Author Topic: Something you know  (Read 19823 times)

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Offline Deep Toaster

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Re: Something you know
« Reply #15 on: February 24, 2011, 05:35:10 pm »
http://en.wikipedia.org/wiki/Euler's_formula#Proofs

You'll need to know some calculus (as a warning).




Offline broooom

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Re: Something you know
« Reply #16 on: February 24, 2011, 05:35:35 pm »
- Oops, wrong mathemathics used :P -
« Last Edit: February 24, 2011, 05:38:06 pm by broooom »

Offline Deep Toaster

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Re: Something you know
« Reply #17 on: February 24, 2011, 05:36:25 pm »
That'd mean:

e^ip + 1 = 0
e^i * e^p = -1
e^i = -1/e^p
i = ln(-e^-p)
i = -p * ln(-e)
That can't be right! :o

It could be; remember ln(x) is undefined when x is negative.




Offline squidgetx

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Re: Something you know
« Reply #18 on: February 24, 2011, 05:37:24 pm »
e^(pi i) does not equal e^(pi)*e^(i)

@ruler501, check this link: http://en.wikipedia.org/wiki/Euler's_formula#Proofs It's a bit hard to understand without a backing in calculus though :P

Generally you can't really conceptualize raising a number to an imaginary power; the main method of going about this sort of thing is creating a power series (a polynomial) that mimicks the behavior of e^x. e^x's power series (which, when taken to an infinite amount of terms is perfectly accurate) then can be used with imaginary values for x and still make sense.
e^x's power series looks like this:

and so e^(ix)'s power series looks like this:

You'll have to take my word for it that that series is actually cosx+i*sinx. The rest of the proof goes from there.
« Last Edit: February 24, 2011, 05:42:58 pm by squidgetx »

Offline Deep Toaster

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Re: Something you know
« Reply #19 on: February 24, 2011, 05:38:50 pm »
e^(pi i) does not equal e^(pi)*e^(i)

Didn't see that.

@ruler501, check this link: http://en.wikipedia.org/wiki/Euler's_formula#Proofs It's a bit hard to understand without a backing in calculus though :P

Ninja'd ;)

With almost the exact words :D
« Last Edit: February 24, 2011, 05:39:47 pm by Deep Thought »




Offline apcalc

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Re: Something you know
« Reply #20 on: February 24, 2011, 05:42:10 pm »
Ah yes!  That has to be the most beautiful mathematical statement that exists! :)

Although I still sometimes refuse to believe in its beauty, this still eludes me more! :)


Offline squidgetx

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Re: Something you know
« Reply #21 on: February 24, 2011, 05:43:56 pm »
How about 1+2+3+4+....=-1/12 :D

Or 1+2^2+3^2+4^2+.....=0 O.o

Also @Deep, yeah I saw but I figured he didn't :P So I reposted it.
« Last Edit: February 24, 2011, 05:45:29 pm by squidgetx »

Offline Deep Toaster

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Re: Something you know
« Reply #22 on: February 24, 2011, 05:44:39 pm »
Although I still sometimes refuse to believe in its beauty, this still eludes me more! :)

Whoa, what? O.O

And slightly off-topic: the Wikipedia URL is awesome too ;D

How about 1+2+3+4+....=-1/12 :D

Or 1+2^2+3^2+4^2+.....=0 O.o

:crazy: Where'd you get that?
« Last Edit: February 24, 2011, 05:45:08 pm by Deep Thought »




Offline squidgetx

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Re: Something you know
« Reply #23 on: February 24, 2011, 05:50:05 pm »
Wiki
Also, 1+1+1+1...=-1/2

Offline ruler501

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Re: Something you know
« Reply #24 on: February 24, 2011, 06:00:44 pm »
EDIT: Fixed the quote
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 how would you calculate n^i with any real number for n
and then from that how would you calculate i^(ni)
None of these things work on my calculator so I'm wondering
@squidgetx I know that that factors into the two polynomial approximations for the trigonometric functions.

Does anyone one know anything that will help me learn more about/grasp imaginary numbers and things like raising things to imaginary powers?
« Last Edit: February 24, 2011, 06:05:54 pm by ruler501 »
I currently don't do much, but I am a developer for a game you should totally try out called AssaultCube Reloaded download here https://assaultcuber.codeplex.com/
-----BEGIN GEEK CODE BLOCK-----
Version: 3.1
GCM/CS/M/S d- s++: a---- C++ UL++ P+ L++ E---- W++ N o? K- w-- o? !M V?
PS+ PE+ Y+ PGP++ t 5? X R tv-- b+++ DI+ D+ G++ e- h! !r y

Offline ruler501

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Re: Something you know
« Reply #25 on: February 24, 2011, 06:03:38 pm »
I was hoping to find/write a program that would do this but I see that that would be very hard to do

EDIT: I was asking about how Zeda got 3^i would be cos(ln(3))+isin(ln(3))
« Last Edit: February 24, 2011, 06:07:04 pm by ruler501 »
I currently don't do much, but I am a developer for a game you should totally try out called AssaultCube Reloaded download here https://assaultcuber.codeplex.com/
-----BEGIN GEEK CODE BLOCK-----
Version: 3.1
GCM/CS/M/S d- s++: a---- C++ UL++ P+ L++ E---- W++ N o? K- w-- o? !M V?
PS+ PE+ Y+ PGP++ t 5? X R tv-- b+++ DI+ D+ G++ e- h! !r y

Offline squidgetx

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Re: Something you know
« Reply #26 on: February 24, 2011, 06:04:15 pm »
Sorry I deleted my post, as it didn't make much sense. Yeah, i'm not quite sure how you would do it :P

Offline ruler501

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Re: Something you know
« Reply #27 on: February 24, 2011, 06:07:23 pm »
i edited my post above with what my question was
I currently don't do much, but I am a developer for a game you should totally try out called AssaultCube Reloaded download here https://assaultcuber.codeplex.com/
-----BEGIN GEEK CODE BLOCK-----
Version: 3.1
GCM/CS/M/S d- s++: a---- C++ UL++ P+ L++ E---- W++ N o? K- w-- o? !M V?
PS+ PE+ Y+ PGP++ t 5? X R tv-- b+++ DI+ D+ G++ e- h! !r y

Offline Deep Toaster

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Re: Something you know
« Reply #28 on: February 24, 2011, 06:07:44 pm »
Wiki
Also, 1+1+1+1...=-1/2

Math makes no sense. That's why I love it :D




Offline Juju

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Re: Something you know
« Reply #29 on: February 24, 2011, 06:12:02 pm »
O_o how the hell adding an infinite number of positive numbers equals a negative one?

Math sure is weird.

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