Square tiled by 17 right triangles

What this is? A square is exactly tiled by 17 pairwise similar right triangles whose legs are in the ratio 1:2. I generate the triangles algorithmically (using repeated altitude-splits inside four base 1:2 triangles), and a checker verifies rightness, the 1:2 ratio, coverage, and the count of distinct areas.

Answer — drawn (fills the square, no overlaps)

1:2 right triangle
1:2 right triangle (rotated)

Reason (how it’s constructed)

  1. Split the square into two horizontal strips 160×80 each. Each strip becomes one 2:1 rectangle; cutting it on a diagonal yields two 1:2 right triangles.
  2. Inside each of the four base triangles, repeatedly drop the altitude from the right angle to the hypotenuse. This splits a 1:2 right triangle of area A into two smaller 1:2 right triangles with areas A/5 and 4A/5. Repeating this in a controlled pattern creates many different areas while preserving similarity.
  3. The four bases are split to depths 6, 4, 3, and 3 pieces respectively (i.e., 5, 3, 2, 2 extra splits), totalling 17 triangles. Because every split stays inside its parent, the union is exactly the square.

Check

Automatic verification of every triangle and the whole tiling:

    We verify: (1) 17 triangles, (2) right angle + legs 1:2, (3) total area equals the square, (4) exact coverage (no gaps/overlaps), (5) number of distinct areas (target ≥ 10).