
Elementary Math Fractions, Percentages, Word Problems, Equations, Inequations, Factorization, Expansion 
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October 2nd, 2011, 12:47 PM  #1 
Newbie Joined: Oct 2011 Posts: 1 Thanks: 0  Rational approximation algorithm
I'm attempting to write a little program to take a fraction and generate the closest approximate fraction with terms below some limit. Such a tool would come in handy at work for doing arithmetic on small 8bit processors, but mostly it's a fun exercise. I have a vague recollection from some long forgotten lecture or textbook concerning a theorem about the "midpoint" fraction. E.g. given two irreducible fractions then are the smallest terms where , or something along those lines. This would then give me a natural method for finding successively better approximations by first normalizing the soughtafter number and starting with the lower bound and upper bound . Then proceed through divideandconquer to home in on by successively replacing either the lower bound if or the upper bound if until the term limit is reached. My only trouble is that I can't seem to remember what the theorem is called or precisely what it states and (more embarrasingly) I haven't been able to prove it to myself. Am I on the right track here? 
October 12th, 2011, 06:31 PM  #2 
Newbie Joined: Oct 2011 Posts: 12 Thanks: 0  Re: Rational approximation algorithm
I think you may have posted this in the wrong section. 

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