Squares can be divided into 45-60-75 triangles: https://twitter.com/mathpuzzle/status/1366756737882218500 (Ed Pegg on twitter, where he seems to be hanging out these days)

This is an interesting variant on something I looked at a long time ago, triangulating the square to minimize the maximum angle (https://www.ics.uci.edu/~eppstein/junkyard/acute-square/). But Pegg's subdivision is not edge-to-edge. And the triangles on my page are not all similar. Do squares have edge-to-edge triangulations by similar acute triangles?