Math Is Fun Forum

haruka-san

Member

Registered: 2006-11-08

Posts: 205

Continued Fraction

Can someone please help me  solve this problem?
i need a solution.

find the continued fraction of

3 minus square root of 29 divided by 5.

^_^

thanks!

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Don’t compare your life to others. You have no idea what their journey is all about. ^_^

bossk171

Member

Registered: 2007-07-16

Posts: 305

Re: Continued Fraction

I'm a little shaky on this, but you're starting with:

Just to make things easy (for me), I'm going to do 3 - sqrt(29) first. After we both get the process down, we can do it with the 5.

we know that:

If you don't believe me, just foil. Now dividing through by (sqrt(29) + 1) we get:

adding 1...

And sow for the Stoke of genius. If we know that the above identity is true (which I don't see any reason why it shouldn't) then we can substitute the sqrt(29) on the right with the right of the equation, allow me to show you:

Sweet, let's do it again. (PS sorry LaTeX is making it shrink, and I don't now how to stop it. If any mods want to jump in and fix my formating problem, pleas do.)

And again and again and again...

Ok, I'm going to take a break, I'll be back to finish this up.

EDIT: changed all the 30s to 28s, thanks mathsyperson

Last edited by bossk171 (2007-08-19 04:42:24)

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There are 10 types of people in the world, those who understand binary, those who don't, and those who can use induction.

bossk171

Member

Registered: 2007-07-16

Posts: 305

Re: Continued Fraction

Well, there definitely seems to be something wrong. I guess you can't have a number other than 1 in the numerator. Anyone want to step in on this?

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There are 10 types of people in the world, those who understand binary, those who don't, and those who can use induction.

mathsyperson

Moderator

Registered: 2005-06-22

Posts: 4,900

Re: Continued Fraction

There was just a slight error right at the start.

If you follow through and replace all the 30's with 28's then it should work.

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Why did the vector cross the road?
It wanted to be normal.

bossk171

Member

Registered: 2007-07-16

Posts: 305

Re: Continued Fraction

That was kinda stupid (Curse you conjugates!) but I still think it's wrong, I thought that continued fractions must have a 1 in the numerator, doesn't having 28 mess it up?

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There are 10 types of people in the world, those who understand binary, those who don't, and those who can use induction.

Ricky

Moderator

Registered: 2005-12-04

Posts: 3,791

Re: Continued Fraction

http://mathworld.wolfram.com/ContinuedFraction.html

The method for calculating starts at (5), don't be scared by the other stuff in there, it's not important for you.  There was a really cool table that we learned in Number theory and it made doing the calculations really fast.  But I can't seem to find my work on it.  Anyone know what I'm referring to?

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"In the real world, this would be a problem.  But in mathematics, we can just define a place where this problem doesn't exist.  So we'll go ahead and do that now..."