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Geek Culture / I found PI!

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Neuro Fuzzy
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Posted: 18th Sep 2010 09:56 Edited at: 18th Sep 2010 09:57
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Well... I was asking someone on how to derive the exponential function e^x from f(x)=f'(x), f(0)=1, and get this:


and I decided to apply the method used to prove that to another problem (euler integration in case anyone asks). Anyways, I derived this:




...just need to brag about that a lil bit

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Zotoaster
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Posted: 18th Sep 2010 11:02
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Still won't give you an exact value for it unless n is infinity... sigh

"everyone forgets a semi-colon sometimes." - Phaelax
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Libervurto
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Posted: 18th Sep 2010 13:47
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Damn, I wish I could do maths that well. So much to learn.

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Interplanetary Funk
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Posted: 18th Sep 2010 13:50
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I understand all of that, except the big e and "lim"

BASIC programmers never die, they GOSUB and don't RETURN.
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Diggsey
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Posted: 18th Sep 2010 13:57
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"big e" (called sigma) means "sum of ...".
ie. For all values of 'm' from 0 to n-1, do the part after the sigma sign, and then add all of the results together.

"lim" means "at the limit of ...". In this case it is at the limit of "n" approaching infinity. Obviously "n" cannot actually BE infinity, but the closer "n" gets to infinity, the closer the value of the formula gets to pi/2. The "lim" means to take the value that the formula approaches (pi/2) as the result.

[b]
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Interplanetary Funk
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Posted: 18th Sep 2010 13:59
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ah, okay. but if m=0 wouldn't m squared just be 1..?

BASIC programmers never die, they GOSUB and don't RETURN.
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Interplanetary Funk
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Posted: 18th Sep 2010 14:01
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wait no... wouldnt it be 0? (sorry i got confused with raising the power to 0, I was doing maths all day yesterday at college and my minds melted a bit.)

BASIC programmers never die, they GOSUB and don't RETURN.
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Neuro Fuzzy
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Posted: 18th Sep 2010 19:07
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lets give an example. For n=1: we take the sum of all sqrt(1/(n^2+m^2)) from m=0 to n-1, which is 0. So we have sqrt(1/(1^2-0^2))=1. That's a pretty crap estimation of pi. For n=4, we take the sum of all of that weird function from m=0 to m=3.
thats:
sqrt(1/(4^2-0^2))+sqrt(1/(4^2-1^2)+sqrt(1/(4^2-2^2))+sqrt(1;(4^2-3^2))
which is a bit better of an estimation. As n approaches infinity, the sum of all of those terms approaches pi/2.

Of course... That is kinda a mind-bending problem to start out learning sigma notation. Usually there are finite sequences. I'd look at something like this:
http://www.regentsprep.org/Regents/math/algtrig/ATP1b/SigmaNotation.htm

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Aaagreen
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Posted: 18th Sep 2010 20:42
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Me too.




I'd love to see things from your point of view but I can't get my head that far up my bum.
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Ocho Geek
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Posted: 18th Sep 2010 22:46
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Isn't that the joke you make when you first hear about PI?
I was 7-ish

Ocho Geek - Pretending to be a useful contribution to the forums since 2005
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Aaagreen
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Posted: 18th Sep 2010 22:49 Edited at: 21st Sep 2010 04:05
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Maths is for retards.

ModEdit(BiggAdd): Stop trolling. Its starting to get really boring.(Banned until the end of September)


I'd love to see things from your point of view but I can't get my head that far up my bum.
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Ocho Geek
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Posted: 19th Sep 2010 00:44
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Thats the way the world works... wait thats no right... at all

I'm not getting into a flamewar (or whatever the name is) but your beloved games you seem to go on about relies a lot on mathematics so please say something semi-intelligent next time

Ocho Geek - Pretending to be a useful contribution to the forums since 2005
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Aaagreen
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Posted: 19th Sep 2010 00:52
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So is your mum.


I'd love to see things from your point of view but I can't get my head that far up my bum.
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Ocho Geek
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Posted: 19th Sep 2010 00:55
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Its nice to make progress in maths

Ocho Geek - Pretending to be a useful contribution to the forums since 2005
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AutoBot
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Posted: 19th Sep 2010 00:59
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Quote: "now now ladies"


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Venge
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Posted: 19th Sep 2010 00:59
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For some reason I took it upon myself to start memorizing several digits of pi back in middle school. And for some other reason, it is now permanently etched in my long term memory (3.141592653589793238462). I suppose it will come in handy if I ever use perfect circles in animation and need to know something that Maya won't tell me.

I will live forever or die trying.
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Neuro Fuzzy
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Posted: 19th Sep 2010 05:16
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You don't have to memorize anything, if you need four or five digits of pi you can just calculate the sum where n is a million or so

Also, tell me this isn't the coolest thing ever:


its like... a chain made out of numbers.

Actually there's a formula for the nth digit of pi...
found it:
http://www.math.hmc.edu/funfacts/ffiles/20010.5.shtml

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AndrewT
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Posted: 19th Sep 2010 05:28 Edited at: 19th Sep 2010 05:28
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pi = lim x→∞ (x tan(180.0 / x))

Although I suppose I'm cheating by using trig functions...

i like orange
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marlou
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Posted: 19th Sep 2010 06:20
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wow..the equations look very nice..
reminds me of how i used to love math..
heheh..

When a person has nothing but a dream, can he dare to dream.
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Neuro Fuzzy
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Posted: 19th Sep 2010 09:41
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or you could say
pi=ln(-1)/i

yeah... using logarithms or trig is kinda cheating

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Metal Devil123
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Posted: 19th Sep 2010 11:48
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Quote: " semi-intelligent next time"

Quote: "Maths is for retards."

Problem solved! :-P

I can count how many toes I have, can you?

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Diggsey
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Posted: 19th Sep 2010 12:29 Edited at: 19th Sep 2010 12:30
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Odd numbers have their uses

[b]
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Aaagreen
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Posted: 19th Sep 2010 15:55
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Quote: "I can count how many toes I have, can you?"


One.. four.. three.. seven. I have seven.


I'd love to see things from your point of view but I can't get my head that far up my bum.
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