  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 uni-modular 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.
