The dissection of a square into an equilateral triangle (or vice versa) is sometimes known as the haberdasher's problem, and can be done in three straight-line cuts.
TIL that Gavin Theobald has produced several dissections from a triangle to a square on the surface of a sphere. Which would make pretty cool 3D-printed desk gizmos: make a ball with a triangular sector removed from one pole, a square sector removed from the other pole, and a set of wedge-shaped pieces that can be used to fill up either hole.
https://mathworld.wolfram.com/HaberdashersProblem.html