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The World's Most Beautiful Equations?
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?"
First thing that sprang into my head when I read the title , those horrible old chat up lines such as :
Me + you = one beautiful equation
Me + you =meyou(Meow)
The only things certain in war are Propaganda and Death. You can never be sure which is which though
Check out Bernar Venet. The web site is a bit crap, a flash plugin or something. But click on 'paintings' and explore. Make sure you find the commutative diagrams the size of a house.
Definitely different.
You are being MICROattacked, from various angles, in a SOFT manner.
Much overrated as an equation. c is just a constant (and in sensible units c=1) so all it really says is that E=constant*m. This is hardly the stuff of mathematical wet dreams, even if the fact that it's true does have some interest for physicists.
I looked at the Four-colour graph and found it .. beautiful.
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?).
The surprise isn't how often we make bad choices; the surprise is how seldom they defeat us.
1 = 2
wait
sigma(i=1, n) = (n*(n+1))/2. There's something very elegant about being able to reduce a huge number of operations into three.
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.
Basically on this post. Well, that post asked users favorite equations, not necessarily beautiful. That leads to another interesting question - are your favorite equation and your most beautiful equation the same thing? I just finished a semester of Electrity and Magnetism, and I'm a big fan of Maxwell's eqastions now.
-Tim
I agree, but in this case this is a Ask Slashdot, so it's normal that a question will be presented. By the way, the question wasn't added by the editors (same reason).
The AACS key is NOT 0xF606EEFD628B1CA427BEA93A9CA9773F
My vote is for the Einstein field equation. Briefly stated: the curvature of spacetime is proportional to its mass/energy content. Very pretty.
sub f{($f)=@_;print"$f(q{$f});";}f(q{sub f{($f)=@_;print"$f(q{$f});";}f});
$ = (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.
We don't see the world as it is, we see it as we are.
-- Anais Nin
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.
"Nature doesn't care how smart you are. You can still be wrong." - Richard Feynman
Add the bed
Subtract the clothes
Divide the legs
Multiply
A proof more than a formula:
We all know that girls require time and money, so
Girls = Time x Money
We also know that time is money, so
Time = Money
Therefore,
Girls = Money x Money = Money ^ 2
Furthermore, it is commonly known that money is the root of all evil, so
Money = sqrt(Evil)
Therefore,
Girls = (sqrt(Evil))^2 = Evil
Hence,
Girls = Evil
The heat equation is beautiful, as it applies to so many different things (heat, diffusion, options pricing).
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.
"Nature doesn't care how smart you are. You can still be wrong." - Richard Feynman
I was always partial to the fundamental theorem of calc... pretty profound (tangents and integrals are opposites) but, unlike for example Maxwell's equations, it is VERY easy to understand and prove.
Omnes stulti sunt.
42
I win!
Lump lingered last in line for brains, and the ones she got were sorta rotten and insane.
Combustion of propane and oxygen.
CH4 + 2O2 --> CO2 + 2H2O
"It is not a dream, It is a simple feat of scientific electrical engineering, only expensive...blind faint-hearted, doub
Sorry if already said, but: 1+3+3=7
- Agilo
Please discuss.
You are in a maze of twisty little passages, all alike.
Not to be a humbug, but isn't the beauty of an equation in it's proof? I mean, mathematically, the difference between 2^(3*4)=4096 and e^(pi*i)=-1 isn't a whole lot. The proof, however, for e^(pi*i)=-1 is real mind-bender that culminates in a simple, beautiful little equation. It's that culmination that makes it beautiful, not the equation itself.
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.
This sig rocks the casbah.
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.
Can't believe no one mentioned Noether's Theorem, so I'll submit it. Proof that the existence of any symmetry in a Lagrangian implies a conserved quantity.
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.
Not an equation, but I find Lagranges Theorem (If H is a subgroup of G, then the order of H divides the order of G) to be beautiful in that it is not very obvious at first why this should be true.
exp(pi*sqrt(163)) is only a near integer, not an exact one. See Ramanujam constant.