Tilings of the plane with unit area triangles of bounded diameter
Combinatorics
2018-02-07 v2 Discrete Mathematics
Metric Geometry
Abstract
There exist tilings of the plane with pairwise noncongruent triangles of equal area and bounded perimeter. Analogously, there exist tilings with triangles of equal perimeter, the areas of which are bounded from below by a positive constant. This solves a problem of Nandakumar.
Cite
@article{arxiv.1712.03118,
title = {Tilings of the plane with unit area triangles of bounded diameter},
author = {Andrey Kupavskii and János Pach and Gábor Tardos},
journal= {arXiv preprint arXiv:1712.03118},
year = {2018}
}