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Greatest Equations Ever
sgant writes "What is your favorite equation? This was the question asked by Physics World in a recent poll. This is also covered in a New York Times article about the same poll. Some of the equations mentioned were the simplistic 1+1=2 and Euler's equation, ei + 1 = 0. What are some of your favorite equations?"
Euler's equation is actually Exp[i*Pi] + 1 = 0 not Exp[i*n] +1 = 0 (unless they say n = Pi, which they don't). I'd have to say this is the most elegant equation of all time. It combines the 5 most important numbers in all of mathematics into a single formula. This formula also has tremendous applications in many fields of engineering and other areas of applied mathematics. If it wasn't for this equation, your cell phone wouldn't work.
Scott
a^3+b^3 = (a+b)(a^2-ab+b^2)
first proof, that i'd seen at least, of the existance of negative numbers.
GENERATION 26: The first time you see this, copy it into your sig on any forum and add 1 to the generation.
Gotta Love V=IR. Works pretty well, I use it daily, well that and P=VI.
Take a look at the username, and take a guess at mine :o)
So.. it has come to this
In my opinion, the most important equations are those that brought together Algebric representation of Geometry -- that has been the single most fundamental basis for today's advancement in mathematics and physics.
B*u*pi * integral of e^x
Hint: Try writing it in mathematical notation.
Happiness = Food x Friends x Fun
From Woz.
It's the most important and beautiful equation I've ever seen.
Projectile equations of motion, very useful in FPS games.
Due to lack of disk space this user has been discontinued
First we state that women require time and money:
Women = Time X Money
And as we all know "time is money"
Time = Money
Therefore by substituting Money for Time we get:
Women = Money X Money
Women = (Money)2
And because "money is the root of all evil" we therefore can state:
Money = (Evil)1/2
And Since
(Money)2 = Women
Then (Money)2 = Evil
And we are forced to conclude by substituting "women" for "(money)2" from above that:
Women = Evil
** "It's not my job to stand between the people talking to me, and the ones listening to me." -- Pego the Jerk
My favorite is the thinkgeek tshirt that says "2+2=5 for extremely large values of 2".
It is not just funny... if you consider the numbers not as integers, but as any float value with that integer as the first number, it is true.
ih/2Pi dPhi/dt = hc/2iPi (A1 dPhi/dx1 + A2 dPhi/dx2 + A3 dPhi/dx3) + A4 mc(squared)Phi
Said by Hotson to be the Equation of Everything. First part, second part. Worth a read IMO.
Maybe we deserve this world ?
My favorite is 0 = 0, because it's the one that most often indicates you're done with the math exercise. :-)
Please correct me if I got my facts wrong.
"What is your favorite equation? ..."
Shashdot has already covered this in a poll! We all already know that E=mc^2 is the overall favorite, closely followed by F=ma.
http://slashdot.org/pollBooth.pl?qid=804
Anyway, just thought I'd share that because E=m^2c^4 + p^2c^2 is my favorite equation and most people think it looks a little familiar but wouldn't know what it was without a little additional explanation.
When things get complex, multiply by the complex conjugate.
The integral of a differential form on the boundry of a manifold is equal to the integral of the exterior derivative on the manifold itself.
S_{dM)w=S_(M)dw
An important special case is the fundamental theorem of calculus. Not only is this a beautiful looking theorem, but important too.
Other special cases are the classical forms of green's theorem, stoke's theorem, and the divergence theorem.
I dunno if its my favorite equation, but its up there.
Everything = 42
If it wasn't for this equation, your cell phone wouldn't work.
If it wasn't for the laws of nature things wouldn't work. The mathematical formulas are our way of expressing them.
Really, I know what I'm doing...Ohhhh, look at the shiny buttons!
b4i (square root)u ru/16
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.
Some beautiful equations of mathematical physics
Banu
No, everybody is correct.
The only thing is that schematix (grandparent) misread the Pi as a 'n', which look very similar, indeed (on my screen anyway).
There are 11 types of people:
Those who understand binary
Those that don't
And those that think they do.
Someone hates these cans.
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?
That's my favorite.
I used to even use "exp(pi^2/12ln2)" as my name in Quakeworld.
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
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
my stupid one would be : lim( sqrt(8) , 8->9) = 3 :)
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.
Of special importance to slashdot:
garbage in = garbage out
Jolyon
Please read my Canon EOS tech blog at http://www.everyothershot.com
0.999999... is just another way of symbolising the value 1. Its the same value, just two ways to write it.
this is not my signature.
I use this in day-to-day life probably more than anything else. Helpful for calculating my home theater projector screen sizes when I need to one-up friedns that get new televisions.
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.
Suppose you have something like this (apologies for loss of indentation)This is ripped off from a web application I once wrote. You should be able to modify the time by typing figures into the box or by using up and down arrows. What happens in practice is that adding 1 actually concatenates "1" on the end of the string, so you find that 1 + 1 = 11, and 11 + 1 = 111.
This is what you get when you borrow one idea from Perl about how the computer should be able to work out from context whether or not something is a number or a string; and one from BASIC about re-using operators obviously out-of-context {strings cannot be added} to mean something different {such as concatenation}. The result, as they say, is a mess. For all practical purposes, JavaScript lets you subtract, multiply and divide numbers; but if you want to add, you'd better subtract a negative number.
I mean, it's not freaking rocket science, is it? = is for telling, == is for asking. + is for adding, . is for joining strings. Sheesh!
Je fume. Tu fumes. Nous fûmes!
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
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
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
us {all,your,base}
Of course if sets aren't your thing...
#hostfile 0.0.0.0 primidi.com 0.0.0.0 www.primidi.com 0.0.0.0 radio.weblogs.com
I would have to say, at the moment, my favorite equation would have to be the one giving the coefficients of the generalized Fourier series involving a set of eigenfunctions {p_n}, ie., c_n = <f, p_n>/||p_n||^2.
Simple stuff, but incredibly cool, considering that Fourier series don't always have to involve just sines and cosines, and you get similar sorts of behaviour.
Come on, folks? The Schrödinger equation!
H*Psi = E*Psi
(note: H is an operator folks, not a number)
Perhaps not as famous as E=mc^2.. or as exact as the Dirac equation (relativistic version of the S.E.),
but.. in terms of practical benefit to mankind, I think this one has done more than any other equation during the last century.
Atoms. Molecules. Semiconductors. Lasers.
The number of things explained and modelled by the Schrödinger equation are just uncountable. You can explain almost* all of chemistry with that thing.
Relativity is nice, but it hasn't had the technical uses quantum physics has.
(*Relativistic effects are important in heavy elements. For instance the yellow color of gold is a relativistic effect.)
The answer is simple. The most beautiful equations, hands down, are those from which all of mathematics can be derived. These are the axioms of ZFC set theory. What could possibly be more beautiful or more important than that? And it's a shame so few people know about them. See Zermelo-Fraenkel Axioms and Metamath Proof Explorer.
Comment removed based on user account deletion
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.
That's only true for horse shoes, hand grenades and 1950s chemotherapy.
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
George Bush still doesn't know if Bin Laden is alive! After numerous rounds of "We don't even know if Osama is still alive", Osama himself decided to send George Bush a message in his own handwriting to let him know that he was still in the game.
Bush opened the letter and it appeared to contain a coded message:
370HSSV-0773H
Bush was baffled, so he typed it out and e-mailed it to Colin Powell. Colin and his aides had no clue either so they sent it to the CIA. No one could solve it, so it went to the NSA and then to MIT and NASA and the Secret Service.
Eventually they asked Britain's M I6 for help. They cabled the White House: "Tell the President he is looking at the message upside down."
A classic misquote. The verse actually runs, "The love of money is the root of all evil," but this joke wouldn't be as funny that way.
It's still funny--you just have to change the punchline to "The love of money is the root of all women."
What part of "shall not be infringed" is so hard to understand?
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.
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.
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.
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
1 Bourbon + 1 Shot + 1 Beer = :)
It is better to be the hammer than the anvil.
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
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?
In layman's terms, in base 1, 1+1=11, 11+1=111, 111+1=1111, and so on. This is consistent with the requirement that the number of symbols in a number represented in base n contains no more than n distinct symbols. But base 1 contains mathematical inconsistencies when representing non integers (or even the integer 0) which can't permit it to be acceptable as a valid base.
File under 'M' for 'Manic ranting'
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)
Well, strictly speaking the axioms are represented as well-formed formulas (wffs) that aren't displayed in the form of equations on the pages I linked to. But using what is called "class notation" in set theory it is always possible to rewrite a wff with an equivalent expression that has form of an equation. For example: "P(x) imples Q(x)" can be expressed as "{x:P(x)} union {x:Q(x)} = {x:Q(x)}" where "{x:P(x)}" means "the class of sets x such that P(x) is true". Or more generally, any statement P(x) that is true of all sets x (such as any of the axioms) can be rewritten "{x:P(x)} = V" where V stands for {x:x=x} i.e. the universe of all sets. Class notation is an extremely powerful device. Classes need not exist as sets, by the way; the class V above is not a set but is called a "proper class". Does this answer your question?
Who needs a calculator anymore? Google cannot be stopped:
e^(pi*i)+1
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!
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.
If vi is power, what about emacs ?
> 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()?
I see the unstoppable and the immovable - now what do I need to do to chop a brick?
Know your pads. One time pad: good for cryptography. Two timing pad: where to take your mistress.
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.