The positive rationals can be arranged in three types of tree with fixed matrix descent and a single root 1/1. Their descent can be taken either high to low or low to high giving a total six trees which have been described separately by various authors.

Some results are obtained on turn sequences, convex hull and minimum area rectangle.

Read draft 5,

- PostScript
`rationals.ps.gz`

(about 428k) - PDF
`rationals.pdf`

(about 444k, 29 pages) - Page of PNG images (about 715k total)
- LaTeX source
`rationals-5.tar.gz`

(about 104k, and sig)

Also by plain HTTP or by FTP or by RSYNC if desired. The sig file is a Gnu PG ascii armoured signature generated from my key.

"Draft" here means believed correct as far as it goes but to be expanded or rearranged in places. The LaTeX source uses PGF for pictures and it generates "postscript specials" so if you process to DVI you'll need a DVI viewer supporting that.

Document copyright 2014 Kevin Ryde. Permission is granted for anyone to make a copy for the purpose of reading it. The PostScript and PDF renditions contain fonts which are Copyright American Mathematical Society and licensed under the open font license.

See Math::PlanePath::RationalsTree for Perl code implementing the trees. The corresponding RationalsTree section of the PlanePath image gallery has some pictures.

See Trees of Primitive Pythagorean Triples for a similar treatment of Pythagorean triples.

This page Copyright 2013, 2014, 2015, 2016, 2017 Kevin Ryde.