In the spirit of the best constants thread, post what you think is the best (most beautiful, useful, elegant, etc) equation from math and physics.
My suggestion: Euler's formula:
e^(ix) = cos(x) + i sin(x)
especially because when x=π, e^(iπ) + 1 = 0 (Euler's identity)
Name:
Anonymous2006-11-04 22:26
sqrt(e^(i(pi))) = i
Name:
Anonymous2006-11-05 9:17
d^2y/dx^2 = (1/v^2) d^2y/dt^2
Or the >1 dimensional version.
Name:
Anonymous2006-11-05 9:36
hay /sci/.
anyone got a good explanation about z-transformation regarding audio signals?
Name:
Anonymous2006-11-05 9:37
whops, wrong input area
Name:
Anonymous2006-11-05 17:39
Euler's indentity is the bestest.
It has e, i, pi, one and zero :D
Name:
Anonymous2006-11-05 18:28
>>6
It has e, i, π, 1, 0, multiplication, addition, and exponentiation, all exactly once.
That's cool.
Name:
Anonymous2006-11-05 22:46
>>6 >>7
the coolest thing about that is: you'll never need any more than that. 0,1... these are all the rational #'s you'll ever need (in a base 2 system). And e, i, π... these are all the irrational constants you'd conceivably need. (φ is cool but you don't really NEED it).
Name:
Anonymous2006-11-05 22:50
the integral of e^x equals f(u^n) such that f(x)=e^x, u=e, n=1, and t is anytime XD
proving 1=2 is the best
if a = b
a^2 = ab [for purpose of writing a^2 = aa)
aa + (aa-2ab) = ab + (aa-2ab)
2aa - 2ab = -ab + aa
2 (aa-ab) = 1 (aa - ab)
2 = 1