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 by bits either high to low or low to high for total six trees which have been described separately by various authors.

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

Read draft 7,

- PDF
`rationals.pdf`

(about 557k, 41 pages) - LaTeX source
`rationals-7.tar.gz`

(about 272k, 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, 2015, 2016, 2017, 2018, 2019, 2020 Kevin Ryde. Permission is granted for anyone to make a copy for the purpose of reading it. Permission is granted for anyone to make a full complete verbatim copy, nothing added, nothing removed, nothing overlaid, for any purpose. The PDF rendition contains fonts which are Copyright American Mathematical Society and licensed under the open font license.

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

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

This page Copyright 2013, 2014, 2015, 2016, 2017, 2019, 2020 Kevin Ryde.