equation
If ax^2 + bx + c = 0
Then x = -b +/- (b^2 - 4ac)^0.5/2a
Couldn't see it in any of the other comments ;-)
It's 19:11:42. Do You Know Where Your Meat Body Is?
S entropy
k Boltzman constant
W number of possible microscopic states avaible.
An equation that ties disorder in the microscopic world (something invisible and fundamental) to such concrete things as temperature and pressure.
And entropy is probably the most fascinating concept in statistical mechanics.
I study particle physics but I always tought this is the most elegant equation I've ever seen.
PS
According to wikipedia:
"S = k log(W) is engraved on Boltzmann's tombstone at the Vienna Zentralfriedhof."
1+2+3+4+...=-1/12 !!!
In fact it's not a joke. It's called a zeta function regularization.
http://junk.niffux.org/blackwhite.gif Maybe you know it :)
The integral of omega on the frontier of theta is equal to the integral of d-omega on theta. In LaTeX: $\int_{\partial\theta}\omega=\int_{\theta}d\omega$
this post contain no useful information, no need to mod it down
Newtionian mechanics, nothing is simpler, more straight forward or less correct. Sure all you hot shot kids with your Relativity or String theory think your cool. Newtonian mechanics, understood and tamed since the greeks, but not written down until Newton. With Newton we get the industrial revolution, had the church been raigned in during Galalio we might have been on the moon hundereds of years eariler. Fewer things can be less obvious yet hit with such impact then Newton.
Of special importance to slashdot:
garbage in = garbage out
Jolyon
Please read my Canon EOS tech blog at http://www.everyothershot.com
1/3 = 0.333333...
2/3 = 0.666666...
3/3 = 0.999999...
Yet we are always told that 3/3 = 1
.nosig
my friend and i came up with this one the other day: stress = work / time
My favourite is any equation with one unknown - that means I'm one step away from (hopefully) getting something useful!
Stuck down a hole! In the middle of the night! With an owl!
The Integral of e to the x is equal to F times mu times N.
But seriously...
One of my favorites is equation 2.36 in my master's thesis (from waaaay back)..
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.
The equation that describes the Ballmer series of jumps in the monkey dance is a good example, as are chemical equations that embody observations about reactions seen under his armpits.
Maybe its me, but many people seem to like the number 4. Perhaps its because lots of people are always showing others that they can count to 4 on their fingers in binary.
My favorite is the integral of e to the x equals the functions (the 'f') of u to the n.
Write it out.
yes, I just copied and pasted from the article.
"Leo Fender was in a 'state of grace' when he designed the Stratocaster." -- Paul Reed Smith
why not f(n) = (phi^n-(1-phi)^n)/(sqrt(5)) ?
(actually I think I'm thinking of some other equation much like this one, but my math text and notes are in another room in this complex. oh well) [points for anyone who knows what phi and f(n) are in this case]
GENERATION 26: The first time you see this, copy it into your sig on any forum and add 1 to the generation.
1,782^12 + 1841^12 = 1922^12
Anthropic principle: We see the universe the way it is because if it were different we would not be here to see it.
I've been taught (BTW during my Electronics lectures) that equations longer than 6 cm are completely useless. Please keep this in mind during YOUR Electronics lectures. :-)
1/3 + 1/3 + 1/3 is interesting too. If expanded to decimal form, .3333.... + .3333.... + .3333.... = .999999....
.000....00001 comes from?
where does the last
I like to ask people if they know how to add, and when they answer 'of course I do', I ask them to explain that one to me.
1) goldener schnitth nittt ik/LineareAl gebra/Themenseitensourcen/Ebenen/ebenen.html ...
http://de.wikipedia.org/wiki/Goldener_Sc
2) hessische normalform
http://www.moses.tu-berlin.de/Mathema
3) the one to make the mandelbrot
f(x) = exp(-(x-mu)^2/(2*sigma^2))/(sigma*sqrt(2*pi))
No matter how much we try to be individuals, whe allways caught under this bell-shaped curve...
Whoever said philosophy and formula's don't mix?
I especially like the quotient rule, where we have f(x)/g(x): f'(x)=(g(x)f'(x)-f'(x)g'(x))/(g'(x))^2. Or, more easily, if we let f(x) be "Hi" and g(x) be "Ho" and say "D" for derivative, it becomes f'(x)=HoDHi-HiDHo/HoHo
sql = "SELECT .. FROM blah WHERE 1=1"
Then you can add any number of conditions with:sql += " AND x=y"
or you can make it even fancier with:sql += " " + operator + " x=y"
where operator = "AND" or "OR"
I've been slowly trying to figure out the Atiyah-Singer index formula. See here and here. Does someone know of a good discussion of this formula?
Apropos to the current discussion was this response:
you've made an error in your initial assumption, which gives a wrong answer
..
First we state that women require time and money:
Women = Time X Money
error--^
this should be
Women = Time + Money
and from there onwards
And as we all know "time is money"
Time = Money
Therefore by substituting Money for Time we get:
Women = Money + Money
Women = 2(Money)
And because "money is the root of all evil" we therefore can state:
Money = (Evil)^1/2
And Since
2(Money) = Women
and
(Money)^1/2 = Evil
And we are forced to conclude by substituting "women" for "(money)2" from above that:
Women = 2((Evil)^1/2)
or in words
women are double the root of all evil
which means absolutely nothing
but hey when you're a maths nazi..
Suchetha
learn from yesterday, plan for tomorrow, party tonight
or one out of three ain't bad
The first law of Unidynamics, formulated by a friend and I during our first year, when we had to move in and out of halls a total of six time:
Possessions expand to fill 110% of available vehicle space.
The second law stated that the final 10% would inevitably be found under the bed just when you thought you'd finished.
Predictive text is shiv!
exp( pi*i ) + 1 = 0
phi^n = F(n) * phi + F(n-1)
\Delta p \Delta x \ge \frac{h}{4\pi}
\frac{ \partial^2 f }{ \partial x^2 } + \frac{ \partial^2 f }{ \partial y^2 } + \frac{ \partial^2 f }{ \partial z^2 } = 0
Integrate Keynote and LaTeX
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
2B or not 2B == FF
In reply to your sig, the human organism is basically an omnivore capable of surviving temporary periods on a vegetarian diet. However, there are sufficient examples of humans suffering allergic reactions to a cereal-based diet for this to be a concern. Animals can be grazed on land unsuitable for growing crops, and are still the best way of creating a textured protein foodstuff.
If you want to deny your own mortality, fine, but just say "I'm in denial of my own mortality" and don't try to rationalise it or justify it with bullshit.
Nothing beats Fibonacci. Useful in many natural aspects of life, and yet so simple. The number is the sum of the two previous in the sequence.
1 59 7...
1,1,2,3,5,8,13,21,34,55,89,144,233,377,610,987,
When life is all around and threatening to destroy you, simply go to your happy place and count your numbers.. I got through many public stonings this way.
-/ demented wizard
I haven't got the full form handy, but these're the three dimensional equations for motion of fluids.. very elegant, very complete, and spawns a huge mass of special cases.
:)
As a former Aerospace student, I just had to pitch for good-old N-S
sale price - sale cost = profit works for me ;-)
B*4*i (U)^0.5 (RU/18)
( write it out longhand, replacing the power function with regular symbol... )
Here's a brain teaser - let's see if YOU can figure it out. And yes, it is correct and provable....
29 - 1 = 30
Have fun....:)
Ron Gage - Westland, MI
This is easy. :-)
E=MC2
Energy=Mornings X 2 cups of coffee
Works every time
Geek Hillbilly
0 + 0 = 0 0 / 0 = 0
alphaQ B Cos UR Sec C
gawds i'm so juvenile..
suchetha
learn from yesterday, plan for tomorrow, party tonight
or one out of three ain't bad
This, of course, is the Mandelbrot set.
Here's the proof:
1) x = y
2) x^2 = xy (multiply both sides by x)
3) x^2 - y^2 = xy - y^2 (subtract y^2 from each side)
4) (x + y)(x - y) = y(x - y) (factor)
5) x + y = y (divide out (x - y))
6) 2y = y (substitute y for x from #1)
7) 2 = 1 (What do you think of that?!)
try { do() || do_not(); } catch (JediException err) { yoda(err); }
Thats easy:
Girls = Time x Money
Furthermore, we take the statement, "Time is money", and we get:
Time = Money
Girls = Money x Money
Girls = Money^2
Moreover, the statement, "Money is the root of all evil" means that:
Evil = the square root of money
Girls = (Evil)^1/2 (Evil)^1/2
which reduces to...
Girls = Evil
Cookie to the first person who uses MathML" to show their favourite equation :)
In my opinion, the really interesting thing about all this is that you've worked out your axioms from your a priori certainty that 1 + 1 = 2. You chose your axioms to suit that truth, right? I mean to say that any old fool who can add one and one will give you "two" as the answer, but talking about identity operators is a rather more sophisticated concept. It's not like we defined the axioms first, and then figured out that "1 + 1 = 2" follows from the axioms, is it? Seems like cheating, doesn't it?
proof, n. A demonstration that a conclusion is implied by certain premises and axioms.
Good old beeb, and no need for registration http://news.bbc.co.uk/1/hi/magazine/3721406.stm
Mine is 1+1=3 where the 3rd one is a little small, helpless, stinky meat-popsicle out to ruin your life the bigger it gets. And the 2nd one gets bigger and bigger afterwards, so that it ends up being 1.5 after a while, sometimes even 2 on it's own. The 1st one is left to wither away on it's own so that it actually gets less and less until it just becomes a zero trapped in the daily rat-race of stress,anger and misery trying to support the other two.
Maybe I'm just bitter...
"I used to have that really cool,funny sig
This was a poll topic in a past life.
proof, n. A demonstration that a conclusion is implied by certain premises and axioms.
E = MC^2
For one simple reasonI've read quite a few books on relativity , still the equation remains the first thing that comes to my mind . Hopefully the grand unified field theory will have such a simple equation behind everything in the world.
Quidquid latine dictum sit, altum videtur
2-1=0
home
How about Ramanujan's equation for PI? It's very simple, but has got some really interesting numbers. A graphical version is available here.
1/PI = sqrt(8) / 9801 * sum (n = 0 to infinity) (((4n)! [ 1103 + 26390 n ])/ ((n!)^4 * 396^(4n)))
1 + 1 = dupe?
In one way, being enthralled with any equation is just self-congratulatory. The world around us is the reality, the equations are just forms of communication that we have invented to talk to each other about it.
1+1=2?? That's just a way to write down on paper what any toddler can show you with two pieces of candy. All else is just higher levels of same.
In school we had a joke going around about Euler's formula and a crackpot professor we have from Kentucky.
It goes like this:
In Kentucky Euler's formula is simipified to:
Ke^ntucky=Kentucky
Damn he had a confused look when he saw that written on his board.
x / 0 = ERROR!!
Buy the President
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.)
I quite like
(1+2+3+4+5+....+n)^2 = (1^3+2^3+3^3+4^3+...+n^3)
It seems to come straight out of nowhere - it's not easy to see WHY it's like that (easy to prove though), and the generalisation to other powers is a messy thing involving Bernouilli numbers.
But under normal circumstances, euler's formula with the e's and the Pis and the square roots of minus one would get my vote.
Or in SKI combinator form:
Y = S (K (S I I)) (S (S (K S) K) (K (S I I)))
Or possibly even in SK form:
Y = S (K (S (S K K)(S K K) )) (S (S (K S) K) (K (S (S K K)(S K K) )))
2 + 2 = Thomas Jefferson
It's that new math.
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.
This simple formula changed the world when Einstein proved it's truth.
t=$
Where:
t=time
$=money
At least that's what they seem to be teaching in U.S. schools.
http://alternatives.rzero.com/
While you basically never use the equation and mostly just look stuff up in tables, any Electrical Engineer or anyone else doing differential equations has to love this one:
Y(s)=integral(exp(-st)*y(t)*d(t),0,infinity).
I remember this making a great many problems in my EE classes easier. Second is the fourier transform, mostly because its Discrete form makes my Digital signals class so much easier. Guess I have a thing for some hard to type equations.
"Some days you just can't get rid of a bomb."
believe nothing...test everything.
There was an unknown error in the submission.
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.
Why hasn't anyone mentioned the Rendering Equation yet? :-)
I'd type it right here, but it's not really ascii compliant. And it's too damn complicated if you want to get it right.
Oh well, forget it. Euler's ain't too bad...
a^2 - a^2 = a^2 - a^2 :=: :=:
a ( a - a ) = (a + a) * (a - a)
a = a + a
substitute 1 for a: 1 = 2.
my other sig is a 500 page novel
ET/k9 = kPAx the famous Western synergy system.
0+1 = 1+1 = 1*1 = 1/1 = 1
Other than that, Euler's jobby, or anything involving j (I'm an electronics engineer, so i is current - and no cracks about 'i am current' either!)
I see this equation on alot of bumper stickers where I live..... Marriage = 1 man + 1 woman Certainly not the most elegant- but is does seem to be popular.............
To denote in Maple notation,
F(s) = int(exp(-s*t)*f(t),x=0..infinity);
Although not officially an equation, more of an operator, the Laplace transform is extremely useful in my program of study (computer engineering) and it makes complex problems much simpler to solve.
There is another kind of evil which we must fear most, and that is the indifference of good men. -- Boondock Saints
Comment removed based on user account deletion
Okay, another take on it.
We know that
1) Time = Money
It is also well known that
2) Knowledge = Power
And most of you will know that
3) Power = Work / Time
Substituting 1 and 2 into 3, we get
4) Knowledge = Work / Money
Rearranging 4, we get the inevitable conclusion
5) Money = Work / Knowledge
Therefore, the more you do, and the less you know, the more money you make. Damn, I should never have gotten this stupid Masters degree!
Music speeds up when you yawn, but does not change pitch.
I'd go with Reynolds Transport Theorem or possibly Bernoulli's equation. A whole lot of the modern world wouldn't exist without mathematical representations of fluids.
Planetes
"One World, One Web, One Program" - Microsoft Promo Ad
"Ein Volk, Ein Reich, Ein Fuhrer" - Adolf Hitl
2+2=5
often used in discussion about synergies.
x=x+1 ? or does that count as two.
GENERATION 26: The first time you see this, copy it into your sig on any forum and add 1 to the generation.
DeltaMi-1=aSigman=1Di(n)(SigmajEC(i)Fij(n-1)+Fexti (n-1))
Ever seen the face in this song ?
http://www.eeggs.com/items/34824.html
This phenomenon can be expressed with expression. This is not special effects but the actually conducted experiment.
Most useful equation in college: alcohol + girl = sex.
I'm pro-Bush but I think you didn't deserve to get modded as troll. I'm still laughing now..
:-)
This is obviously a plot to show that republicans don't have a sense of humor. I bet you got modded down by a democrat
Please login to access my lawn
lim 5->4 sqrt(5) = 2
Apache guy, Open Source enthusiast, runner
That's only true for horse shoes, hand grenades and 1950s chemotherapy.
sqrt(-1) == j
You can't just start throwing around meaningful things like i. You insensitive clod.
exp(j theta) = cos(theta) + j sin(theta)
There should be a moderation category "Dumbest Comment EVER"
"All men are mortal
:-)
Socrates is a man
Therefore, all men are Socrates."
"The last scene was interesting from the point of view of a professional logician because it contained a number of logical fallacies -- that is, invalid propositional constructions and syllogistic forms -- of the type so often committed by my wife."...
Monty Python
i^2=-1
or Sqt(-1)=i
oe for all the EEs out there
j^2=-1
cos(theta)^2 + sin(theta)^2 = 1 That one's just fun to derive, imo.
WARNING: DO NOT LET DR. MARIO TOUCH YOUR GENITALS. HE IS NOT A REAL DOCTOR.
" Congratulations, a^2 = b - 1, you are the Equation of the Week!"
(There was a tshirt available, but it's been discontinued as of just last week. Sorry)
I think my favorite of all time is the integral of 1/x from 0 to infinity, which diverges, and the integral of the rotation of 1/x, which is the integral of pi*(1/x)^2 which converges to pi. I always found that to be kinda cool
I really like the reference to Hamilton inside the wave equation. Back in the early 1800s Sir William Rowan Hamilton was working with ways to express optics and dynamics with a single equation framework. At the time, the effects were mainly felt in optics, but it presaged quantum mechanics.
The living have better things to do than to continue hating the dead.
1+1=9
;)
The point is this: he who sows sparingly will also reap sparingly, and he who sows bountifully will also reap bountifully.
I'm expecting that slashdotters don't get how those two things are connected.
For some have might have seen this in version 1+1=3 but I think the text explains why thats my favourite equation in that form
Emacs is good operating system, but it has one flaw: Its text editor could be better.
E=MC Hawking!
Monstar L
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.
Still, people's "serious" attacks on various Christian attitudes towards money usually hinge on the misquote. Just some trivia to brighten your day.
You cannot apply a technological solution to a sociological problem. (Edwards' Law)
So have \. polls evolved? Rather than voting, we're skipping straight to bitching about choices.
My best liked equasion:
2 + 2 = 5 (for large values of 2)
how about the proof that girls are evil?
Merlin
*ducks*
Rewrite x+1=S(x) as x+S(0)=S(x).
Substitue x = S(0), S(0)=S(0)=S(S(0))
What am I missing?
That should have been S(0)+S(0)=S(S(0))
The following sentence is true. The preceding sentence was false.
Sorry, had an accounting midterm last week...
Integral of z^3 over (1, 3^(1/3)) *cos(4*pi/9) = log(e^1/3))
Integral z cubed dz From 1 to the cube root of 3 Times the cosine Of four pi over nine Equals log of the cube root of e!
(I may have gotten this wrong, as the two terms are only identical to three decimal places on my calculator.)
Without a doubt the most important equation of all time is the theorem of Pythagoras:
a^2 + b^2 = c^2
It is found virtually everywhere in mathematics and physics: from grade school geometry, trigonometry, calculus, non-Euclidian geometry..., to the Tanyama Shimura Conjecture.
an ill wind that blows no good
Not mine, I saw this on http://pasky.ji.cz/
First we state that girls require money and time:
girls = money * time
As we all know, 'time is money':
time = money
Therefore:
girls = money^2
And because 'money is the root of all evil':
money = sqrt(evil)
Therefore:
girls = sqrt(evil)^2
And we are forced to conclude that:
girls = evil
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."
Buffon's Needles has always amazed me. It is a theory that finds the value of pi.
pi = 2*n/c
Just get a table with parallel lines on it drawn one inch appart, and get lots of needles one inch long. Lay down the needles randomly. (Diagonally, too)
n = number of needles layed down
c = number of times a needle crosses a line.
f(x) = \frac{1} {\sqrt{2 \pi \sigma^2}}
e^{\frac{{x-\mu}^2}{\sigma^2}}
X*1=X
X^1=X
Without these, algebra comes significantly harder.
Kime = FV @ impact.
.sig for you! NEXT!
It's a martial arts thing. Kime, or focus, equals force times velocity at impact. I.E. The harder you hit them the harder they fall.
-- No
-- coding for the proletariat since 1977
How can you deny the goodness of the master theorem?
-
ping -f 255.255.255.255 # if only
Fractals of course can be produced from many different equations, but the iterative process of many simple equations produces amazing fractals:
x=x^2+1 where the "=" should be a two way arrow.
P.S. is there a keyboard encoding for a two way arrow? How about in UTF-8?
To this day if I get a whiff of that perfume she used to wear I can't help thinking about mass balance equations.
Those were great days.
That's our life, the big wheel of shit. - The Fat Man, Blue Tango Salvage
'nuff said.
1 + 1 + 1 = 3
Got to be good looking cause he's too hard to see.
Quite a few here have suggested that elegance could be sought in the geometric realm. a^2 + b^2 = c^2 is quite interesting, very useful for many things.
However, one equation does stand out. In 1637, a Frenchman who had mathematics as a hobby made a seemingly innocent note in the margin of one of his surprisingly few math books (Arithmetica):
"It is impossible to split a cubus into a sum of two cubi, a 4th power into a sum of two numbers in the 4th power, and in general any power greater than 2 into a sum of two powers equal to the first, for which I have found a truly wonderful proof. This narrow margin, however, cannot contain it."
Sounds interesting? Unfortunately, when he died in 1665, the proof was never found. A proof, but unlikely the same, was announced in 1993, and published in 1995.
Pierre de Fermat was the name. Mathematicians like Euler and Cauchy failed to prove this. This was the problem that sparked my interest in mathematics, not only because of the statements simplicity, but also the history of the problem. Blood, sweat and tears, indeed!
1.99999 = 2
A^2 + B^2 = C^2 By far, my favorite.
Pretty Pictures!
Maxwell Equations! They just work! They were formulated before relativity theory was out, yet they proved relativity invariant. As soon as you write them for real media instead for the void they work a little worse, though...
don't ask me why. I always liked that one.
And people wonder why women are discouraged from pursuing math and science.
I was amused to see the ideal gas law amongst the contenders, written as PV = nRT where n is in some weird units and R is some weird constant.
A much nicer form is:
P = nkT
where n is the number density of particles and k is Boltzmann's constant.
For some reason chemists persist in using 12 divided by the mass of the proton in grams as the basis for all measurement, and this choice leads to a proliferation of strange constants and units. I know there are historical reasons for this, but one only has to look at the way physics has re-invented its notation and concepts repeatedly over the years to realize that historical reasons are no excuse.
Written in a sensible form, the idea gas law is a very beautiful equation, though not so beautiful as the Dirac equation, which is the only differential equation in physics that I'm aware of that describes reality and only reality.
All the other equations we use have non-physical as well as physical solutions, and we quietly throw out the non-physical solutions. We sometimes even try to maintain that mathematics is "unreasonably successful" as a means of describing reality, when we know perfectly well that half of what our equations describe has no physical counter-part, but is just an ugly artefact of an imperfect description.
Blasphemy is a human right. Blasphemophobia kills.
My personal favourite, as found in "Pi and the Arithmetic Geometric Mean" by JM Borwein and PB Borwein, Wiley, 1987.
Surely a serious contender for most elegant equation must be M = PQ and the associated factoring problem when given M and the knowledge that {P, Q} are prime and P Q. This is without doubt one of the simplest bit of maths to explain to anyone. It is also almost as old as multiplication itself and fundementally uncracked by modern number theory. A number theory problem that is expressed by 4 symbols and can be explained to a child of 10 that has confounded mathemeticians for centuries and continues to do so. How elegant and wonderfully fiendish is that?
...and, on the seventh day, God switched off his Mac.
The foundation of all computation.
http://en.wikipedia.org/wiki/Lambda_calculus
Higher Logics: where programming meets science.
This news story was in The Times about a month ago... I can recall it interviweing some of the people that voted for 1 + 1 = 2 as the best equation. Euler's was probably the best of them. In itself it seems to show the beauty and... strangeness of math in that three entirely irrational numbers that you'd feel have no link whatsoever can be so intristically linked.
My favorite equation is from the Beatle's song "Come Together": 1+1+1=3
John Lennon's formulation of the Christian Trinity.
The theorem is: let {a_n} be a series of independent and identically distributed random variables with variance sigma^2, S_n be its partial sum (in other words, S_n=a_1+a_2+...+a_n), then
lim sup_{n->infinity} abs(S_n)/(sigma*sqrt(2*n*log(log(n))))=1, almost surely.
To put it more plainly, suppose you do a random walk, starting from origin, and every second you goes one step right or left with equal probability and independent from your earlier steps. Intuitively, as time goes by, you will reach places farther and farther from the origin. Indeed, after n seconds and for very large n, according to the central limit algorithm (which is taught in most elementary probability classes) your position will almost follow the Gaussian distribution with a standard deviation of sqrt(n) steps. In other words, after n seconds, you will have about 5% chance to be more than 1.96*sqrt(n) steps from the origin, a 0.1% chance to be more than 3.29*sqrt(n) steps from the origin, etc. However, it is always possible that you be as far as 10*sqrt(n) or 100*sqrt(n) from the origin (of course no farther than n steps), though the probability is very small. This theorem in a sense puts a limit on this variation of your distance from the origin. It basically means that almost every time you do such a random walk ("almost surely" means "with probability one", so it can fail to happen in principle but not in real life), you are going to get farther than sqrt(n), or 10*sqrt(n), 100*sqrt(n), etc., at some (possible very large) time n; indeed you will get as far as sqrt(1.999*log(log(n)))*sqrt(n) for infinitely many times; however, if you happen to get as far as sqrt(2.001*log(log(n)))*sqrt(n), take care to record that splendid event, for it will happen only for a finite number of times, after which you will never get this far (relative to n) during this random walk! Sounds a little complex, but simpler propositions such as "you will never get farther than 5*sqrt(n) before time n" are obviously wrong.
It is fascinating because stuff like log(log(x)) does not occur very often in fundamental mathematics (except maybe in the complexity analysis of algorithms), but it occurs here as a very strong and important result concerning a problem often met in everyday life.
Slashdot + link = server meltdown
2 + 2 = 5
Integral from 10 to 13 of 2*X dx.
You'll have to prove you're a real nerd and solve that one.
lorenz, founder of chaostheory, he made a simple model to describe the climate of earth, where the whole weather system is described with 3 variables, so this is NOT to predict the weather
dx/dt = s (y - x),
dy/dt = r x - y - x z,
dz/dt = x y - b z,
where x,y,z are variables
and s,r,b are constant parameters
i would give more fractal equations, but lorenz remains my favourite
Mainly because using them is somewhat an art form.
I Think your browser Sucks. I would suguest that you stop using IE. In Mozilla I get e^(i) + 1 = 0 and (the Greek Simbol of Pi) != n although they look simular in the small font
If something is so important that you feel the need to post it on the internet... It probably isn't that important.
Power = VI
twinkly twinkle little star
circumference equals 2 pi 'r'.
I'm a sucker for rhymes.
or A = Pi*r^2
I've known this equation for over twenty years and yet I still find new meanings and uses.
Proof right here: http://www.math.toronto.edu/mathnet/falseProofs/fi rst1eq2.html
Of course everyone here knows that I divided by 0.
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!
========
77 77 77 2e 6d 65 6c 76 69 6e 73 2e 63 6f 6d
And to further prove my point I actually screwed up. You have to have a more complex multiplication for this to be a field at all. The counter example still workse since any vector added to itself is 0 but not all vectors are invertable in my original.
nm
-- Boycott Shell
(you - clothes / legs) * (me - clothes)
The Jargon File quotes that one as "pi = 3, for small values of pi and large values of 3."
(particularly unfunny in FORTRAN, where you could redefine the value of integers by saying things like "LET 1 = 4". Try debugging the code that comes after THAT!
- mark
-----
I tried an internal modem, but it hurt when I walked.
is \int_{\-infty}^{\infty}e^{-x^2}dx = \sqrt{\pi} with the associated quotation from Lord Kelvin:
A mathematician is one to whom that is as obvious as that twice two makes four is to you. Liouville was a mathematician.
test
1 Bourbon + 1 Shot + 1 Beer = :)
It is better to be the hammer than the anvil.
How about: Re[Zetafunction] = 1/2.
Prove it and get a million dollars!
I has all sorts of links to the gamma function (factorials), and primes. Good stuff galore.
For the benefit of those who can't read TeX, that's
where is a binomial coefficient.As a computer scientist, I quickly learned:
1+1=2 (already knew that)
1+1=1 (boolean)
1+1=10 (binary)
1+1=11 (unary)
Come on? My favorite equation? Wha?
2+2=4, you know the Reference
http://open-encyclopedia.com/Drake_equation that estimates alien civilizations
/ x n
|e = f(u)
Need I say more?
If a + b = c
then
(4a-3a)+(4b-3b) = (4c-3c)
4a + 4b -4c = 3a + 3b -3c
4(a+b-c) = 3 (a+b-c)
4 = 3
More here
To measure the power of a gas boiler, knowing the flow rate V litres per minute and the inlet and outlet temperatures, just multiply the temperature difference by the flow rate by 0.07.
..... (1)
Q = m * c * theta
In one minute (=60"), we have V litres of water flowing, or about V kg. So dm/dt = V/60 kg s-1. c is about 4168 J kg-1 K-1. But it'll be easier to handle power in kilowatts, so we shall divide everything by 1000.
Power = flow rate [LPM] / 60 * 4.168 * temp diff [C]
= flow rate [LPM] * temp diff [C] * 4.168 / 60
= (about) flow rate * temp diff * 0.07
That's as close as you're likely to get it anyway due to system inaccuracies.
Je fume. Tu fumes. Nous fûmes!
6 x 9 = 42 It sums up all life. IE You never get what you expect from life.
ln(-1) = PI * i
...
sqrt(-1) = 1 * i
PI = (Taylor's eulerian logarithm of -1) * -i
PI = (Euler's taylorian logarithm of -1) * -i
PI = Ramanujan's equation
Who did first invent the equation of the longest real of PI?
open4free ©
Obviously...
Originally seen as integral of e^x = F(u^n), but tough to make integral sign without special characters.
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
Avagadro's number: N=6.02*10^23
Hey, that's really deep. Maybe you should get together with this guy.
It isn't that great an equation.
I distinctly remember reading somewhere, that there is nothing special about the equation
e^{i\pi} = -1 % (TeX notation)
It's just the consequence of the way that exponentiation on complex numbers is defined.
Sorry, can't find the link to it now.
Robert
Bastard Operator From 193.219.28.162
1 + 1 = 10
The function of multiplying s times the exponentional of x is equal to a function of u to the nth power. This is the greatest equation of all. S*e(x)=f(u^n)
Though it was mentioned in the article lead-in, I prefer the form
e**(pi)i = -1
to the form
e**(pi)i + 1 = 0.
Don't underestimate the power of The Source
Drake Equation : N = R* fp ne fl fi fc L
--
Try Nuggets , the mobile search engine. We answer your questions via SMS, across the UK.
-1 = i^2 = i * i = sqrt(-1) * sqrt(-1) = sqrt(-1 * -1) = sqrt(1) = 1
My discrete math teacher in uni got us scratching our heads for a while before he explained what was wrong with that "equation".
E=MC2
is the most important equation...
After 7 years in college getting fancy degrees in Math and Physics, there's still something I don't get: Thermodynamics. So my Favorite is my Nemesis: PV=nRT. I can only thank God I took statistical thermo instead of physical thermo, or that blessed C wouldn't have allowed me to postpone being a grown up for a few more years in grad school :-)
I've always been intrigued by Bayes Theorem myself.
For those who's eyes glass over while reading the explanations in that wiki link, you may find this intuitive explanation of Bayes Theorem (complete with Java applets) a bit easier to wrap your mind around. As for why folks think it's important... it's the basis for the Scientific Method. It's also a candidate for one of the fundamental principles of AI: the ability to draw conclusions intelligently. Be careful, reading about this could suck up half of your day. Of course, if you wanted to be productive, you probably wouldn't be reading Slashdot in the first place.
Hell is being intelligent in a world full of idiots.
--
Try Nuggets , the SMS search engine with question answering technology.
Grad skul joke:
Knowlege = Power
Power = Work / Time
Time = Money
Therefore,
Knowledge = Work / Money
(The more you work, the more you know. And if you want to know alot, you go to grad skul, where you hardly get paid...)
F(n) = F(n-1) + F(n-2). This has got to be up there. This series is supposed to show up practically everywhere in nature.
I would rather be killed by a terrorist than enslaved by my government.
0/0 = 1
1/infinity = 0
What makes you think IE doesn't display Pi correctly? Next time you might as well say Pi does not display correctly on Mozilla compiled by Microsoft/RIAA/MPAA/SCO/RFID/DRM/LOL/LMAO.
a^2 + b^2 = c^2
...who actually sees a Pi in the original posting formula?
I don't have a sig.
mmmm, P=IE!
I remember being 11 and since I was in the "advanced" math group, we were being taught the beginnings of algebra. Basic stuff like exponents and solving x + 7 = 5 solve for x, etc. I noticed an interesting shortcut for figuring out the square of a number. I could always just get the square of the previous number and add two, and it was always an odd number. So, not knowing all the symbols and stuff I wrote down an explanation of this somewhat like "If you have x^2, then all you have to do is start with 1, and for every square bigger the difference is you add two." A little while after this I was graphing Y=X and noticed that the row and columns that intersected it were always one larger each time Y=X grew by one. I knew the area of the square covered by it was related, and when I worked out the numbers I figured out how it related to what I was talking about earlier, and then wrote that down too.
My teacher, when I showed this too her just went "that's nice, but you shouldn't use shortcuts for things like squaring numbers because shortcuts don't always work and you might get it wrong and then if you can't show your work you get no credit." My parents did something similar. Even when I used the same things for a "math project" we were made to do in 9th grade or so a few years later, I got alot of "Well it's interesting but so what?" even though by then I'd found a way to expand it to more than squares. The way I did was after alot of agonizing time with a calculator trying to figure out the shortcut for cubes, I figured out that all you have to do to make a bigger cube is take the existing cube, throw a square of depth 1 on each side, throw 3 lines of length one an depth 1 inbetween those squares, and then throw an extra 1x1x1 in the corner. Doing it with a 4D version (which I didn't know the name for at the time but I'd assume it's a tesseract) I guessed would involve adding some cubes, some squares, some lines, and the 1 block again. After a bunch of work with a pocket calculator doing trial and error I figured out it was 4 cubes, 6 squares, and 4 lines. And from there I figured out a way to get the answers for higher numbers in the X^N series.
But nobody ever really cared when I showed it to them.
10 years later, I was forced to retake calculus 2 in college after my school decided my AP credit now only counted for calc 1 instead of 1 and 2 because they'd switched from 3 credit to 4 credit classes. Since I barely remembered my precalc stuff I had my mother ship out all my math notebooks (which is easy when you've been colorcoding your notes by subject all through HS) so I'd at least have all my old cheatsheets.
When I got the oldest yellow book in the stack, I flipped through it and found the pages where I'd first written this stuff. I reread it and then it suddenly made alot more sense when I knew what symbols you'd really use to express that idea. They were:
X^2 dy/dx = 2x+1
and
(integral)2x = X^2
and the expanded form from later?
x^3 = 3x^2 + 3x + 1
x^4 = 4x^3 + 6x^2 + 4x + 1
and from there figuring out if you lined them up in a row and added the two numbers on either side from the row above you go the next row, like this:
1
1 2 1
1 3 3 1
1 4 6 4 1
1 5 10 10 5 1
1 6 15 20 15 6 1
etc.
These days of course, nobody ever believes me when I tell them I figured all this stuff out between the ages of 11 and 14.
To this day I still hate math, and can't do algebraic long division because I use my own shortcuts for doing it with actual numbers, much to the dismay of my statistics professor who was amazed I could divide 5 numbers into 9 in my head in less than 10 minutes but not simplest algebraic equations into another even with writing it out and all the time in the world.
Introducing the new Occam Fusion! Now with sqrt(-1) fewer blades!
Pythagoran Theorem
a^2+b^2=c^2
I'm fond of Euler's equation, but in my line of study (Computer engineering) However Ohm's law I see nearly every day in some form or other (Lab work or Network theory classes)
If you can't see the value in jet powered ants you should turn in your nerd card. - Dunbal (464142)
Richard Feynman once famously remarked that Euler's Identity was the most remarkable equation in mathematics, since it combined all the really important numbers into one formula. Recently while attempting to formulate a technically-oriented conlang, I was considering what numbers really were important and concluded that there was one number of massive significance that was left out, and another was formulated somewhat arbitrarily.
Firstly, 2 is a very important number. 0 is null and the origin, 1 is unity - but 2 is the purest expression of difference and distinction. Dualism is everywhere: 0-1, On-Off, Up-Down, Left-Right, In-Out, Real-Imaginary. Everything has its opposite. Many concepts can only be considered in the context of two objects or states. 2 is the base of the humble but indispensible bit - and consequently the base of the logarithm that yields the number of bits necessary to express a number or code. 2 is indispensible.
Secondly, Pi was chosen somewhat haphazardly. For the unit circle of radius 1, Cir = 2*Pi. Pi is the ratio of a circle's circumference to it's diameter. But from a mathematical standpoint the diameter is not what's important - the radius is. Wouldn't it make just as much sense if not more to use the ratio of the Circumference to the radius (here designated as Cir)? The way things are formulated now, Pi is half a cycle in radians, halfway around the unit circle. Wouldn't a constant that represents a full cycle, Cir, make more sense? Have we grown so used to Pi that we have forgotten the arbitrariness of it's formulation?
Of course if you choose to use Cir, 2 naturally works its way into Euler's equation as well.
Exp[i*Cir/2]+1=0
Mathematicians, please respond.
---If you can't trust a nerd, who can you trust?
0! = 1 Not for its beauty, but for it's craftsmanship.
Me: Nevermind
The Angleof the Dangle is Inversely Proportional to the Heat of the Meat.
--Beavis and Butthead
followed by SQRT(69)
Maxwell's equations cannot be topped, IMO. Not only do they look cool, but I hear you can actually calculate stuff with them. Maybe.
N+1=N
-=[ Who Is John Galt? ]=-
ELI the ICE man!
Remembering that EMF is just another name for voltage:
V = L * ( dI / dt)
I = C * ( dV / dt)
COMEDY = TRAGEDY - PANTS
indeed..
.999... = 1
that just messes with my head.
I don't have the charset to write it up here, but those of you that are familiar with it no that there is no bound (no pun intended) to it's utility. Here's a link to the equations on MathWorld.The extensions of this theorem, the Laplace integral and Z-transform are equally important. These equations enable us to project functions of time onto periodic functions which we can then use to analyze the frequency content of the original function. They also enable us to easily solve differential equations and discrete difference equations.
Mike
Intel transfer the difficult from Hadware to software, for get more power, programmer need more technology. -- chinaitn
Isn't it amazing that:
for any value of n,
n * 0 = 0
yet n / 0 = either infinity or is undefined
that I ever learned in college:
R(yE)^12=Pi(EyD)
IANALOOA
My favorite has got to be 1 = 2. Here's the proof.
x = x
x^2 = x^2
x^2 - x^2 = x^2 - x^2
x*(x-x) = (x+x)*(x-x)
x = x+x
x = 2x
1 = 2
Ie: 2 raised to the power of the number of integers,
equals the number of real numbers. I think this
can be credited to George Cantor.
What does that mean? :)
In this world nothing is certain but death, taxes and flawed car analogies.
Doubleplusgood.
--
If I actually could spell I'd have spelled it right in the first place.
1 + 1 = 69
;-).
Beats anything you geeks can come up with and I doubt that most of you can solve it
That's not an 'n', but a pi symbol. Anyway, my favorite equation is: t1=t0(sqr(1/(v/c))), known as a Lorentz Transformation Equation.
2 + 2 = 11
all in radix-3, of course.
Since you mentioned ThinkGeek, the concept is more in lines with this one.
This is not my sig.
It's a truncated taylor series expansion. At home I have a copy of the paper that Einstein published. Anyway, here is the first link that poped up on Google showing this. The point is, if v is a significant fraction of c, then you cannot neglect the higher order terms.
"Uh... yeah, Brain, but where are we going to find rubber pants our size?" --Pinky
7129 / 6105195
So just that you know, my fav:
2 x 2 sometimes= 5
Not as solid as 1 + 1 = 2, but nothing compares to the beauty of unknown, unpredictable and breaking rules.
Eventually everything we know for certain, becomes boring, no matter how exciting it might have been initially.
Just a Random.Idea.
42
How come we still can't render these beautiful, important equations in XHTML?
Har dee har har!
I like to place meaningful quotes in my sig, so people will know that I know what meaningful quotes are.
You + me... + her too, simultaneous
You + me... + your momma + your sister =
Simultaneous lovin' baby, * two or three...
P ? NP It was even floating around in that episode of the Simspons where homer goes into the dimensional warp, lol.
This one is easy because it describes static thermodynamics (ie a system that isn't continually changing).
So, here we go. Let's assume we have a little ball filled with a gas. The ball has a volume V. The gas inside the ball is at a pressure P. The number of moles of gas we have pumped into the ball is n. The temperature at which the gas inside of the ball is at is T. And scientists before us have determined that all of these parameters are related to each other through a constant, R. So, we know all of this information: we know the V of the ball, we know the P of the gas, we have put in n moles of gas, we know the constant R, and we know the T of the gas.
Now, the equation states PV=nRT is always true for this little 'system' (our ball). So, let's change one of the parameters and see how it affects the other parameters. Let's heat the ball up to raise the T a known certain amount. So, we place the ball in the oven and let it heat up a tad. Now, what has changed? Well, let's assume that the heat does not deform the ball at all, so V doesn't change. We have not put in or let out any moles of gas, so n doesn't change. R never changes (it's a constant). And we have changed T ourselves, so that means that P must change.
So, using the same V, n, and R values as before, plug in the new T temperature value (after heating) and solve for our new P pressure value. This is what the pressure will be after we heat the ball to our new T temperature.
This is the most basic example of how to use this equation. As well, this equation is called the "Ideal or Perfect Gas Law" and assumes all gasses act in a ideal or perfect manner. In reality, gasses don't act exactly ideal or perfect and the ideal gas law needs modification to accurately predict the behavior of real gasses. However, this is a good start and let's you 'roughly' approximate how 'close-to-ideal' gasses behave in simple laboratory experiments.
Arithmetic identity: 37 * 3 * 7 = 777
Algebraic identity: a^2 - b^2 = (a + b)(a - b)
Trigonometric identity: sin 2x = 2 sin x cos x
Also, 2dL + N = kb + d, which doesn't mean anything to any of you because I haven't told you what the letters stand for.
P = NP
Now, if I could just prove it!
... saw these as grafitti on the engineering building walls in the university I went to.
lim GPA = B.A. (self explanatory)
GPA->0
sin(x)
------ = 6 (the n's cancel each other out)
n
I think Intel's least favorite simple equation is:
4195835.0 / 3145727.0 < 1.3338
Here
are
a
few
articles to refresh your memory.
Gotta love calculus.
first proof, that i'd seen at least, of the existance of negative numbers.
negative numbers exist by definition, dude. you start with natural numbers - 0,1,2,3,4.. and summation. once you want to reverse 'the plus', you define negative numbers. then when you want to invert multiplication, you get rationals. then when you want to invert exponentiation - you get irrationals. get it ?
3.243F6A8885A308D313
This one was e-mailed to me by a teacher
When asked to answer a question about circular math proof(I don't know) the written answer was
Fork + Spleen = shoe
The student appeared to be panicking at that point in the paper.
Negative numbers exist in nature, in electricity.
The equation I use the most is definitely "F = m a" in all of its interesting forms. I would give that a number one rating.
But the most intriguing are the Navier-Stokes Equations. It's amazing that just by changing the boundary conditions on these dynamical equations, you can completely change the behaviour of the flow.
For incompressible flows of common fluids, these 3 simple equations make incredibly accurate predictions:
du/dx + dv/dx = 0 (incompressibility eqn)
du/dt + u du/dx + v du/dy + dP/dx = 1/R ( d^2 u/dx^2 + d^2 u/ dy^2 ) (momentum-x eqn)
dv/dt + u dv/dx + v dv/dy + dP/dy = 1/R ( d^2 v/dx^2 + d^2 v/ dy^2 ) (momentum-y eqn)
4(x+2) = 5(x+2)
4 = 5(x+2)/(x+2)
4 = 5
This sig is better than nothing!
Here's a few that harken back to my college days in elecrical engineering (EE):
lim Engineer = Business Major
GPA ->0
lim EE = Industrial Engineer
GPA ->0
The PC Weenies: Tech toons for tech enthusiasts.
The PC Weenies: 11 Years of Online Tech 'Too
I would post my very best secret formula here on Slashdot, watching with a smile how it gets unnoticed and zero score, just becouse I would submit it as Anonymous Coward.
Just a Random.Idea
Maxwell's equations in the quaternion form are simultaneously deep, simple, symmetric, and intuitive, but for mind-expansion you can't beat the quantum wave equation.
-I like my women like I like my tea: green-
x++;
Know your pads. One time pad: good for cryptography. Two timing pad: where to take your mistress.
pp
___ = bb
tt
- these are not the droids you are looking for -
I was objecting to P=VI. The power dissipated in an AC circuit, or indeed any circuit where the voltage is changing and inductance or capacitance is present, is neither instantaneously equal to VI, nor is the energy dissipated the integral of VI by t.
Clearly some people were so anxious to show how clever they were, they didn't make it to the second half of the original post.
In fact, V=IR is of limited real world use. To be really pedantic, it is the sum of all the instantaneous potential differences around a loop that is equal to the series resistance multiplied by the current. When AC is applied to real world devices like tungsten lamps, there is temperature variation of the resistive part which makes the whole equation much more complex. I stand by my original comment, which is that in real-world AC applications, which EEs come up against daily, the simple formulae are of limited use.
And, if we are being really sticky, voltage and current are measured in vector fields. Unfortunately /. doesn't allow me to reproduce the formulae I had to master as an undergraduate, but they are more fun than the simple versions suggest.
I don't mind people correcting my mistakes, but I do mind people who don't really know the subject trying to be clever.
Panurge has posted for the last time. Thanks for the positive moderations.
B4I4Q RU/18 QTpi
Srinivasa Ramanujan: He was self-taught but had an uncanny mathematical manipulative ability. Independently, he discovered results of Gauss, Kummer and others on hypergeometric series. He is known for major contributions in Number Theory and Modular Function theory.
f
Ramanujan worked out the Riemann series, the elliptic integrals, hypergeometric series and functional equations of the zeta function on his own. On the other hand he had only a vague idea of what constitutes a mathematical proof, and occasionally did state incorrect results.
Ramanujan was reported to have dreams where Indian deities would paint this an other equations in blood on his mind.
This formula as far as I can tell came from nowhere but a strangely tuned up mind
http://www.bath.ac.uk/~ma2lg/project/ramanujan.gi
Slashdot's inferior "lameness" filter won't allow formulas to be written textually with elegance.
1/pi = [sqrt(8)/9801] * summation of variable i from 0 to infinity [{(4i)! [1103 + 26390i]} / {(i!)^4 (396)^4i} ]
Where there sqrt(8)/9801, 1103, 26390, 396 all come from is anyone's guess. The thing generate 8 places of pi every cycle.
Edward Witten's work on unifying the string theories is another set of equations that probably deserve mention, but the practical use for Ramanujan's series and the Chodnovsky improvements to it are undeniable.
Archimedes understood infinity and how to work out the volumes of shapes around 212 BC (The year of his death - he was killed by a Roman soldier invading Syracuse when he said; "Stop disturbing me and my circles!" The soldier was supposed to take Archimedes custody and bring him to Rome).
He has written a book called, The Method, the last surviving copy of it was overwritten for prayers in 1000AD, and then the manuscript was partially discovered in the early 1900's, and just now is the rest being restored using modern technology. Archimedes understanding of infinity and the fundamentals of Calculus would take humanity until Newton / Leibniz, the modern world is probably "off" by possibly 500 years due to The Method having been lost.
Legalize the constitution. Think for yourself question authority.
Combine that with using the smallest, hardest striking surface you can deliver, and you understand why perfectly good bricks can be broken when struck correctly.
You also intuitively understand why it is best not to try to mug someone who seriously studies a striking art.
I've fallen off your lawn, and I can't get up.
Looks like somebody was having trouble with question #12...
Who needs a calculator anymore? Google cannot be stopped:
e^(pi*i)+1
Speed=Distance/Time
Quite useful you know...
--
I refuse to answer that question on the grounds that I don't know the answer.
There are 10 kinds of people in the world
Those who understand trinary
Those who dont
and those who mistake it for binary.
Other favorite is the pseudoscience behind marketing industry equations like
opportunities to see (OTS). I can never remember these offhand because they are so meaningless, but it is fascinating to think of the millions of dollars spent on ie outdoor billboards, where the advert is sold on the basis of these "opportunities to see." See also A Test of the Direct/Indirect BBD and Other Exposure Distribution Models.
As any mathematician who's ever been on a date might have wondered:
b 4 i root(u) r u / 18 ?
I am only slightly ashamed that I spotted that error.
This one I find interesting because the two sides are not only equal, but anagrams of each other when spelled out in English:
11 + 2 = 12 + 1
ELEVEN + TWO = TWELVE + ONE
Use Ctrl-C instead of ESC in Vim!
that's my favorite
My friends and I back in high school would argue constantly over the following equation:
:)
0/0 = 1
Or at least, that's the case I keep trying to make: that the ratio of nothing to nothing is indeed, one. However, alternative principles instruct that ANYTHING divided by 0 is undefined. Yet when graphed on a cartesian coordinate system, a function like 'x = y/0 + a' dictates that for every y, there is a vector or dimension perpendicular to x at a (which is, inherently, a value of x). It basically defines an infinite open-ended ray at a 90 degree angle to x.
It is indeed undefined how to express this. "[+/-] infinity" would be my best guess. But then I guess I'd have to update my equation to:
0/0 = [+/-] 1
Which, is structurally sound if you accept that 0, in being neither postive or negative, can also be said to be both simultaneously. The net effect, of course, is nothing. Yet principally, it illustrates a sort of "optional" element of math, wherein the questionable pre-existing values (such as sqrt(x)) are determined in relation to the answer AFTER completion, or otherwise ambiguously tagged with [+/-].
x = y + 2
for:
x = 0; y = -2
x/0 = (y + 2)/0
[+/-] 1 = (-2 + 2)/0
[+/-] 1 = [+/-] 1
Anyone else care to participate in some junk math?
Thank you for reading One Man's Opinion. No participation necessary. Offer void where deemed by law or PATRIOT Act.
hey baby you + me = calculus
In the context of the upcoming election, my favorite equation is one of Niven's Laws:
F dot S = K
aka the product of freedom and security is a constant.
Looking to tell that special geek in your life how much you care? The following inequality graphs the shape of a heart:
r - 0.2e^(-10 | theta - 1.5 * pi |) < root( 0.5 * (1 + cos( theta + 0.5 * pi ) ) )
And this one makes the yin & yang symbol:
(cos (theta - r) - sin theta)(r^4 - 2r^2 cos( 2 * theta + 2.4 ) + 0.9) + (0.62r)^1000 < 0
2*(wrongs)~=(right)
A => ass in kg
D => Entry angle in degrees
O => Wave vector of highly saline, large volume of H2O
In other words,
"The Mass of the Ass times the Angle of the Dangle equals the Motion of the Ocean."
:)
"I'm just here to regulate funkiness."
Comment removed based on user account deletion
Well,
the breast equation sounds pretty interesting.
Got to try to visualize it someday to see how well it corresponds with the reality.
Everyone who makes generalizations should be shot.
(e^(2 * pi * i)) - 1 = 0
Contains, e, pi, i, 2, 1, and 0.
Why do chemists use an unattractive form of the Ideal Gas Law? Well, using numbers ending in 6.022e23 is kind of inconvenient for any mass of material that a chemist would use on a daily basis. Chemists work with mg-kg of material; at those scales, counting particles as a unit of mass is impractical and inconvenient. It's better instead to convert to units that approximate the unit scale on which one works.
Physicists are likely to deal with particles, hence the use of particles as a unit is reasonable, in addition to the fact that they are more likely to work with equations that get ugly when using molar units (the same goes for some physical chemists). For most chemists, molar weights are a far more useful measure of mass than particles would be. The beauty of the IGL if particles were used as the unit is far outweighed by the awkwardness of the use of particles as units for most things chemists do.
The additional factor is the IGL is only an approximation - a good starting point for understanding how gases behave, but not useful for high precision measurements, at low temperatures or at high pressures. The more accurate versions of the IGL for these circumstances are much uglier. Changing things for the sake of the IGL, in this case, is like sacrificing one's schedule to be with an accurate doll rather than a girlfriend/SO - you would be altering a useful units system for an equation that is interesting but has lost much of what is real about the phenomena it models.
yes, I am a chemist....
1 + 0 = 1
The realization of zero was a major breakthrough, IMHO.
Tiller's Rule: Never use a word in written form that you've only heard and never read. You will end up looking foolish.
x + y + ??? = Profit!!!
Flying is easy, just throw yourself at the ground and miss. -Douglas Adams
Yeah, simple I know, but I love the way it takes a line and converts it to two simple parameters.
I use this equation a lot of times by way of analogy. I often draw little graphs in management meetings where we are discussing the merits of different strategies and discussing the relationship between initial investment, marginal costs and planning horizon.
It's very simplistic I know, but it turns out that drawing a picture can often change the framework in which people make decisions, even if the mathematics is not precisely right. Many people one works with are not inclined to think about decisions mathematically, but they can understand that a line can be described by slope and intercept, thanks to the efforts of the benighted Algebra teachers of yore.
Post may contain irony: discontinue use if experiencing mood swings, nausea or elevated blood pressure.
Use on females:
U + I = 69
How about this one: limit as GPA -> 0 of F(engineering) = Y(business)
That really blew my mind when I first saw it in high school, and it made no sense at all until I saw the Taylor series of e^x, vs. those of sine and cosine. But man, is it easier to work with exponentials than with sinusoids. Just like it's a lot easier to work with Laplace transforms via arithmetic than to try to manually solve differential equations.
The Wikipedia article shows the Taylor series expansion proof.
Si la vida me da palo, yo la voy a soportar Si la vida me da palo, yo la voy a espabilar
Sometimes, only the name is enough.. :-).
At last...
I thought that was course 1.
TWELVE + ONE = ELEVEN + TWO
Charles Proteus Steinmetz(read the last item on the page 1st) took on old theoretical idea of complex numbers (real + imaginary)
a + bi
and turned it into a way to quantify impedences in alternating current circuits
Z = R + jX
gewg_
Unfortuneately I can't type it adequately as I don't have the HTML tag for SuperScript memorized:
Write the integers 2,3,4,5 with one plus sign and one equals sign as an equation.
Answer (replacing the superscript with ^) 4+5=3^2
SJW: a person who perceives an injustice, and while correcting it, commits a greater injustice.
Why is it my favourite while being so simple? Because its elagance lies in its very simplicity. There are not many other equations that have so much power yet are so simple that a child with very little formal education can quickly learn and understand it.
Anthony Papillion
Advanced Data Concepts, Inc.
"Quality Custom Software and IT Services"
c'mon. we all know 1 + 1 = 0 (with an overflow)
"May the force be with you and may the sum of the forces equal zero"
-Bounced around the Naval Academy in the mid '80s
The circumference of a pumpkin divided by its diameter = pumpkin pi.
"Windows really sucks, I hope they burn in the afterlife!" == (Score: 5, Insightful)
"Linux could use a little bit of improvement." == (Score -1, Troll)
"Derp de derp."
y = mx + b. So simple, yet, I never got algebra.
ROMANES EUNT DOMUS
0 + .l. + 0 = yummy... that's my equation for an FMF threesome!
Better get your calculator fixed. Exp(i*Pi) + 1 is equal to 0, and Exp(2*Pi) = 535.491655524764736503...
e^x dy dx e^x dx
tangent(secant(cosine(sine(3.14159)))
Go Tech, Go!
Here's a simple proof: 1/3 = 0.33333... 0.333... + 0.333... + 0.333... = 0.999... 1/3 + 1/3 + 1/3 = 1 0.333... + 0.333... + 0.333... = 1/3 + 1/3 + 1/3 0.99999... = 1 It can also be proven with limits and stuff, but this proof is easier. Strange things happen when you start dealing with infinities.
Fricken' idiots - and no, I won't be their customer any time this next century....
"The most sensible request of government we make is not, "Do something!" But "Quit it!"
In my opinion, one of the most beautiful equations is the one that computes natural cubic splines. Given a set of knots (points) on a graph, this equation figures out a smooth curve between each point. This is called "curve-fitting". Very cool calculus, and it includes a tridiagonal matrix equation, which gives it extra beauty points! See this page for an excellent discussion on it:
Cauchy-Schwarz Inequality: For any x and y in an inner product space,
<x,y> <= ||x|| ||y||
Very useful in a lot of branches of mathematics.
Also, the every so interesting identity,
SUM{n=1, infinity}( 1/n^2 )= (pi^2)/6
Very interesting how pi shows up where you least suspect it!
Actually, Bud Adams would not release the rights to the name Oilers and so the City of Houston had to pick something else.
a ** x = e ** (x ln a)
Much prettier than a lot of the other equations I've seen here.
De Moivre theorem DOES NOT contain e:
i sin(n x) + cos (n x) =[i sin(x) + cos(x)]^n
De Moivre 17th Century
Euler 18th Century
De Moivre was a French protestant who immigrated to England to escape religious persecution. He died poor. Euler died filthy rich, the emperor of Russia paid him a huge salary.
Dude, 1+1=2 is a matter of definition not a "free standing" equation, e.g., in binary 1+1=10. I vote for E^(ipi)+1=0 that equation ties so much to together. The first time I saw it derived was a cathartic experience. A puely personnel reason for my vote. But, I'll never forget that moment.
1 + 1 = 0 in binary when you only have one bit, lousy overflow!!!
1/3 = 0.333333...
:-)
2/3 = 0.666666...
3/3 = 0.999999...
Yet we are always told that 3/3 = 1
Try subtracting 0.9999999..... from 1.
1 - 0.999999... = ???
If you can come up with any other answer than 0, then I'll think you're onto something.
- Give a man a fire and he's warm for a day, but set him on fire and he's warm for the rest of his life.
b4 i u^0.5 (ru)/16 QT Pi
4(Wr)^2-2Wr^4/((x-y)^2+(y-????? = r
caption from the cartoon "Yes, yes, I know that, Sidney..._very_body knows _that_!...But look: Four wrongs _squared, minus two wrongs to the fourth power, divided by this formula, _do_ make a right."
gdfj12
Work is mass accelerated over a distance.
W = mad
Work is mad! mad I say!
"Love heals scars love left." -- Henry Rollins
I NEED gravity almost as much as I need my computer.
1+1=window
If vi is power, what about emacs ?
F=MA think sex.
./revolution
...wasn't funny to either type actually
N = N* fp ne fl fi fc fL
Okay, it may sound corny, but even with relatively low numbers, it still gives me hope that there is someone out there smart enough to leave us alone.
Karma: 0 (But I wield a mean +10 Vorpal Apathy)
like this (the sum of squares of the 7 first prime numbers)
2^2+3^2+5^2+7^2+11^2+13^2+17^2=666
or this(the sum and difference of the first 3 6th powers)
1^6-2^6+3^6=666
eeek this starts giving me the chills
X~
anything involving computers (i.e. transistors) is not one of them
if rho is a scalar field than if:
d(rho)/d(t) + grad(rho*position vector) = 0 in a region
than the integral of rho over that region is a constant.
Sorry guys just got my physics degree on Saturday.
P.S. d-> partial derivative
Considering most 3-D rendering engines make heavy use of vector mathematics, all you'd really have to do is develop the interface.
Not that you necessarily *want* players doing arbitrary transforms on the gaming environment, but hey, I think it'd be fun.
Tweet, tweet.
screw you. n/t
> Euler's Formula is breast milk??
No, it's
99 + 20 + 9 + 6 + 15 + 31 + 21 + 23 + 22 + 26 + 17 + 19 + 4 + 14 + 24 + 33 + 11 + 28 + 18 + 5 + 10 + 32 = 1 * (Stanley Cup)
You're welcome.
Do daemons dream of electric sleep()?
Pi + HoMer = 0Pi
Wine + Flowers = SEX
2 + 2 = 4096
0 - 1 = -1
infinity/2 = infinity
The Kruger Dunning explains most post on
A mathematical proof which explains why managers and others in authority make so much money.
From your physics course, you will recall that:
Power = Work / Time
From the world of business, we know that:
Knowledge = Power
and also that:
Time = Money,
Substituting these identities into the original equation, we get:
Knowledge = Work / Money
Solving for money, we get:
Money = Work / Knowledge
Thus, Money approaches infinity as Knowledge approaches zero, regardless of the Work done.
What this means is: The Less you Know, the More you Make.
Taking this analysis and proof one step further, we know that:
Knowledge = Education x Time
Solving for Time:
Time = Knowledge / Education
and then substituting for Time back into the Power equation, we get:
Power = (Work x Education) / Knowledge
From which we can see that the closer Knowledge gets to 0, the more power one will have.
Note:You can also increase Power through increasing either Work or Education, but it should be noted that this approach doesn't have the same type of leverage as lack of knowledge.
This equation is also known as the MANAGEMENT equation, since it provides a clear and concise mathematical explanation of why managers, executives, politicians and most other highly unknowledgable individuals get paid so much.
Also explains why us highly knowledgable techies get paid nothing.
How much nicer would all these posts be if we had real MathML suport!!!
Here is what Mozilla is doing about it, but is any other browser supporting this [much needed!] standard?
The angle of the dangle is inversely proportional to the heat of the meat.
Tone
I've got mod points but I can't use them here, so unfair!
Please read my Canon EOS tech blog at http://www.everyothershot.com
My favourites are the Lagrangian (and Hamiltonian, for that matter) formulation of Newtonian dynamics. The Lagrangian one is: d/dt(dL/dq') + dL/dt = Q (where all derivatives are partial)
Not only does this sum up all of Newtonian mechanics, it also has the Newtonian part of Noether's theorem as a trivial corollary.
Noether's theorem, for the uninitiated, is a very deep law of nature. It states, more or less, that for every symmetry in a physical system, there is a corresponding conserved quantity. Examples:
sub f{($f)=@_;print"$f(q{$f});";}f(q{sub f{($f)=@_;print"$f(q{$f});";}f});
"Its like asking what's the square root of a million. No one will ever know"
of the modern era. Mathematicians at St. Petersburg were still publishing his stuff seventy years after he died. I sometimes see mathematicians claiming that Gauss was the greatest but I don't think he stacks up against Euler.
"sweet dreams are made of this..."
is one of the weirdest I've ever seen, another one that brings pi and e together.
n! = ((n/e)^n)*sqrt(2*pi*n)
It's only approximate, but it gets more accurate (relatively) as n increases.I figure by 2030 or so my 6-digit UID will be something to brag about.
P = NP
This was posted TEN WHOLE DAYS ago (08:28 PM:, 15 Oct 2004) at the blog Making Light. Are we gonna let a bunch of Science Fiction writers and editors get away with being nerdier than us?
::: (view all by) ::: October 15, 2004, 08:28 PM:
"... Great equations change the way we perceive the world. They reorchestrate the world -- transforming and reintegrating our perception by redefining what belongs together with what. Light and waves. Energy and mass. Probability and position. And they do so in a way that often seems unexpected and even strange...."
The Nerdier, Newsier Blog Jonathan Vos Post
not an equation per se but a core statement from a theorem:
"This statement is unprovable."
sweet
...would I lie to you?
Halloween is the same as Christmas because:
Oct 31 = Dec 25
| x n
| e = f(u )
|
\-/
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
But you're skipping a step that changes the solution....
Money = Evil^(1/2)
then
Money^2 = (Evil^1/2)^2
Women = Money^2
Women = (Evil^1/2)^2
so....
Women = +/- Evil
The practical applications? Confusion, angst, and our eternal love/hate relationship with that species.
How about any equasion that shows an identity or the most simple 0=0 to a more complex one. I guess this is a group of equasions but I think they are the most beautiful.
My UID is prime is yours?
I've always been very impressed with the central limit theorem, which states that the sum of a large number of random variables is approximately normally distributed -- regardless of the distribution of the individual random variables.
The CLT basically explains why the normal distribution appears so often -- since large systems usually combine a large number of random variables together.
Off the top of my head, I would guess that the formula for the CLT is something like this:
Y = lim(n->infinity) SUM(i=1..n)X(i) -> Y ~ N(mu,sigma^2)
Plus auxiliary formulas to define mu and sigma^2.
I like:
0.99999... = 1
Which is easily proven by:
x = 0.99999...
10x = 9.99999...
9x = 9 (subtract the 1st from the 2nd)
x = 1
QED
...And God Said,
... and there was light.
:(
E.dA = q/e0
B.dA = 0
E.ds = -d/dt( B.dA)
B.ds = m0.( I + d/dt (e0. E.dA))
Dammit, integral symbol won't render
help me i've cloned myself and can't remember which one I am
(1)+(-1)=0
mmmmm proof of existence
"... 5 most important numbers ..."
...
Funny, it's my understanding that zero isn't considered a number
For sheer ballsiness, I have to admire Fermat's last theorem, even though most of the proofs offered are flawed. Euler's work is pretty cool, though.
The second is Shannon's theorem. It says the ultimate information carrying capacity of a channel is the bandwidth times the log of the number of states you can distinguish over the noise.
These may actually be more fundamental to reality than E = mc**2.
Did you forget
(x^y)-((x^x)/y)*C(#78b)
Have you read my journal today?
This formula as far as I can tell came from nowhere but a strangely tuned up mind
Are you saying there is no proof of the formula?
I've read that Hardy invited Ramanujan to England where he quickly succumbed to British food and weather.
I also have this T-Shirt, which I think is cool.
integer divide by zero!
bwhahaha.
so what of bijections vs surjections and injections?
GrimRC
(function of real number) = (imaginary part of the complex number)
Shortly ...
ln(-1) = PI * i
...
sqrt(-1) = 1 * i
PI = (Taylor's eulerian logarithm of -1) * -i
PI = (Euler's taylorian logarithm of -1) * -i
PI = Ramanujan's equation
Who did first invent the equation of the longest real of PI?
Thanks to Ramanujan, Taylor & Euler, Cheby???chev, Cauchy, ... ... ;)
Can we find quicker equations of any polynomial or function?
Possibly, but it's not easy to find
open4free ©
Let a=1
Let b=1
Therefore a=b
Multiplying both sides by a gives a^2=ab
Subtract 1 from the left and b (which equals 1) from the right: a2-1=ab-b
If you remember your quadratic equations, this factors to: (a+1)(a-1)=b(a-1)
Dividing both sides by a-1, we have a+1=b, or 1+1=1
Therefore 2=1
To be sure, this is a counterintuitive result, and math purists will no doubt find fault with it. Well, I just have three words to say to them: E pluribus unum. Got a problem with America, Math Boy?
This is by far the best equation ever made. (B + I) * (L^2) * (G / A) + (T - E) * S = M$
My favorite equation is: Derivative of e to the x = e to the x plus C Not quite mathematically correct (missing a "dx" before the equals sign) but if you write it out, it spells "Sex = Ecstasy" :D
Oh dear, Mr. Flibble, we can't do anything like THAT... who would be left to clean up the MESS???
Augustus deMorgan told us:
log(-1) / sqrt (-1) = C / D
where C and D are the circumference and diameter of a circle.
Both terms on the left side are imaginary; both on the right side are real!
earle
*
Hey, "gotta be a winner" is wrong....
"A WINNER IS YOU" is correct!
obligatory simpsons quote:
Toy pinball machine: "Ha Ha Ha! You a winna!! Ha Ha Ha! You a winna!! Ha Ha Ha! You a winna!!"
"You are only young once, but you can be immature forever." -www.animemusicvideos.org
The Gibbs free energy equation, G = H - TS, is pronounced "Garlic is Hell without Tartar Sauce"
404555974007725459910684486621289147856453481154 in hex is "You sank my Battleship?"
[GPG key in journal]
I think I understand the sentiment, but I have no idea what that stupid equation is supposed to prove.
The real Captain Avatar is a fictional character, so I suppose he doesn't mind if I impersonate him.
It's been proven here:
a t=application/pdf&identifier=oai%3AarXiv.org%3Amat h%2F9306213
http://citebase.eprints.org/cgi-bin/fulltext?form
But from what I understand, this guy came up with most of his best work with only a vague idea of what a mathematical proof was.
He did get invited to England, was decorated academically but did die of disease brought on by an intense dislike of the food and he was not aware of how to properly sleep under covers, and the cold nights caused his health to deteriorate along with malnutrition.
This is not a joke, I've read somewhere reliable that he was never told how to properly put himself to bed - he slept without the covers never knowing (or being shown for that matter) how the bed was to be used.
Apparently, the first 3-4 letters received in England were thought of as hoaxes because he had his own notation for everything, but it was (luckily) discovered that he was no hoax.
Legalize the constitution. Think for yourself question authority.
Why am I not surprised that this was posted anonymously? And for the record, I'm raising a baby, so I've got books full of stuff about allergies. The main ones are: shellfish, eggs, milk, peanuts, chocolate, any kind of animal flesh, and then wheat and corn. Wheat and corn are full of vitamins, but the same vitamins are to be found in many less allergenic grains such as spelt, quinoa, amaranth, rice, and so on.
The human organism is a herbivore. But much like chimpanzees, we require trace quantities of vitamin b12. Well so what? Chimps get it from shit - they don't wash their vegetables, and from insects - they don't wash their fruit. I choose to get mine from a supplement but I could eat an egg or a glass of milk every couple of weeks if I didn't think that was GROSS!!
Animal flesh sits in your colon festering. It's really yucky. A carnivore has a really short intestine with really acidic stomach juices to digest it and get it out. Anywho, I eat just fine.
If the land is unsuitable for growing crops then it's about 7 times more unsuitable for grazing animals.
The food with the highest proportion of protein is the nut. Then come the legumes. Then comes (yuck) the animal flesh.
Actually, I'm a vegetarian because I don't want to eat animal flesh AND I DON'T HAVE TO!!! It's quite a relief to know that I don't have to - I was quite concerned until I did enough research.
If you keep eating that crap it won't necessarily kill you... it's not the most dangerous thing people do. But it's pretty bad, actually. But I guess it's your own business.
*#*#*#*#*#******* I love peanut butter sandwiches!
That would be "Food + Heat = Cooking" by Alton Brown
L+U+E=42
--- "1.21 Jigawatts!" -Doc