## The World's Most Beautiful Equations? 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?"*
## Much better equation art (Score:4, Informative)

## Re:Einstein was onto something... (Score:5, Informative)

## Arithmetic series (Score:4, Informative)

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.

## RSA Encryption (Score:4, Informative)

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

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.

## Heat Equation (Score:3, Informative)

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.

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

## Emmy Noether! (Score:5, Informative)

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.

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

## Re:Girls are Evil (Score:3, Informative)

Girls = +/- Evil