Ford gets Complex!

    Not too complicated and just a different view of Ford’s circles and a way of morphing them along with a bit of animation. It’s a continuation of the previous post and there are two parts to it – the real bit and the imaginary part. The Real Part To start with we take fractions not between 0 and 1 but rather between -n and n. A rough and ready way is

where we take all possible pairs and reduce them. Note we allow 0 as a denominator so as to be consistent with the Farey sequence. For Read More

Count the Fractions.

This is the first in a series of posts about sequences of fractions, circles, trees of fractions, binary search trees and ways of representing rational numbers as paths through these trees . The idea is to enjoy a bit of recreational mathematics and to use Haskell to express some of the notions in its own succinct way. One Lot Of Fractions First we’ll look at all unique and simplified fractions between 0 and 1 with a denominator no larger than a given value. For example, with a maximum denominator of 3, 4 and then 5 we have     For Read More

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