Good Things Come in Threes: A Ternary Tree for Triangular Triples

Summary A common saying is that good things come in threes. In 1934, B. Berggren may have agreed when unearthing three matrices which generate a ternary tree of all primitive Pythagorean triples from the initial triple . We show that a similar structure exists when replacing primitive Pythagorean triples with triangular triples. The construction of both ternary trees are intertwined, involving Berggren’s three matrices and a third ternary tree. Perhaps good things really do come in threes!