Tilings with noncongruent triangles
Combinatorics
2018-04-12 v3 Discrete Mathematics
Metric Geometry
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.
Keywords
Cite
@article{arxiv.1711.04504,
title = {Tilings with noncongruent triangles},
author = {Andrey Kupavskii and János Pach and Gábor Tardos},
journal= {arXiv preprint arXiv:1711.04504},
year = {2018}
}