The Pythagorean Tree: A New Species
Abstract
In 1967 the Dutch mathemetician F.J.M. Barning described an infinite, planar, ternary tree*. Seven years later, A. Hall independently discovered the same tree. Both used the method of unimodular matrices to transform one triple to another. A number of rediscoveries have occurred more recently. In this article we announce the discovery of an entirely different ternary tree, and show how it relates to the one found by Barning and Hall.
 Publication:

arXiv eprints
 Pub Date:
 September 2008
 arXiv:
 arXiv:0809.4324
 Bibcode:
 2008arXiv0809.4324P
 Keywords:

 Mathematics  History and Overview;
 Mathematics  Number Theory;
 1199;
 11D68;
 11B39;
 05B07;
 05C50
 EPrint:
 14 pages,6 figures, LaTeX *Note (10/24/2011): The classic tree described by Barning, Hall, and others may have been first discovered by B. Berggren in 1934. See: B. Berggren,(1934). "Pytagoreiska trianglar" (in Swedish). Tidskrift for elementar matematik, fysik och kemi 17: 129139