A walk along the branches of the extended Farey Tree
Jeffrey C. Lagarias, Charles P. Tresser · IBM Journal of Research and Development · 1995
The rational numbers can be presented as the set of vertices of a degree-tree tree. If p/q and p'/q' are two rational numbers written in lowest terms, the difference pq'—p'q depends only on the shape of the path joining p/q to p'/q' on this tree.