This puzzle was solved by Erich Friedman first.  It did appear to be a new discovery.
This puzzle was solved by Andrej Jakobcic, Ilan Mayer, Evan Whitney, and Clive Tooth.

Later, Michael Reid sent info that Michael Reid sent an article by H. Kaiser (Perfekte Dreieckzerlegungen, El. Math Vol 46, 1991, pages 106-111) that shows that my triangle problem from several weeks ago isn't new.  Any triangle except the equilateral can be cut into differently sized similar triangles.  Here is an example.