While some of the "mathematical tablets" known as sangaku are elementary from a geometric standpoint, others sometimes draw on far more sophisticated properties, resulting in arduous calculations. Although the famous golden ratio often appears in geometry (see our feature "La vérité sur le nombre d’or", Tangente 203, 2022), few of these "wooden puzzles" from Japanese temples make use of it. Here are the sangaku involving the golden ratio that we managed to find.
Let's start simple… ----------------------

A first example.