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)
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Anonymous2006-11-04 22:26
sqrt(e^(i(pi))) = i
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Anonymous2006-11-05 9:17
d^2y/dx^2 = (1/v^2) d^2y/dt^2
Or the >1 dimensional version.
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Anonymous2006-11-05 9:36
hay /sci/.
anyone got a good explanation about z-transformation regarding audio signals?
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Anonymous2006-11-05 9:37
whops, wrong input area
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Anonymous2006-11-05 17:39
Euler's indentity is the bestest.
It has e, i, pi, one and zero :D
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Anonymous2006-11-05 18:28
>>6
It has e, i, π, 1, 0, multiplication, addition, and exponentiation, all exactly once.
That's cool.
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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).
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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
Ohm's Law, I = V/R, was pretty handy for all the ohmic conductors, but won't do shit for computer transistors, or heated metals etc.
Still pretty cool though
>>67
1/3 = .3333333...
3 X .33333... = .99999...
hence 3 X 1/3 = .99999...
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Anonymous2007-01-19 11:23
3 X 1/3 = .999999... = 1
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Anonymous2007-01-19 13:28
No, that's only in the sense that .9999... is so close to 1 that it is one.
Yes, I know .3333 repeating is roughly equivalent to 1/3, and 1/3 * 3 = 1, but that does not mean .9999 repeating equals 1. You are just saying that it is so close to 1 that it might as well be one.
You see, .333 repeating =/= 1/3. .3333 repeating is just infinately close to 1/3.
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Anonymous2007-01-19 15:21
>>73
Go fuck yourself in the ass. 'Infinitely close' (note the spelling, dumbfuck) has no meaning other than as 'equal'.
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Anonymous2007-01-23 1:48
∫(-1 -> 1)(sqrt(1+(d/dx(sqrt(1-x^2)))^2)dx) = π
I know it's relatively simple, it's the arclength of a circle of radius 1 on the positive end. If it's actually written in proper form it's a lot cooler looking.