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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.
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.
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.
I prefer the actual Euler's formula instead of the special case. e^x = cosx+jsinx
$ = (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
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
42
I win!
Lump lingered last in line for brains, and the ones she got were sorta rotten and insane.
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.
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.