Tilings with noncongruent triangles

11/13/2017

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by   Andrey Kupavskii, et al.

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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 no convex polygon with more than three sides can be tiled with finitely many triangles such that no pair of them share a full side.