In the Mondrian Art Problem, a square is divided into non-congruent integer-sided rectangles so that the largest area and smallest area are as close as possible.
A lattice square can be divided into non-congruent lattice-vertex triangles so that all areas are identical. Pick's theorem, Area = 2 Interior + Boundary/2 - 1, is handy. Below, all triangles have area 3. Define a Perfect Pick as a dissection into non-congruent lattice-vertexed triangles of the same area.
What is the largest possible smallest angle within a a Perfect Pick square dissection?