# The World's Most Beautiful Equations?

#### Cliff posted more than 8 years ago | from the aesthetics-and-mathematical-elegance dept.

137
music4l numb3rs asks: *"'An exhibition of the world's most beautiful equations...and some of the ugliest ones too' is how the artist Justin Mullins describes his upcoming show in London. He's exhibiting a number of old favourites such as Maxwell's equations and Euler's relation plus some I've not come across such as entanglement. As for ugliness, he points to the four color theorem. My question to contemplate over the holiday period is: what do Slashdot readers think are the most beautiful equations, and the most ugly ones too?"*

## Einstein was onto something... (1)

## N1ghtFalcon (884555) | more than 8 years ago | (#14341826)

Nothing more beautiful then that!

## Re:Einstein was onto something... (4, Informative)

## Darius Jedburgh (920018) | more than 8 years ago | (#14341898)

## Re:Einstein was onto something... (0)

## Anonymous Coward | more than 8 years ago | (#14342084)

## Re:Einstein was onto something... (1)

## ceoyoyo (59147) | more than 8 years ago | (#14342739)

## Re:Einstein was onto something... (4, Funny)

## Walt Dismal (534799) | more than 8 years ago | (#14342130)

$ = (size of lie x price of product x number of suckers x number of PCs x number of years of great products) - (cost of legal defense + cost of penalties + cost of political contributions + cost of Bill's house + cost of Indian programming labor) + K,

where K = a factor I shall explain but you have to pay me first.

## Re:Einstein was onto something... (2, Informative)

## pyite (140350) | more than 8 years ago | (#14342175)

Nothing more beautiful then that!Except that it's only half the equation.

E^2 = (mc^2)^2 + (pc)^2

E = mc^2 only includes the energy contributed by the rest mass.

## Re:Einstein was onto something... (3, Informative)

## Quadraginta (902985) | more than 8 years ago | (#14342722)

## Re:Einstein was onto something... (1)

## Geoffreyerffoeg (729040) | more than 8 years ago | (#14343041)

You and the OP are probably using different m's. His equation (E = m c^2) is correct at all energies if m is the inertial mass. Your equation is correct if m is the rest mass.Yeah, well inertial/relativistic mass is simply energy in different units via E=mc^2, so you may as well call it energy use mass to refer to rest mass.

Otherwise you'd have to say photons have mass.

## Re:Einstein was onto something... (1)

## Quadraginta (902985) | more than 8 years ago | (#14343059)

## Obligatory bad chat-up line equation (3, Funny)

## FidelCatsro (861135) | more than 8 years ago | (#14341833)

Me + you = one beautiful equation

Me + you =meyou(Meow)

## Most Beautiful.. (0)

## Anonymous Coward | more than 8 years ago | (#14341838)

or

E=mc^2

## Quadratic Formula (1)

## NaNO2x (856759) | more than 8 years ago | (#14341855)

## Re:Quadratic Formula (0)

## madsenj37 (612413) | more than 8 years ago | (#14341897)

## And I ask the slashdot editors... (0, Troll)

## phoenix.bam! (642635) | more than 8 years ago | (#14341869)

## I agree, but... (2, Insightful)

## rbarreira (836272) | more than 8 years ago | (#14342104)

## Re:And I ask the slashdot editors... (1)

## GoofyBoy (44399) | more than 8 years ago | (#14342105)

## Re:And I ask the slashdot editors... (0)

## Anonymous Coward | more than 8 years ago | (#14342146)

## Re:And I ask the slashdot editors... (1)

## jpmkm (160526) | more than 8 years ago | (#14342377)

## Re:And I ask the slashdot editors... (2, Funny)

## ConceptJunkie (24823) | more than 8 years ago | (#14342427)

## definition of a derivative (0, Offtopic)

## radical_dementia (922403) | more than 8 years ago | (#14341887)

## Re:definition of a derivative (1)

## ClamIAm (926466) | more than 8 years ago | (#14341997)

art?## Re:definition of a derivative (1)

## name773 (696972) | more than 8 years ago | (#14342787)

## Much better equation art (3, Informative)

## Darius Jedburgh (920018) | more than 8 years ago | (#14341888)

## Best Equation? (1, Funny)

## pipingguy (566974) | more than 8 years ago | (#14341891)

## Re:Best Equation? (1)

## rbarreira (836272) | more than 8 years ago | (#14342201)

## Re:Best Equation? (1)

## pipingguy (566974) | more than 8 years ago | (#14342262)

True. But I can't think of another combination of "stuff" that could be more important for us humans.

## Best Equation?-Dry Well. (0)

## Anonymous Coward | more than 8 years ago | (#14342484)

(Man + Man) = (Women + Women)

## Re:Best Equation? (1)

## alicenextdoor (910558) | more than 8 years ago | (#14343854)

## e^(i*pi) = -1 (2, Insightful)

## SpaceLifeForm (228190) | more than 8 years ago | (#14341894)

## Re:e^(i*pi) = -1 (1)

## hcg50a (690062) | more than 8 years ago | (#14341922)

## Re:e^(i*pi) = -1 (3, Interesting)

## confusion here (827020) | more than 8 years ago | (#14342097)

## Re:e^(i*pi) = -1 (2, Interesting)

## confusion here (827020) | more than 8 years ago | (#14342162)

## Re:e^(i*pi) = -1 (1)

## MaskedSlacker (911878) | more than 8 years ago | (#14343748)

## Re:e^(i*pi) = -1 (1)

## Ignominious Cow Herd (540061) | more than 8 years ago | (#14342257)

I guess it says more about the relationship between e and pi and not so much about i, right?

## Re:e^(i*pi) = -1 (5, Interesting)

## iced_773 (857608) | more than 8 years ago | (#14342272)

No no no.

e^(i*pi) + 1 = 0

There. Fixed your equation. Now it contains all five principal numbers: e, i, pi, 1, and 0.

## Does it really matter? (2, Interesting)

## GoofyBoy (44399) | more than 8 years ago | (#14341912)

From an infinate number of maps to 633 maps. The graph its like browsing through freshmeat or Wikipedia and discovering a world of variety and viewpoints. (sorry it reality does not meet some your expectations of a more "beautiful" number such as 0, 1 or 1,000)

Ugly? I find the the simple formulas. Try explaing what these mean to a child without resorting to "Its because its by definition..." (eg. ALEPH ONE) or having to explain some really complex background on the subject (STARBIRTH, what does pi have to do with this? What is with using the Boltzmann constant?).

## Re:Does it really matter? (1)

## Pseudonym (62607) | more than 8 years ago | (#14342056)

Hail Eris!

## Re:Does it really matter? (1)

## Vellmont (569020) | more than 8 years ago | (#14342149)

## Re:Does it really matter? (1)

## poopdeville (841677) | more than 8 years ago | (#14342380)

## The jury is still out. (1)

## TheLink (130905) | more than 8 years ago | (#14343549)

That is about as cool as a programmer starting with an "infinite number of choices" to solve a problem and ending up with a program with 633 if-then-else statements.

Now if it turns out that that is the shortest program possible to solve the given problem then I guess one will have to accept that as "as cool as it gets".

However if the 633 if-then-else statements can be reduced to a few loops and conditionals, or even a one liner then that would be a lot cooler.

I figure the mathematicians are looking for a far "better compression" than 633 conditionals.

That said, I do wonder whether the mathematicians and physicists will ever be able to compress the laws of the universe to a single theorem.

## The most beautiful equation is... (1)

## exp(pi*sqrt(163)) (613870) | more than 8 years ago | (#14341916)

I never did believe that stuff about beauty and truth...

## Re:The most beautiful equation is... (0)

## Anonymous Coward | more than 8 years ago | (#14342565)

## Re:The most beautiful equation is... (1)

## John Miles (108215) | more than 8 years ago | (#14343168)

## Re:The most beautiful equation is... (1)

## Majik Sheff (930627) | more than 8 years ago | (#14343272)

## Re:The most beautiful equation is... (3, Informative)

## Anonymous Coward | more than 8 years ago | (#14343510)

## Boltzman (1)

## the eric conspiracy (20178) | more than 8 years ago | (#14341933)

## How about e^(2*(pi*i)) (1)

## wrathpanda (63661) | more than 8 years ago | (#14341987)

## I got better. (1)

## FooAtWFU (699187) | more than 8 years ago | (#14342129)

You got e, pi, i, 0 and 1 all in a simple equation. Hard to beat. And curse Slashcode not allowing a graphical paste-in of the letter...

## Huh? (0, Offtopic)

## The NPS (899303) | more than 8 years ago | (#14341999)

## Mine (5, Funny)

## ClamIAm (926466) | more than 8 years ago | (#14342014)

wait

## Re:Mine (1)

## iLogiK (878892) | more than 8 years ago | (#14343351)

0 = 0

1-1 = 2-2

1*(1-1) = 2*(1-1) |:(1-1)

1 = 2

## Arithmetic series (3, Informative)

## Metasquares (555685) | more than 8 years ago | (#14342046)

p = (2^(n-1)) ((2^n)-1) always struck me as beautiful as well (where p is a perfect number and 2^n - 1 is a Mersenne prime). It just has a sort of symmetry.

## This has been asked before... (2, Interesting)

## emplynx (735511) | more than 8 years ago | (#14342085)

## I vote for... (2, Insightful)

## Pseudonym (62607) | more than 8 years ago | (#14342115)

My vote is for the Einstein field equation [wikipedia.org] . Briefly stated: the curvature of spacetime is proportional to its mass/energy content. Very pretty.

## Ideal gas law (1)

## kaos_ (96522) | more than 8 years ago | (#14342140)

PV=nRT

## Re:Ideal gas law (1)

## McTaggart (893466) | more than 8 years ago | (#14343037)

Sure, it's a bit more tedious to use but it looks (to me at least) more elegant and has none of this R crap.

## Re:Ideal gas law (0)

## Anonymous Coward | more than 8 years ago | (#14343139)

Thank you, and the grandparent, for a flashback to 1st year chemistry which I really didn't need...

## 1 = 2... (1, Interesting)

## Luigi30 (656867) | more than 8 years ago | (#14342147)

## Re:1 = 2... (1)

## magicchex (898936) | more than 8 years ago | (#14343054)

## Re:1 = 2... (1)

## Vaevictis666 (680137) | more than 8 years ago | (#14343143)

Dividing by zero, on the other hand...

## Re:1 = 2... (1)

## iLogiK (878892) | more than 8 years ago | (#14343369)

## The funniest equation (1)

## Rude Turnip (49495) | more than 8 years ago | (#14342168)

If you determine the rate of change in this curve correctly, I think you'll be pleasantly surprised!

## Re:The funniest equation (1)

## shobadobs (264600) | more than 8 years ago | (#14342308)

## RSA Encryption (3, Informative)

## DrJimbo (594231) | more than 8 years ago | (#14342171)

phi(n)is Euler's Totient function which is the number of integers less thannthat are relatively prime ton. The numbernis chosen to be the product of two primes,pandq. Even ifnis known, it is hard of findpandq. Thenphi(n) = (p-1)(q-1)and it is easy to pick adand anesuch that You give outnandeas your public key and usenanddas your private key. Public en/decryption is done with: Private en/decryption is done with:## A valuable experience. (0)

## Anonymous Coward | more than 8 years ago | (#14342172)

[Beautiful]

(Time + Effort) = (Exchangable Value + Intrinsic Value)

[More beautiful]

(Time + Effort) + Compensation = Everyone's Happy.

[Ugly]

(Time + Effort) / copyright violations = Market Dilution.

[Uglier]

(Time + Effort) - (Middle finger to Artist) = (F***K You! I'm becoming an Electrician) = (Empty Stocking for Consumer)

## The most beautiful equation (2, Funny)

## Anonymous Coward | more than 8 years ago | (#14342186)

Subtract the clothes

Divide the legs

Multiply

## Girls are Evil (5, Funny)

## DeltaHat (645840) | more than 8 years ago | (#14342224)

We all know that girls require time and money, so

Girls = Time x MoneyWe also know that time is money, so

Time = MoneyTherefore,

Girls = Money x Money = Money ^ 2Furthermore, it is commonly known that money is the root of all evil, so

Money = sqrt(Evil)Therefore,

Girls = (sqrt(Evil))^2 = EvilHence,

Girls = Evil## Four Constants == Beauty (0, Redundant)

## rickwood (450707) | more than 8 years ago | (#14342228)

e^(pi *i)) + 1 = 0 [google.com]## Re:Four Constants == Beauty (0)

## Anonymous Coward | more than 8 years ago | (#14343291)

(e^(pi * i)) + 1 = 0But that's five constants...## Heat Equation (2, Informative)

## pyite (140350) | more than 8 years ago | (#14342252)

u_t = k*u_xx or, more generally, u_t = k*$\Delta$u

Sigh, I wish slashdot supported some sort of LaTeX markup. u_t = k*/_\u

That's the Laplace operator, in case you couldn't tell.

## Fundamental Theorem of Calculus (2, Insightful)

## sinclair44 (728189) | more than 8 years ago | (#14342256)

## Re:Fundamental Theorem of Calculus (1)

## poopdeville (841677) | more than 8 years ago | (#14342407)

a lot, and Stokes' formula looks just like it.## When I posted this there were 42 comments (4, Funny)

## Ignominious Cow Herd (540061) | more than 8 years ago | (#14342267)

I win!

## What about chemistry (2, Interesting)

## hvnerd (903682) | more than 8 years ago | (#14342326)

CH4 + 2O2 --> CO2 + 2H2O

## Re:What about chemistry (0)

## Anonymous Coward | more than 8 years ago | (#14342550)

## Re:What about chemistry (1)

## hvnerd (903682) | more than 8 years ago | (#14343097)

## Re:What about chemistry (1)

## Vo0k (760020) | more than 8 years ago | (#14343528)

## Solids (1)

## shobadobs (264600) | more than 8 years ago | (#14342336)

## Sky high pie (1)

## wooferhound (546132) | more than 8 years ago | (#14342371)

not mine, My

Pie are round

## 1+3+3=7 (2, Interesting)

## Agilo (727098) | more than 8 years ago | (#14342390)

## the Geller formula (1)

## lucm (889690) | more than 8 years ago | (#14342395)

## Gauss's Law: (1)

## rpresser (610529) | more than 8 years ago | (#14342502)

In words, Gauss's law states that "if you add up the surface integral of the displacement vector

Dover a closed surfaceS, what you get is the sum of the total charge enclosed by that surface."I was taught this as a basic theorem in Physics, and thought it interesting as a tool. Then my girlfriend, who was far smarter than I, told me she was learning the same equation in Calc II, and that it could be proven using regular calculus (and had been proven, in fact, by Gauss, hence the name). I was stunned. Took me a week to come down off the glow.

## The Gauss-Bonnet Theorem (1)

## msuarezalvarez (667058) | more than 8 years ago | (#14342525)

The Gauss-Bonnet theorem asserts that the integral of the curvature of a (compact, oriented) surface equals 2 pi times its Euler characteristic, giving an extraordinary beautiful and deep formula.

(This is just one instance of what's called an index-theorem, which usually provide über-beautiful, über-general, über-deep formulas, but tend to be, well, less accessible to the masses...)

There is a semi-ugly rendition of Gauss-Bonnet'd formula into a GIF (Wolfram does GIFs...) here [wolfram.com] .

## Symmetric ones will win...(?) (1)

## bergeron76 (176351) | more than 8 years ago | (#14342560)

I bet that's why the chicks dig me - because I happen to be lucky enough to have 2 equidistant nostrils.

## F=(MV^2)/2 (1)

## jkerman (74317) | more than 8 years ago | (#14342641)

so simple. so pretty. describes so so much.

## Re:F=(MV^2)/2 (1)

## Hikaru79 (832891) | more than 8 years ago | (#14342782)

## The beauty is in the proof. (3, Insightful)

## Vorondil28 (864578) | more than 8 years ago | (#14342649)

On the other hand, an ugly one would be an equation that's long and complex with just as long and complex a proof.

Just my $0.02.

## My favorites: (1)

## Vilim (615798) | more than 8 years ago | (#14342721)

## Emmy Noether! (5, Informative)

## Quadraginta (902985) | more than 8 years ago | (#14342754)

Hence, the fact that force laws do not change with time implies conservation of energy, that they do not change with position implies conservation of linear momentum, and that they do not change with rotation implies conservation of angular momentum. Highly awesome.

## My postulate is pretty ugly (1)

## DanThe1Man (46872) | more than 8 years ago | (#14342802)

"Infinity does not exist for item x if total volume of x is continuously increaseing faster then the universe."

Dude, did I blow your mind?

## Re:My postulate is pretty ugly (1)

## Vo0k (760020) | more than 8 years ago | (#14343520)

## Im really glad for this post. (1)

## guardianfox (853748) | more than 8 years ago | (#14342914)

## Lagrange's Theorem (3, Interesting)

## siwelwerd (869956) | more than 8 years ago | (#14343087)

## Britney Spears (1)

## MrWa (144753) | more than 8 years ago | (#14343128)

## Newton's Second Law (1)

## Spock the Baptist (455355) | more than 8 years ago | (#14343158)

F= dp/dt## my vote (1)

## The Clockwork Troll (655321) | more than 8 years ago | (#14343483)

## Truth is beauty, so here's some truth (1)

## Curien (267780) | more than 8 years ago | (#14343501)

girls = time x money

And eveyrone knows that money is the root of all evil.

money = sqrt(evil)

Finally, it is trivially shown that time is money.

time = money

girls = time x time

time = sqrt(evil)

girls = sqrt(evil)^2

Therefore,

girls = evil

## Heard this one? (1)

## Vo0k (760020) | more than 8 years ago | (#14343562)

So all the functions rush to the exit, just the exponent remains at the bar, unshaken, finishing his beer.

And then The Great Derivative enters the bar.

- I AM THE GREAT DERIVATIVE YOU SHALL BE DIFFERENTIATED.

- Oh, but I'm e^x and I'm not afraid of you, differentiate all you want.

- Oh, yes? And I'm an y derivative, sucker.

## Most Beautiful... (1)

## tooth (111958) | more than 8 years ago | (#14343771)

## Fibonnaci (1)

## arkanoid.dk (895391) | more than 8 years ago | (#14343786)

If you square both sides, you can remove the first squareroot:

x^2 = 1+sqrt(1+sqrt(1...))

Because the other value on the right side has an infinite number of squareroots itt is almost equal to x itself. Therefore, we can write:

x^2 = 1 + x

And that is the equation that defines the golden proportion. Find r1 and r2:

r = (1 ± sqrt(5))/2

Discard the negative vlues and you get

r1 = (1 + sqrt(5))/2. This is approximately close to 1.6180339887...

The golden mean is quite absurd

It's not your ordinary surd.

If you invert it (this is fun!)

You'll get itself, reduced by one;

But if increased by unity,

This yields its square, take it from me.

- Paul S. Bruckmann