Sunday, April 20, 2008

Listing the rational numbers

Here's a nice series of posts about how to list every rational number in its lowest terms, with no repeats (ie. only include 2/5 not 4/10). The key is to make a tree with 1/1 as the root and for each node i/j, put i+j/j as the left child and i/i+j as the right child. It's all laid out very clearly in the series of post which is based on a terse maths paper.

In the comments I found a link to another paper which comes at this using matrices and relates this tree with another previously known tree that also lists the rationals. It's a fairly readable paper too but a bit more technical.

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