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?"

correction

[schematix]

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.

Re:correction

[niks42]

Actually, isn't Euler's formula Exp[i*theta] = cos[theta] + i*sin[theta] ? and then substitute in the value of pi into theta, and the more famous result appears.

Re:correction

[Anonymous Coward]

There's a difference between "Euler's formula" and "Euler's Formula", depending on whether you're referring to one of his formulae or the specific formula called "Euler's Formula".

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

Re:correction

[SamSim]

...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

[Anonymous Coward]

Euler has a ridiculous amount of stuff named after him.

A hockey team in Edmonton, Alberta...

Re:correction

[AuMatar]

Ever wonder why they named 2.71... e? One guess.

Re:correction

[Anonymous Coward]

e for exponential?

Re:correction

[TildeMan]

Actually, it's not named after Euler, just by him. He did pick the name for the constant, but only picked 'e' because a, b, c, and d were already common elsewhere.

Re:correction

[cocotoni]

As they say, in maths things are usually named after Euler, or the first person to discover them after Euler.

Re:correction

[Venner]

Yep. There was a (somewhat tongue-in-cheek) footnote in one of my college math books that the tradition in mathematics was
"...to name [things] after the second person who discovered them. Because Euler probably got there first."

Re:correction

[ralphclark]

Actually,

F+V = E+2

is generally known as Euler's relation, probably to distinguish it from Euler's equation.

Re:correction

[SamSim]

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

Re:correction

[ari_j]

Actually, the most important result, albeit not as famous, is that taking an irrational number to the power of an irrational imaginary number and adding a rational number gives you zero. For example, sqrt(2)^sqrt(-2) + 7 = 0.

Re:correction

[Ford Prefect]

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

[Anonymous Coward]

Too bad my mathematical abilities don't reach beyond spelling rude words on calculators held upside-down.

Oh well. 5318008.

Joke Time

[TrentL]

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."

Re:correction

[UnknowingFool]

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...

[yoshi_mon]

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...

[beaverfever]

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...

[Phekko]

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...

[psbrogna]

For example, MS Windows.

Re:Actually...

[Rich0]

e^i*pi=-1 isn't a law of nature.

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...

[rsidd]

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 could define them as two real wavefunctions and work out the appropriate algebra, but it's exactly complex algebra. So i could 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...

[dwbassett42]

This difference in views is similar to a fundamental difference between engineers and physicists: Engineers feel their equations are a reasonable approximation of reality, and physicists feel that reality is a reasonable approximation of their equations. And mathematicians? They see no relation between the two. ;)

Re:Actually...

[Mikkeles]

'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...

[Smidge204]

Nonono, any researcher will tell you that. They just want to cover up the TRUTH. Those complex mathematical formulas are actually mystical runes that describe ancient spells. The formulas themselves DO make your phone work!

=Smidge=

Re:Actually...

[Vintermann]

It's what I always said, maths is in fact magic.

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

[Enigma_Man]

that is Pi up there, not n. It's a very small font, so it may look like an n, but it's actually a PI symbol...

-Jesse

Exp[ i*Cir/2] + 1 = 0

[cryptochrome]

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

Re:Submitter and Parent are stupid

[pD-brane]

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).

Re:Submitter and Parent are stupid

[sgant]

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.

Re:correction

[sgant]

It was my mistake in the original posting. Not the article from Physics world, as I couldn't put in special characters.

Talk about throwing the baby out with the bathwater!

sum of cubes

[themusicgod1]

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.

Re:sum of cubes

[Kippesoep]

I wish I could deny the existence of negative numbers. My bank, on the other hand, insists that is how much money I have...

Re:sum of cubes

[themusicgod1]

I mean, you're right it does. But man, was I skeptical.

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

[themusicgod1]

ok[still grappling as to how exactly to reply to the earlier reply. it much more specifically hits at the critical point here; that systems of knowledge can be expressed as different sets of axioms, if expressable as axioms at all; and while my axioms may begin with additive inverses before subtraction, you may be able to go the other way, although I think it would be much less elegant. Stranger harmonies have erupted in mathematics than that, however... ]

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

V=IR

[oddbudman]

Gotta Love V=IR. Works pretty well, I use it daily, well that and P=VI.

Re:V=IR

[djdead]

When I was taking physics for the first time in high school, a EE from MIT taught me the following:

twinkle twinkle little star
power equals I squared R

I remembered it.

Re:V=IR

[Quantum Jim]

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

[Hatta]

I happen to like the Gibbs free energy equation:

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

[Technician]

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

[klaasvakie]

Obviously another person who never uses AC

At 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

[AuMatar]

You're making a big mistake- you're assuming R has to be a constant. It doesn't need to be. R is the resistance, which can be a formula. Actually, it is a formula- R=l*psi/A where l is length, A is cross sectional area, and psi is the resistivity of the substance (which again, can be a formula that takes in temperature, or may be a constant for given material and temperature).

Take a guess....

[oneandoneis2]

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....

[Ford Prefect]

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

But shurely 1 /\ 1 = 1 ? [wikipedia.org]

Re:Take a guess....

[Speare]

But shurely 1 /\ 1 = 1 ?

No, I'm serious. And stop spelling it 'shurely.'

Re:Take a guess....

[RupW]

I don't get the whole mystery over 1+1=2 and huge proofs.

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....

[bigdreamer]

"The difficulty of formal logic was demonstrated in the monumental Principia Mathematica (1925) of Whitehead and Russell's, in which hundreds of pages of symbols were required before the statement 1 + 1 = 2 could be deduced."

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

Re:Take a guess....

[archeopterix]

I don't get the whole mystery over 1+1=2 and huge proofs.

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?

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

1+1=2 in the most popular form

Re:Take a guess....

[PenguiN42]

Try 1+0=0 - this should be a bit harder :-)

You're right, that would be a hard proof ;)

Geometry and Algebra

[metlin]

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.

Well...

[Anonymous Coward]

I'm quite fond of this one...

B*u*pi * integral of e^x

Hint: Try writing it in mathematical notation.

Re:Well...

[Anonymous Coward]

thats buttsex for those of you who dont know how to write an integral

Re:Well...

[metlin]

Slashdot - the only place where you could stay ontopic and mention buttsex and integral in the same sentence _and_ get modded informative.

Yay!

H = F ^ 3

[Rob_Warwick]

Happiness = Food x Friends x Fun
From Woz.

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

How about...

[Paster Of Muppets]

x = x0 + V * cos (theta)* t, y = y0 + V * sin (theta) * t - (1/2) * g * t^2.

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

that's an easy one.. the answer is

[peculiarmethod]

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

and driving the joke into the ground we get ..

[Suchetha]

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

(Mone

Re:one of the more famous misquotes there

[Zak3056]

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

[bokmann]

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.

Dirac's equation of 1/2 spin:

[Jesrad]

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 [zeitlin.net], second part [zeitlin.net]. Worth a read IMO.

0 = 0

[RAMMS+EIN]

My favorite is 0 = 0, because it's the one that most often indicates you're done with the math exercise. :-)

Re:0 = 0

[_xeno_]

Conversely, my "favorite" is 1 = 0, because it means that you get to spend another 5 minutes figuring out what you did wrong.

dupe of old poll

[Gathers]

"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 [slashdot.org]

Einstein's FULL equation

[physicsphairy]

The equation everyone knows offhand is E=mc^2 (even if they don't know what it means), but few people know that the full equations is E=m^2c^4 + p^2c^2. 'p' is momentum, so when you're talking about just the rest mass of the particle you have E=mc^2.

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

[dasnake]

I think your favorite equation should be E^2=m^2c^4+p^2c^2.
Nah?

Re:Einstein's FULL equation

[physicsphairy]

*sheepish grin* That's the second time I've done that now.

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

Re:Einstein's FULL equation

[Paster Of Muppets]

It's actually E^2 = (m^2 * c^4) + (p^2 * c^2), so for objects with no momentum (only rest mass energy) you can sqaure-root both sides and get E = m * c^2

Re:Einstein's FULL equation

[ggeens]

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

More like: E^2 = (m0^2 * c^4) + (p^2 * c^2)

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

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

(Generalized) Stokes equation

[Ibag]

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.

Re:(Generalized) Stokes equation

[Just Some Guy]

That's very similar to Farfegnugen's Law of Inverse Transients relating the comb structure of the polymassive decay groupings to the unthorped resident pressures:

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

Oh, crap, why don't you admit that we both just made this stuff up to sound intelligent on Slashdot?

Everything = 42

[marcovje]

Everything = 42 :-)

Re:Everything = 42

[martinde]

Reminds me of a fun trick with google. Google's calculator knows all kinds of constants - "c", "pi", "e", etc. (Just put those in the standard search box and hit search and you'll see what I mean. Now you can use them in equations - "2*pi+7" or whatever.)

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

[lewger]

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.

Paper on this

[mukund]

Some beautiful equations of mathematical physics [arxiv.org]

khinchin's constant

[harlows_monkeys]

For almost all real numbers r, let {Pn/Qn} be the sequence of convergents of the continued fraction expansion of r. Then limit as n goes to infinity of Qn^(1/n) exists and is equal to exp(pi^2/(12 ln 2)).

That's my favorite.

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

Google calculator

[Knx]

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

That is, if you're suspicious...

1+1=10

[notany]

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

Re:1+1=10

[216pi]

and what are the other eight?

Re:1+1=10

[juhaz]

How about this instead:

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

[SamSim]

Point nine recurring equals one.

The Slashdot Equation

[jolyonr]

Of special importance to slashdot:

garbage in = garbage out
Jolyon

The Pythagorean Theorem

[syntap]

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 importance of notation

[tootlemonde]

Over at the Historia-Matematica [mathforum.org] discussion list, the members debated [mathforum.org] a similar question:

As you know, notation has helped the progress of mathematics. Consider, for example, the limitations of the Roman number system, the importance of the invention of a symbol for zero, etc.

Which were, in your opinion, the notations that have permitted the greatest advances in mathematics?

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

the interest of the question:

> Which were, in your opinion, the notations that have permitted the
> greatest advances in mathematics?

(which is very different from any question concerning the history of math. notations) is very close to the interest of the question: who has been the greatest mathematician in the history, e.g. near zero.

Gotta be a winner:

[tod_miller]

us {all,your,base}

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

At the moment... generalized Fourier series

[dysprosia]

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 [wikipedia.org] 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.

Schrödinger!

[k98sven]

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 axioms of set theory

[ortholattice]

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 [wolfram.com] and Metamath Proof Explorer [metamath.org].

Re:The axioms of set theory

[ortholattice]

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

Comment removed

[account_deleted]

Comment removed based on user account deletion

Theorem of Pythagoras

[amightywind]

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

[radtea]

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.

Women = Evil

[static0verdrive]

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!

Re:Women = Evil

[rpillala]

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

[Shotgun]

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.

Re:Impressions of math equitations.

[ajs318]

1 + 1 = 11? It does in Javascript.

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

function min_up() {
if (document.theform.mins.value < 59) {
document.theform.mins.value += 1;
};
};
function min_down() {
if (document.theform.mins.value > 0) {
document.theform.mins.value -= 1;
};
};
...
<form name="theform" method="post" action="<? echo $this_script?>">
...
<input type="text" name="mins" value="<? echo date('i') ?>" />
<a href="JavaScript:min_up()"><img s

Re:Impressions of math equitations.

[Associate]

There are 11 types of people:
Those who understand binary
Those that don't
And those that think they do.

Re:Impressions of math equitations.

[mark-t]

For any number base n, there are n distinct symbols that can be used to represent the magnitude of that value. Any representation of a number with more than n distinct symbols in it cannot possibly be taken as a number in base n.

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

[crull]

0.999999... is just another way of symbolising the value 1. Its the same value, just two ways to write it.

what about

[themusicgod1]

x=x+1 ? or does that count as two.