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<aFlag> i haven't i'd just take out 254 turns ehhe
<de1337> wonder what he means with rebuild it though
<encoded> akan01n: a rectangle has only 4 sides...
<aFlag> i think he wants to take the 255 turns
<akan01n> yes.. its a engine component.. i dont rememeber the name
<aFlag> and make one big rectangle
<encoded> u need an optimization formula
<encoded> l * w=.45m^2
<encoded> 2l* 2w= .45m^2
<akan01n> pick up a rectangle.. and put a cord around it.. i will have 2*a+2*b = P, if a and b are the sides
<akan01n> but i have 255*(2*a+2*b) = P
<de1337> well, if you make the rectangle twice as big in scale turns would be about half, correct?
<encoded> not necesarily
<de1337> why no
<de1337> t
<de1337> *about, if he want the same scale, form of the new rectangle
<akan01n> and i want to make a gigante rectangle only knowing the area A = 0.45 m^2
<akan01n> maybe the sides would be, a=0.9m b=0.5m
<de1337> he wants to "rebuild this rectangle", not only make a new one, i suppose that means something?
<dbrock> why do you call the new rectangle "giant" if it's to have the same area as the one you started with?
<encoded> dude its just a equation system solve for 1 and get the other { l=.45/2w w=.45/2l
<akan01n> http://servlab.fis.unb.br/matdid/1_1999/Alex-Jair/guias/magnetis/espira.jpg
<akan01n> this is what i mean.. i have the area of the circle.. but i have N turns
<akan01n> i want to make a big circle.. if this line
<encoded> ohhhhhh
<Safrole> Anyone care to walk me through the proof of <a^k> = <a^(gcd(k,n))> where n = |a|?
<akan01n> same for the rectangle
<Safrole> any k is any integer
<Safrole> and k is any integer
<Tokenizer> hi, is there a shortcut to factor ((x^)-1)
<Tokenizer> sorry
<Tokenizer> ((x^5)-1)
<encoded> akan01: the link u gave doesnt work
<Catfive> = (x^5 - 1^5)
<akan01n> encoded going to upload on imageshack, wait
<Safrole> oh and a is an element of a group G
<Tokenizer> catfive. i know
<Tokenizer> what's the shortcut for that?
<Tokenizer> that's not a difference of squares
<astrolabe_> Tokenizer: Do you know the formula for the sum of a geometric series?
<Tokenizer> no
<encoded> i do
<akan01n> http://img469.imageshack.us/my.php?image=espira2qb.jpg
<akan01n> i have a circle area.. but N turns around the same area!
<encoded> astrolave_: E[a(n)]^r converges when |r|>1
<akan01n> i want to take this and rebuild a giant circle.. but with the rectangle with area A= 0.45 m^2
<akan01n> N = 255
<astrolabe_> Hmmm. Do you know that if f(a)=0 then (x-a) divides f(x)?
<astrolabe_> encoded: right, I was really talking about a finite one though.
<encoded> ok astrolabe, and i was wrong it converges when |r|<1 just in case
<akan01n> encoded take a look.. u will understand what i mean now. =)
<Tokenizer> so is there any easy way to factor ((x^5) -1) ?
<encoded> akan01n i do, let me think(that may take a while)
<akan01n> ok =P
<astrolabe_> Tokenizer: I've given two answers, I don't know of any others that are easier.
<Tokenizer> astrolb... i didn't see any comments forwarded towards me
<astrolabe_> Tokenizer: Well, all mine were meant for you, except the one for encoded.
<Tokenizer> sorry, can you be more specific.... all i need is a short cut for factoring. ... i think what you are trying to say has to do with delta/epsilon limits
<encoded> what is the circumference(perimeter) of the circle?
<Tokenizer> diameter times pie
<int80_h> I need three integers where all three integers are greater than the average
<int80_h> it's a test case for this haskell code I'm writing. And I just can't think of any
<int80_h> average meaning (x + y + z)/3
<koala_man> uhm
<akan01n> encoded.. the circle is an example.. i want with rectangle.. with N = 225 turns and area A = 0.45 m^2
<joblot> int80_h : what metric space are you operating in?
<int80_h> joblot: eep?
<joblot> int80_h : because it is not possible in the reals
<int80_h> I was suspecting so but I wasn't sure
<int80_h> well then this code is useless, I should remove it
<encoded> akan01n my mind went on strike, i cant find the anwser
<Catfive> Let a = (x + y + z)/3 and suppose x,y,z > a. Then a < (a + a + a)/3 = a.
<astrolabe_> Tokenizer: I'm reluctant to just answer a homework problem for you, but you might find this page helpful. http://mathworld.wolfram.com/PolynomialFactorTheorem.html
<Tokenizer> astrolbe, i can factor it the long way.. i needed a general formula, if you don't know..... no need to comment
<dbrock> akan01n: I still don't get what the problem is
<Catfive> (... Then a > ... rather)
<dbrock> you have a cord wrapped around a rectangle 255 times
<dbrock> the rectangle's area is 0.45 m^2
<dbrock> then what?
<encoded> how big is the circle?
<encoded> right?
<Safrole> Anyone care to walk me through the proof of <a^k> = <a^(gcd(k,n))> where n = |a|?
<astrolabe_> Tokenizer: You didn't ask about a general formula. Anyway, if you solved this problem, the generalisation to x^p-1 should be obvious.
<joblot> Safrole : is that the discreet log thm?
<Safrole> No it's group theory
<Safrole> a is a member of a arbitrary group G
<encoded> omg number theory!
<akan01n> dbrock.. take a look http://img469.imageshack.us/my.php?image=espira2qb.jpg
<dbrock> akan01n: yes, I've seen that
<dbrock> akan01n: that doesn't really tell me anything
<astrolabe_> Safrole: Do you know that gcd(k,n) = x k + y n for some integers x and y?
<Safrole> yes
<akan01n> i have a rectangle with N = 225 turns, A = 0.45 m^2, i want to make a big rectangle with this cord, lets say!
<Safrole> a^(xk)*a^(yn)
<Safrole> = a^(xk)
<dbrock> akan01n: so the new rectangle will have a different area?
<Safrole> how do I show a^k = a^xk ?
<akan01n> yes.. a bigger one
<encoded> akan01n, dbrock with the same cord? just n<255?
<encoded> 225
<dbrock> akan01n: first of all, you don't know how long the cord is; second of all, there are infinitely many ways of making a rectangle with a given perimiter length
<Safrole> astrolabe have any suggestions?
<astrolabe_> You have shown that a^ gcd is in <a^k>, you need to show a^k is in < a ^ gcd>
<akan01n> encoded sorry.. is 225 turns and not 255
<Safrole> I thought that was the argument
<encoded> yeah... i said that 1 line below
<Safrole> a^k is definitely a subset of a^(kx)
<akan01n> with the book answer it says that the N = 1 turn, A = 22811 m^2
<astrolabe_> Do you mean <a^(kx)> is a subset of <a^k>?
<encoded> of course it does, the book doesnt lie
<Safrole> I believe a^k is a subset of a^(kx)
<Safrole> I think that's obvious
<encoded> a=pi*(r^2)
<encoded> a/225=.45m^2
<astrolabe_> Safrole: Are you skipping the '<>' signs?
<encoded> or something like that
<akan01n> a = 101.25 m^2
<akan01n> its to far from 22811 m^2
<Safrole> yes sorry astrolabe
<akan01n> dbrock but i think we can get a possible values to a and b sides of the rectangle, right?
<akan01n> lets say a=0.9m b=0.5m
<astrolabe_> Safrole: That's ok, but you are implying for instance in (Z,+) that <1+1> (ie, the even numbers) is a subset of <1+1+1+1>.
<astrolabe_> Unless you have a particular value in mind for x.
<astrolabe_> Oh, are you using my x ? :)
<Safrole> okay...
<Safrole> <a^k> = {a^k*alpha where alpha is any integer}
<astrolabe_> Safrole: right
<Safrole> <a^kx> = { a^(kx)*beta where beta is any integer}
<dbrock> someone help akan01n with his extremely simple geometry problem
<dbrock> I have to run
<Safrole> The thing is I want to show these two sets are equal
<Safrole> so I have to show containment in both directions
<Safrole> and hmmm...
<Safrole> well x*beta is an integer
<Safrole> so <a^kx> is a subset of <a^k>
<astrolabe_> Safrole: good :)
<Safrole> now I'm kind of stumped going the other way...
<Safrole> x is a specific value
<astrolabe_> Safrole: Well you know that gcd(k,n) divides k.
<Safrole> right
<Safrole> but I'm dealing with x... which is an integer
<astrolabe_> <a^gcd(k,n)> = <a^kx>
<Safrole> that is true
<Safrole> so <a^gcd(k,n)> = <a^kx> is a subset of <a^k> because {a^m*gamma where m is the gcd(k,n)} where m|k
<Safrole> therefore <a^gcd(k,n)> contains all multiples of m, where k = q*m where q is any integer.... so replace q with gamma
<Safrole> I'm a little confused...
<astrolabe_> It shows ;)
<Safrole> lol
<astrolabe_> I'll recap
<Safrole> thank you
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