English

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}
}
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