## Greatest Equations Ever 1017

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, e*^{i}+ 1 = 0. What are some of your favorite equations?"
## correction (Score:5, Insightful)

## Re:correction (Score:5, Insightful)

## Re:correction (Score:5, Informative)

Guy created so many darn formulae that "Euler's formula" is ambiguous.

## Re:correction (Score:5, Interesting)

...Which is in turn not to be confused with Euler's

equation, which is V+F=E+2.Euler has a ridiculous amount of stuff named after him.

## Re:correction (Score:5, Funny)

Euler has a ridiculous amount of stuff named after him.A hockey team in Edmonton, Alberta...

## Re:correction (Score:5, Funny)

## Re:correction (Score:3, Funny)

## Re:correction (Score:3, Informative)

afterEuler, justbyhim. He did pick the name for the constant, but only picked 'e' because a, b, c, and d were already common elsewhere.## Re:correction (Score:5, Funny)

## Re:correction (Score:4, Funny)

"...to name [things] after the second person who discovered them. Because Euler probably got there first."

## Re:correction (Score:3, Informative)

relation, probably to distinguish it from Euler's equation.## Re:correction (Score:3, Informative)

That would be the Euler-Lagrange [wolfram.com] equation.

## Re:correction (Score:3, Interesting)

## Re:correction (Score:5, Informative)

It combines the 5 most important numbers in all of mathematics into a single formula.It's also got the other important mathematical concepts - exponentiation (i.e. raising something to the power of something else), multiplication, addition and equals. Essentially, it's a huge nugget of maths in a tidy little wrapper.

I've got an old Sharp graphics calculator, which has both proper notation layout and a complex numbers mode. I still like keying in the 'e^(pi*i)+1', pressing 'Enter', then getting the zero, all perfectly laid out on a little LCD display...

## Re:correction (Score:5, Funny)

Oh well. 5318008.

## Joke Time (Score:5, Funny)

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."

## Re:correction (Score:5, Funny)

Too bad my mathematical abilities don't reach beyond spelling rude words on calculators held upside-down.Oh well. 5318008.Wouldn't it more appropriate to be: 55378008

## Actually... (Score:4, Insightful)

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.

## Re:Actually... (Score:3, Informative)

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.

Mathematical formulas indicate an understanding of such laws, so without that understanding, your cell phone wouldn't work.

## Re:Actually... (Score:4, Insightful)

Mathematical formulas indicate an understanding of such laws, so without that understanding, your cell phone wouldn't work.I believe there are quite a few inventions that have been stumbled upon without any understanding about mathematical formulas whatsoever. Amazing what can be accomplished with the old trial and error method =)

## Re:Actually... (Score:5, Funny)

## Re:Actually... (Score:5, Insightful)

It is a mathematical relationship which is completely abstract - none of those values are physical quantities, although all of them are used in other physical equations.

In theory an alien in a completely different universe could come up with the same formula.

Think about it - e is related to the integral of 1/x on a flat plane - which doesn't exist in real life. i is the square root of -1, which is about as abstract a concept as you'll ever come up with - it certainly doesn't correspond to any physical quantity (unless you define a physical system using complex coordinates for the sake of convenience). Pi is a number which is very useful in practical measurements, but which can be described completely in the abstract.

In any case, an equation like Euler's formula reflects our understanding of mathematics in general more than it reflects our knowledge of any particular physical process.

## Re:Actually... (Score:5, Interesting)

i is the square root of -1, which is about as abstract a concept as you'll ever come up with - it certainly doesn't correspond to any physical quantity (unless you define a physical system using complex coordinates for the sake of convenience).Quantum mechanical wavefunctions are complex. You

coulddefine them as two real wavefunctions and work out the appropriate algebra, but it's exactly complex algebra. Soicould correspond to the phase difference of two wavefunctions, which would be observable via interference effects.Not disagreeing with what you're saying though -- the equation is fundamental mathematics, independent of the physical universe, it doesn't make sense to imagine an "alternative universe" where it doesn't apply.

## Re:Actually... (Score:5, Funny)

## Re:Actually... (Score:4, Informative)

'As far as the laws of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality.'- Albert Einstein, Sidelights on Relativity

## Re:Actually... (Score:5, Funny)

=Smidge=

## Re:Actually... (Score:3, Funny)

It would be cool with a game like final fantasy where spells were named after mathemathical concepts.

Quick! Do a Laplace transformation and invoke the Jacobi symbol!

## Re:correction (Score:4, Informative)

-Jesse

## Exp[ i*Cir/2] + 1 = 0 (Score:3, Interesting)

Firstly, 2 is a very important number. 0 is null and the origin, 1 is unity

## Re:Submitter and Parent are stupid (Score:3, Informative)

The only thing is that schematix (grandparent) misread the Pi as a 'n', which look very similar, indeed (on my screen anyway).

## Re:Submitter and Parent are stupid (Score:3, Interesting)

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.

## Re:correction (Score:5, Informative)

Talk about throwing the baby out with the bathwater!

## sum of cubes (Score:5, Interesting)

first proof, that i'd seen at least, of the existance of negative numbers.

## Re:sum of cubes (Score:5, Funny)

## Re:sum of cubes (Score:5, Interesting)

I say, that until I saw the sum of cubes I internally denied the existance of negative numbers. I mean I could work with them and all, I just didn't believe in them. If you deny the existance of negative numbers, you cannot have an expression 0-1, because -1 is meaningless, so therefor the result is meaningless. It's circular reasoning, and this is why[according to my youthful very non-standard way of thinking of things]:

there is a number -1

there is a number 0

if you have two numbers, there is a third number which represents their sum.

there is a number -1 + 0

if there is a number -1 + 0 there must be a class of numbers known as negative numbers

[the direction you were going in?]

but if you cannot prove there is a number -1 + 0, you cannot even get that far.

a^3+b^3 = (a+b)(a^2 - ab + b^2 ), on the other hand, shows quite clearly that no matter what numbers a and b you pick, you end up, in your equation, with a negative number.

## Re:sum of cubes (Score:3, Interesting)

a-a=0, is not totally far off. Comutativity even

## V=IR (Score:5, Interesting)

## Re:V=IR (Score:5, Interesting)

twinkle twinkle little star

power equals I squared R

I remembered it.

## Re:V=IR (Score:5, Funny)

There was once a football player who was teetering on the edge of academic eligibility. To help the poor guy with his physics test, the coach told him:

Remember this ryme, to get the power in a circuit:

Twinkle twinkle little star,Power equals I squared R.Well the school day before the exam, the football player also had a big game. He tackled alot of people and had a really good day. However, the next day he failed his test! The coach couldn't understand, so he asked the player if he remembered the ryme. The football player said:

Of course, coach:

Twinkle twinkle star in the sky,Power equals R squared I!There's a moral in there somewhere. :-)

## Re:V=IR (Score:3, Interesting)

delta G = delta H - T(delta S)

This equation balances the contributions of entropy (S) and enthalpy (H) and tells you if a given reaction is energetically favorable. delta H is the total energy in a reaction, while T(delta S) is the energy unavailable for work. A quick rearrangment shows that delta G is the energy available for doing work.

I'm also fond of Shannons juggling theorem. [bc.edu]

## Re:V=IR (Score:4, Informative)

Obviously another person who never uses AC.

What's wrong with AC. R is resistance, not impedance or reactance. If you add reactance to the equasion, then you need a new formula, but that equasion has current, voltage and resistance. The formula holds true. Don't read in inductance and capacatance where there isn't any.

This is Ohm's law, not Kirkoff's law.

For formulas that include reactive components, they are listed here;

http://www.tpub.com/neets/book2/6.htm

## Re:V=IR (Score:3, Informative)

Obviously another person who never uses ACAt any moment in time the equation V=IR holds for any circuit (yes, even AC circuits). It is just that when you have caps and inductors in your AC circuit their impedance changes all the time, making the V=IR equation less usefull.

When one only has resistive impedance elements it is possible to use V=IR for AC circuits by replacing V with Vrms, and I with Irms, the Root-Mean-Square value of the AC voltage or current, giving Vrms = Irms*R.

## Re:V=IR (Score:4, Informative)

## Take a guess.... (Score:5, Funny)

Some of the equations mentioned were the simplistic 1+1=2 and Euler's equation, e^in + 1 = 0. What are some of your favorite equations?"Take a look at the username, and take a guess at mine :o)

## Re:Take a guess.... (Score:5, Funny)

Take a look at the username, and take a guess at mine :o)But shurely 1

## Re:Take a guess.... (Score:4, Funny)

But shurely 1 /\ 1 = 1 ?No, I'm serious. And stop spelling it 'shurely.'

## Re:Take a guess.... (Score:3, Interesting)

Let's construct a number system from the very basics. We'll construct an infinite field over addition and multiplication. We have an additive unit which we'll call 0 and a multiplicative unit which we'll call 1. So we can add two multiplicative units to get 1+1. We call this 2. Therefore 1 + 1 = 2 *by definition of 2*.

So what am I missing?

## Re:Take a guess.... (Score:5, Interesting)

http://mathworld.wolfram.com/Logic.html [wolfram.com]

## Re:Take a guess.... (Score:3, Interesting)

Usually "from the very basics" means "from zero and the successor operation".

1+1=2 in the most popular form

## Re:Take a guess.... (Score:4, Funny)

Try 1+0=0 - this should be a bit harder :-)You're right, that would be a hard proof

## Geometry and Algebra (Score:5, Interesting)

## Well... (Score:5, Funny)

B*u*pi * integral of e^x

Hint: Try writing it in mathematical notation.

## Re:Well... (Score:5, Informative)

## Re:Well... (Score:5, Funny)

Yay!

## H = F ^ 3 (Score:4, Insightful)

From Woz.

It's the most important and beautiful equation I've ever seen.

## How about... (Score:3)

Projectile equations of motion [anl.gov], very useful in FPS games.

## that's an easy one.. the answer is (Score:3, Funny)

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

## and driving the joke into the ground we get .. (Score:3, Informative)

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

(Mone

## Re:one of the more famous misquotes there (Score:4, Insightful)

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."

## ThinkGeek t-shirt (Score:5, Funny)

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.

## Dirac's equation of 1/2 spin: (Score:5, Interesting)

Said by Hotson to be the Equation of Everything. First part [zeitlin.net], second part [zeitlin.net]. Worth a read IMO.

## 0 = 0 (Score:5, Funny)

## Re:0 = 0 (Score:3, Funny)

another5 minutes figuring out what you did wrong.## dupe of old poll (Score:5, Informative)

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 [slashdot.org]

## Einstein's FULL equation (Score:4, Informative)

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.

## Re:Einstein's FULL equation (Score:5, Informative)

Nah?

## Re:Einstein's FULL equation (Score:3, Informative)

I sure hope my calculations aren't where all that inexplicable "dark matter energy" has been coming from. . .

## Re:Einstein's FULL equation (Score:3, Insightful)

## Re:Einstein's FULL equation (Score:5, Informative)

It's actually E^2 = (m^2 * c^4) + (p^2 * c^2)More like: E^2 = (m

0^2 * c^4) + (p^2 * c^2)m0 is defined as the mass at rest (v = 0). If you substitute m = m0 / sqrt(1 - v^2/c^2), you can rework that to E = mc^2. And, if v = 0, you get E0 = m0c^2, the "energy at rest" of an object.

I agree with the original poster, the full version is much more useful than the E = mc^2 form. The short form hides one of the most important conclusions of relativity theory: that mass is a function of speed.

## (Generalized) Stokes equation (Score:5, Insightful)

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.

## Re:(Generalized) Stokes equation (Score:3, Funny)

S_{pD0^(42e)}pi=23^ln(volume)

Oh, crap, why don't you admit that we

bothjust made this stuff up to sound intelligent on Slashdot?## Everything = 42 (Score:4, Funny)

Everything = 42

## Re:Everything = 42 (Score:3, Interesting)

Anyways, it knows this constant too:

"the answer to life the universe and everything"

Made me chuckle the first time I saw it...

## One my calc teacher showed me (Score:5, Funny)

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.

## Paper on this (Score:3, Interesting)

Some beautiful equations of mathematical physics [arxiv.org]

## khinchin's constant (Score:3, Interesting)

That's my favorite.

I used to even use "exp(pi^2/12ln2)" as my name in Quakeworld.

## Google calculator (Score:3, Funny)

sqr(-1) [google.com]

e^(i.pi)+1 [google.com]

1+1 [google.com]

That is, if you're suspicious...

## 1+1=10 (Score:5, Funny)

There are 10 kinds of people: those who understand binary and those who don't.

## Re:1+1=10 (Score:3, Funny)

## Re:1+1=10 (Score:3, Funny)

There are 10 kinds of people in the world:

Those who understand quaternary, those who don't, those that think it's binary or ternary, and then there's are the ones who insist on making stupid jokes about numeric systems.

## Point nine recurring equals one (Score:3, Interesting)

## The Slashdot Equation (Score:5, Funny)

garbage in = garbage out

Jolyon

## The Pythagorean Theorem (Score:4, Insightful)

## The importance of notation (Score:5, Interesting)

Apropos to the current discussion was this response [mathforum.org]:

## Gotta be a winner: (Score:5, Funny)

Of course if sets aren't your thing...

## At the moment... generalized Fourier series (Score:5, Interesting)

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.

## Schrödinger! (Score:4, Informative)

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 axioms of set theory (Score:5, Informative)

all of mathematicscan 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 [wolfram.com] and Metamath Proof Explorer [metamath.org].## Re:The axioms of set theory (Score:3, Interesting)

But are axioms equations ? Or some axioms are equations ?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 th

## Another.. (Score:5, Interesting)

Z = z^2 + c

^^ This simple equation is the generator of Mandelbrot (and Julia) set, arguably the richest fractal known to us..

## Theorem of Pythagoras (Score:3)

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.

## Getting the Ideal Gas Law Right (Score:3, Interesting)

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.

## Women = Evil (Score:4, Funny)

First we state that women require time and money:

Women = Time x MoneyAnd as we all know "time is money"

Time = MoneyTherefore by substituting Money for Time we get:

Women = Money x MoneyWomen = (Money)^2

And because "money is the root of all evil" we therefore can state:

Money = (Evil)^1/2And Since

(Money)^2 = WomenThen

(Money)^2 = EvilAnd we are forced to conclude by substituting "women" for "(money)^2" from above that:

Women = EvilCan't argue with mathematical proof!

## Re:Women = Evil (Score:3, Interesting)

It's such an old joke and I'm such a math teacher that I'm forced to point out that:

let x = -3then x^2 = 9

if you take the square root of both sides you get x = 3.

Technically you should instead write |x| = 3 which covers the actuality that x is in fact -3. I had to find a way to explain the + or - part of the quadratic formula to my Algebra 2's and that's what I did.

What you've really proved is that women are either evil or the opposite of evil.

## A^2+B^2=C^2 (Score:4, Insightful)

This is the only equation that will give you the quickest way from here to there in an airplane.

## Re:Impressions of math equitations. (Score:3, Interesting)

Suppose you have something like this (apologies for loss of indentation)

## Re:Impressions of math equitations. (Score:5, Funny)

Those who understand binary

Those that don't

And those that think they do.

## Re:Impressions of math equitations. (Score:3, Informative)

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 represe

## Re:What about (Score:3, Insightful)

## what about (Score:3, Interesting)