Tiling an Equilateral Triangle

Michael Beeson

Tiling an Equilateral Triangle

Combinatorics 2024-05-30 v3 History and Overview Metric Geometry

Authors: Michael Beeson

Abstract

Let $ABC$ be an equilateral triangle. For certain triangles $T$ (the "tile") and certain $N$ , it is possible to cut $ABC$ into $N$ copies of $T$ . It is known that only certain shapes of $T$ are possible, but until now very little was known about the possible values of $N$ . Here we prove that for $N>3$ , $N$ cannot be prime, and study more closely the possible tilings when the tile has a $\pi/3$ angle.

Keywords

tilings triangulations manifolds

Cite

@article{arxiv.1812.07014,
  title  = {Tiling an Equilateral Triangle},
  author = {Michael Beeson},
  journal= {arXiv preprint arXiv:1812.07014},
  year   = {2024}
}

Comments

24 pages, 11 figures. This version added pictures of new tilings found by Herdt, and a table of unsolved values of N

Tiling an Equilateral Triangle

Abstract

Keywords

Cite

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