Problem of the Week 1199

Diverse Triangles

Show how to tile the plane with triangles so that all the triangles have the same area, but no two of the triangles are congruent.

Note: A triangle is here viewed as the open set that is the interior of a triangle. "Tile" means the triangles are to be disjoint.

Open question: Can this be done so that the perimeters of the set of triangles are bounded?

Source: R. Nandakumar, Amrita School of Arts and Sciences, Kochi, India.

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