Tilings with noncongruent triangles. (October 2018) - Kupavskii, Andrey; Pach, János; Tardos, Gábor
Abstract: We solve a problem of R. Nandakumar by proving that there is no tiling of the plane with pairwise noncongruent triangles of equal area and equal perimeter. We also show that any tiling of a convex polygon with more than three sides with finitely many triangles contains a pair of triangles that share a full side.