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arXiv · 1711.04504

Tilings with noncongruent triangles

Andrey Kupavskii·János Pach·Gábor Tardos
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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 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.

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Andrey Kupavskii, János Pach, Gábor Tardos. 2018-04-11. Tilings with noncongruent triangles. https://arxiv.org/abs/1711.04504

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