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Greatest Equations Ever

timothy posted more than 9 years ago | from the comic-shop-guy's-revenge dept.

Science 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, ei + 1 = 0. What are some of your favorite equations?"

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correction (5, Insightful)

schematix (533634) | more than 9 years ago | (#10618970)

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 (0)

Enzo90910 (547270) | more than 9 years ago | (#10618995)

Quite true and such a mistake more or less disqualifies the whole paper in my mind. The guy doesn't know what he's talking about, nothing to learn here.

Re:correction (1)

illuvata (677144) | more than 9 years ago | (#10619117)

Why would the fact that the /. submitter made a mistake disqualify the original?
If you follow the links, you'll see that originally was used for Pi. Granted, it does look quite like n in some fonts, but you'd still think the submitter (or at least the editor) would have figured it out

Re:correction (5, Insightful)

niks42 (768188) | more than 9 years ago | (#10619025)

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 (1)

schematix (533634) | more than 9 years ago | (#10619037)

yes exactly

Re:correction (5, Informative)

Anonymous Coward | more than 9 years ago | (#10619085)

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 (1)

bsiggers (57684) | more than 9 years ago | (#10619030)

Also great is the derivation of this equation - one on the classic 'pulling a rabbit out of the hat' lecturer performances back in Uni.

Re:correction (5, Informative)

Ford Prefect (8777) | more than 9 years ago | (#10619058)

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 (5, Funny)

Anonymous Coward | more than 9 years ago | (#10619089)

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

Oh well. 5318008.

Actually... (4, Insightful)

yoshi_mon (172895) | more than 9 years ago | (#10619066)

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.

Submitter and Parent are stupid (1, Informative)

sheapshearer (746106) | more than 9 years ago | (#10619070)

All these corrections and still the answers are wrong.

Eurler's equations is Exp(i*theta) = cos(theta) + i*sin(theta).

Cos(theta) = -1 for theta being **ODD** multiples of PI radians [not any multiple].

Thus, the equation should be

Exp( (2n+1)*PI ) + 1 = 0, where n is a Natural number (1,2,3,4..).

2n+1 gives us all the odd positive integers...

The parent said Exp(i*PI) +1 = 0, but Exp(2*Pi)= +1, not -1....

--
Please, I need the mod points!

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

pD-brane (302604) | more than 9 years ago | (#10619108)

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 (1)

pD-brane (302604) | more than 9 years ago | (#10619125)

Oh sorry, I only RTFA... the submitter (sgant) was the one misreading the pi.

Re:correction (0)

Anonymous Coward | more than 9 years ago | (#10619098)

I had a Physics professor my first semester at college who never bothered to remember the formula for the Law of Cosines. So as he was doing proofs on the board, he redirived it from Euler's equation EVERY TIME.

Re:correction (-1, Offtopic)

buzy buzy (594932) | more than 9 years ago | (#10619100)

MMM pi

Re:correction (0)

metlin (258108) | more than 9 years ago | (#10619101)

Nothing's geekier than a guy who writes down Euler's equation with a bunch of numbers and signs off as Scott.

Beam anyone up lately, mayt?

sum of cubes (4, Interesting)

themusicgod1 (241799) | more than 9 years ago | (#10618971)

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.

ok not the greatest (1)

themusicgod1 (241799) | more than 9 years ago | (#10618983)

but my personal favorite :)

Re:ok not the greatest (-1, Redundant)

Anonymous Coward | more than 9 years ago | (#10619027)

Your .sig link dangles!

actually this is on topic, strangely enough (1)

themusicgod1 (241799) | more than 9 years ago | (#10619063)

thank you sir. for those still doubtful, check out my sig. Specifically, this section [moonside.org] .

Re:actually this is on topic, strangely enough (0)

Anonymous Coward | more than 9 years ago | (#10619116)

I find it quite cool that you mention your WPM in your resume - been quite a while since I saw anyone do it :-)

(meant that as a compliment, just in case you misinterpret)

Re:sum of cubes (1)

mikeage (119105) | more than 9 years ago | (#10619073)

Does the expression 0-1 prove there's a negative number?

Re:sum of cubes (5, Interesting)

themusicgod1 (241799) | more than 9 years ago | (#10619107)

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.

donald duck frist ps0t (1)

DonaldDuckBigO (749237) | more than 9 years ago | (#10618972)

Donald Duck is now having a SCREAMING ORGASM for his fr1st ps0t!!! om gom gomg omgomg omg so HOT

(ot) d: (-1, Troll)

themusicgod1 (241799) | more than 9 years ago | (#10618991)

you suck

and also missed

V=IR (5, Interesting)

oddbudman (599695) | more than 9 years ago | (#10618973)

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

Impressions of math equitations. (0)

Anonymous Coward | more than 9 years ago | (#10618974)

1 + 1 = 11

I was impressed by the technical background of it.

Re:Impressions of math equitations. (1, Funny)

Paster Of Muppets (787158) | more than 9 years ago | (#10619019)

No, 1 + 1 = 10...

Waiting for everyone to switch their calculators to binary mode...

Re:Impressions of math equitations. (1)

ZigMonty (524212) | more than 9 years ago | (#10619120)

Maybe they were using base 1?

Re:Impressions of math equitations. (0)

Anonymous Coward | more than 9 years ago | (#10619039)

1 + 1 = 11

Insufficiently geekazoid -- everyone knows 1 + 1 = 10.

Re:Impressions of math equitations. (1, Funny)

DarkDust (239124) | more than 9 years ago | (#10619051)

1 + 1 = 11

There are 10 types of people: those who understand binary arithmetics and those who dont :-)

Re:Impressions of math equitations. (1)

LittleBigLui (304739) | more than 9 years ago | (#10619082)

1 + 1 = 11


There are 10 types of people: those who understand binary arithmetics and those who dont :-)


Except your arithmetics are unary (or at least "unique"), not binary.

Re:Impressions of math equitations. (0)

Anonymous Coward | more than 9 years ago | (#10619083)

And it's obvious to whom you belong... ;)

Need I point out that 1+1=10 in binary?

Re:Impressions of math equitations. (1)

Frogbert (589961) | more than 9 years ago | (#10619088)

That equation is in base 1 you fool!

Re:Impressions of math equitations. (1)

El_Muerte_TDS (592157) | more than 9 years ago | (#10619128)

Would base 1 just have 0. So:
0+0=00

Re:Impressions of math equitations. (4, Funny)

Associate (317603) | more than 9 years ago | (#10619109)

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. (1)

rooijan (746599) | more than 9 years ago | (#10619113)

those who understand binary arithmetics and those who dont

Would it be rude of me to point at that, in binary arithmetic at least, 1 + 1 = 10?

Take a guess.... (5, Funny)

oneandoneis2 (777721) | more than 9 years ago | (#10618975)

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.... (5, Funny)

Ford Prefect (8777) | more than 9 years ago | (#10619071)

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

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

Re:Take a guess.... (1)

Domini (103836) | more than 9 years ago | (#10619096)

Nevermind Shashdot Id: Check out my e-mail/domain.. ;)

Re:Take a guess.... (2, Interesting)

RupW (515653) | more than 9 years ago | (#10619112)

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.... (1)

node 3 (115640) | more than 9 years ago | (#10619121)

The Internet: Proof that a million monkeys with keyboards won't produce the complete works of Shakespeare.

The Complete Works of Shakespeare [allshakespeare.com]

Yeah, I know. :-)

sing it...!! (0)

Anonymous Coward | more than 9 years ago | (#10618977)

Nothing from nothing leaves nothing!

Geometry and Algebra (4, Interesting)

metlin (258108) | more than 9 years ago | (#10618979)

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... (5, Funny)

Anonymous Coward | more than 9 years ago | (#10618981)

I'm quite fond of this one...

B*u*pi * integral of e^x

Hint: Try writing it in mathematical notation.

Re:Well... (5, Informative)

Anonymous Coward | more than 9 years ago | (#10618988)

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

Re:Well... (5, Funny)

metlin (258108) | more than 9 years ago | (#10619123)

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

Yay!

Euler's equation (1)

etnoy (664495) | more than 9 years ago | (#10618984)

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.

Re:Euler's equation (1)

faragon (789704) | more than 9 years ago | (#10619035)

As historic curiosity, Euler said that the idea was given directly by God. Previous posts were right: mobile phones couldn't work without it as far as filters and modulation is required. The Euler formula is used extensively on signal processing (neighbor to Fourier's frequency analysis).

Another quite cool formula could be: s = e^(jw)
(tribute to Laplace et al)

whatthe? (-1, Offtopic)

RocketRainbow (750071) | more than 9 years ago | (#10618990)

surely not!

H = F ^ 3 (3, Insightful)

Rob_Warwick (789939) | more than 9 years ago | (#10618996)

Happiness = Food x Friends x Fun
From Woz.

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

Re:H = F ^ 3 (1)

cwebb1977 (650175) | more than 9 years ago | (#10619020)

Happiness = Beer x (Women + Beauty(Women))

How about... (2)

Paster Of Muppets (787158) | more than 9 years ago | (#10618999)

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.

Clearly the best (1)

obi-1-kenobi (547975) | more than 9 years ago | (#10619002)

C^2=A^2+B^2 or or Volume = 4/3 * pi r^3

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

peculiarmethod (301094) | more than 9 years ago | (#10619003)

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

Re:that's an easy one.. the answer is (1)

faragon (789704) | more than 9 years ago | (#10619087)

Absolutelly brilliant. Yours is the funniest commentary, still wrong, I've seen in weeks :-)
Anyway, my woman takes a 30% of my spare time, then I spend the 60% left to my Idle process.

ThinkGeek t-shirt (5, Funny)

bokmann (323771) | more than 9 years ago | (#10619010)

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.

Re:ThinkGeek t-shirt (1)

dabigpaybackski (772131) | more than 9 years ago | (#10619055)

My favorite is the thinkgeek tshirt that says "2+2=5 for extremely large values of 2".

I believe that one is referred to in literary circles as "Orwell's Postulate."

I'd have to go for the classic: (0)

Biotech9 (704202) | more than 9 years ago | (#10619011)

Drugs+Money=Chicks [redbrick.dcu.ie]

Dirac's equation of 1/2 spin: (4, Interesting)

Jesrad (716567) | more than 9 years ago | (#10619012)

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 (5, Funny)

RAMMS+EIN (578166) | more than 9 years ago | (#10619018)

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

Gauss (1)

dasnake (738419) | more than 9 years ago | (#10619021)

I() means integral in the proper space I(div(F)dV) = I(Fda) That's damn useful.

F=ma (1, Funny)

Colin Smith (2679) | more than 9 years ago | (#10619028)

Gotta love motorcycles. Mmmwwhahahaaaa.

1+1 = 3 (0)

pyrros (324803) | more than 9 years ago | (#10619029)

1 + 1 = 3
For large values of 1 (and small values of 3)

dupe of old poll (5, Informative)

Gathers (78832) | more than 9 years ago | (#10619031)

"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]

Confused... (1)

pavese (543540) | more than 9 years ago | (#10619062)

If that's the so called favourite, then why is there no light, in xtc?

Sometimes greatness is in the eye of the beholder (0)

Anonymous Coward | more than 9 years ago | (#10619033)

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."

my favourite physics equation (1)

JaF893 (745419) | more than 9 years ago | (#10619036)

C^2 = 1 /(0*0)

A political one :) (-1, Troll)

vandan (151516) | more than 9 years ago | (#10619041)

1 Bush + 1 Dick = 1 fucked country.

Einstein's FULL equation (3, Informative)

physicsphairy (720718) | more than 9 years ago | (#10619043)

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 (5, Informative)

dasnake (738419) | more than 9 years ago | (#10619056)

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

Re:Einstein's FULL equation (2, Insightful)

Paster Of Muppets (787158) | more than 9 years ago | (#10619064)

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 (2, Insightful)

physman (460332) | more than 9 years ago | (#10619091)

Another way of writing the equation E=mc^2 is to we write what m is. m = m0 / [1 - v^2/c^2] (Where m0 is the rest mass - i.e. the mass of the particle when it is stationary - relativity states that the mass of a particle changes when its velocity increases - f=ma is only a newtonian approximation). Therefore, E = m0 c^2 / [1 - v^2/c^2}

Quotation from non-mathematical world (1, Funny)

Anonymous Coward | more than 9 years ago | (#10619046)

Beauty * Brains = Constant

Re:Quotation from non-mathematical world (1)

Zilquis (633850) | more than 9 years ago | (#10619052)

You forgot one bit Its Brains * Beauty * Availability = Constant

Big Constant? (0)

Anonymous Coward | more than 9 years ago | (#10619075)

I have a first class with honours degree in electronics sytems and I modelled for a short time in my youth!

I like this one too (1)

MachDelta (704883) | more than 9 years ago | (#10619086)

Though its more famously attributed to in words, it works in math too:

Intelligence * WorldPopulation = Constant

Physics/Mathematics equation top 20 (1)

MoobY (207480) | more than 9 years ago | (#10619047)

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)

(Generalized) Stokes equation (4, Insightful)

Ibag (101144) | more than 9 years ago | (#10619049)

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.

Fermat's Last Theorem (1)

cloudkj (685320) | more than 9 years ago | (#10619050)

x^n + y^n = z^n has no non-zero integer solutions for x, y and z when n > 2.

Everything = 42 (4, Funny)

marcovje (205102) | more than 9 years ago | (#10619057)


Everything = 42 :-)

Some important ones... (1)

lithium100 (624098) | more than 9 years ago | (#10619061)

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)

an old favourite (2, Funny)

Anonymous Coward | more than 9 years ago | (#10619067)

b4i (square root)u ru/16

OBLIGATORY: (1, Funny)

marktaw.com (816752) | more than 9 years ago | (#10619069)

Life, The Universe & Everything = 42

Re:OBLIGATORY: (1, Funny)

SamSim (630795) | more than 9 years ago | (#10619124)

6x9=42

0+2=1 (1)

Dr.Opveter (806649) | more than 9 years ago | (#10619076)

i like that equation best when it comes to music (nomeansno)

One my calc teacher showed me (5, Funny)

lewger (648379) | more than 9 years ago | (#10619078)

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.

Re:One my calc teacher showed me (1)

Jesrad (716567) | more than 9 years ago | (#10619106)

Nice :) It works in french too.

Re:One my calc teacher showed me (1)

stud9920 (236753) | more than 9 years ago | (#10619115)

you won't understand this one, but cheval/oiseau= vachel/oiseau = bete a pis l / bete a ailes = beta pi l / beta l = pi. Therefore horse/bird=pi

rigid polyvinyl chloride aka PVC (0)

Anonymous Coward | more than 9 years ago | (#10619093)

3600/sec. per part*length of part/12000*MFT=lbs/hr

Distribution of answers (1)

skraps (650379) | more than 9 years ago | (#10619103)

The most normal answer:
integral(e^(-(x^2)/2),x)/sqrt(2*pi)

Worst equation ever (1)

shoppa (464619) | more than 9 years ago | (#10619105)

x = ( -b +/- sqrt(b^2-4ac) )/2a

Somehow manages to take the beauty of a quadractic curve and turns it into a grunge problem.

y = r^3/3... har-de-har-har! (2, Funny)

Anonymous Coward | more than 9 years ago | (#10619110)

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?

the fundamentals (0)

Anonymous Coward | more than 9 years ago | (#10619111)

what no S = k.ln(W) ?

khinchin's constant (2, Interesting)

harlows_monkeys (106428) | more than 9 years ago | (#10619122)

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.

'e' is for "cool formula" (1, Interesting)

Anonymous Coward | more than 9 years ago | (#10619130)

= 1/0! + x/1! + x^2/2! + x^3/3! + x^4/$! + ...

Google calculator (3, Funny)

Knx (743893) | more than 9 years ago | (#10619133)

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...

Use the (HTML) source, Luke! (2, Informative)

eric.t.f.bat (102290) | more than 9 years ago | (#10619135)

It's OK to use HTML on a website, you know. I suggest:

<i>e<sup>i&pi;</sup> - 1 = 0</i>

... which will work nicely in most browsers.

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