Andrey Kupavskii, János Pach, Gábor Tardos
Published 2017-11-13Version 1
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.
An order-refined and generalized version of the Erdos-Szekeres theorem on convex polygons
Colored partitions of a convex polygon by noncrossing diagonals
On the Regions Formed by the Diagonals of a Convex Polygon
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