Author Topic: Something you know  (Read 17319 times)

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Offline Deep Toaster

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Something you know
« on: February 23, 2011, 11:54:01 pm »


I'm still amazed every time I see it.

Offline Xeda112358

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Re: Something you know
« Reply #1 on: February 23, 2011, 11:58:36 pm »
I bet it has to do with taylor series for e^x and pi

Offline Deep Toaster

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Re: Something you know
« Reply #2 on: February 24, 2011, 12:00:39 am »
« Last Edit: February 24, 2011, 12:01:37 am by Deep Thought »




Offline shmibs

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Re: Something you know
« Reply #3 on: February 24, 2011, 12:58:22 am »
hey, that's my favourite equation!
it's not really worth anything, but it definitely looks pretty.

SirCmpwn

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Re: Something you know
« Reply #4 on: February 24, 2011, 01:04:31 am »
I'm a hard core atheist, but that's probably the most reasonable evidence of creationism I've seen.

Offline Builderboy

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Re: Something you know
« Reply #5 on: February 24, 2011, 01:27:20 am »
That is, in my opinion, the most beautiful mathematical formula ever :) It uses the 5 most important numbers, uses 3 numbers from each large field of mathematics (i for imaginary, e for logarithmic, and pi for trigonometry) and it uses the 3 main mathematical operations (addition, multiplication, exponentiation)

Offline ralphdspam

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Re: Something you know
« Reply #6 on: February 24, 2011, 01:41:35 am »
 O.O  :w00t:
Absolutely amazing.
ld a, 0
ld a, a

Offline Xeda112358

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Re: Something you know
« Reply #7 on: February 24, 2011, 03:12:36 am »
And it is a very useful equation, too! I ♥ it.

Offline AngelFish

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Re: Something you know
« Reply #8 on: February 24, 2011, 03:32:31 am »
That is, in my opinion, the most beautiful mathematical formula ever :) It uses the 5 most important numbers, uses 3 numbers from each large field of mathematics (i for imaginary, e for logarithmic, and pi for trigonometry) and it uses the 3 main mathematical operations (addition, multiplication, exponentiation)

Personally, I'm a fan of this guy:

http://farm5.static.flickr.com/4120/4816933933_ccdc87cf0a_b.jpg
∂²Ψ    -(2m(V(x)-E)Ψ
---  = -------------
∂x²        ℏ²Ψ

Offline Deep Toaster

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Re: Something you know
« Reply #9 on: February 24, 2011, 09:19:30 am »
And it is a very useful equation, too! I ♥ it.

How do you use it?

That is, in my opinion, the most beautiful mathematical formula ever :) It uses the 5 most important numbers, uses 3 numbers from each large field of mathematics (i for imaginary, e for logarithmic, and pi for trigonometry) and it uses the 3 main mathematical operations (addition, multiplication, exponentiation)

Not to mention it's even set equal to zero. And you forgot to mention that the other two numbers (1 and 0) are pretty important in math two. Both the identity numbers at once :)
« Last Edit: February 24, 2011, 09:19:44 am by Deep Thought »




Offline Xeda112358

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Re: Something you know
« Reply #10 on: February 24, 2011, 11:52:53 am »
Think about how you would do something like raising something to an imaginary power :D You can set up ratios and stuff and do more stuff and stuff. Also, e^(ix)=cos(x)+isin(x), so 3^i would be cos(ln(3))+isin(ln(3))

EDIT: so you can say with that the idea that e^(i2pi)-1=0 (that is i times 2 times pi)

Offline ruler501

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Re: Something you know
« Reply #11 on: February 24, 2011, 05:27:06 pm »
Think about how you would do something like raising something to an imaginary power :D You can set up ratios and stuff and do more stuff and stuff. Also, e^(ix)=cos(x)+isin(x), so 3^i would be cos(ln(3))+isin(ln(3))

EDIT: so you can say with that the idea that e^(i2pi)-1=0 (that is i times 2 times pi)
so what you are saying is that e^i*n*pi)-1=0 where n is any natural number(possibly negative)

this is confusing could someone please explain how you bring numbers to imaginary powers and why you do it that way. I did not think you could bring a number to two separate powers and still have them equal the same number
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Offline squidgetx

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Re: Something you know
« Reply #12 on: February 24, 2011, 05:28:43 pm »
Actually no, n needs to be a multiple of 2. The reason for this is because, as Xeda said, e^ni= cos n + i sin n and the values of sin and cosine repeat themselves over a period of 2pi (Graph it to see). That part actually doesn't have to do with imaginary numbers.

« Last Edit: February 24, 2011, 05:30:14 pm by squidgetx »

Offline Deep Toaster

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Re: Something you know
« Reply #13 on: February 24, 2011, 05:30:38 pm »
so what you are saying is that e^i*n*pi)-1=0 where n is any natural number(possibly negative)

Nope, e2nπi-1=0, while e(2n+1)πi+1=0.
« Last Edit: February 24, 2011, 05:30:57 pm by Deep Thought »




Offline ruler501

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Re: Something you know
« Reply #14 on: February 24, 2011, 05:33:25 pm »
so it is e^(pi*2n*i)-1=0
while e^(pi*(2n+1)*i)+1=0

could somene please explain the proof behind bringing numbers to imaginary powers?
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