Question: Is it possible to tile the plane with triangles that are (1) mutually similar, (2) pairwise non-congruent and (3)non-right? No other constraints.
Note 1: Reg requirement 3 above: since any right triangle can be cut into 2 pieces similar to itself and non-congruent, we can start with any right triangle and grow a plane-tiling layout outwards with progressively scaled copies of itself.
Note 2: If the question has a "yes" answer, one could consider a more constrained version of the question is got by demanding the tiles to have bounded size. Even if the basic shape of the triangle is a right triangle, this constrained version could be asked.
Note 3: This question was mentioned - briefly, among several others - here: https://nandacumar.blogspot.com/2016/06/non-congruent-tiling-ongoing-story.html
