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arXiv · 1711.08903

Tilings of convex sets by mutually incongruent equilateral triangles contain arbitrarily small tiles

Christian Richter·Melchior Wirth
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Abstract

We show that every tiling of a convex set in the Euclidean plane $\mathbb{R}^2$ by equilateral triangles of mutually different sizes contains arbitrarily small tiles. The proof is purely elementary up to the discussion of one family of tilings of the full plane $\mathbb{R}^2$, which is based on a surprising connection to a random walk on a directed graph.

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Christian Richter, Melchior Wirth. 2017-11-24. Tilings of convex sets by mutually incongruent equilateral triangles contain arbitrarily small tiles. https://arxiv.org/abs/1711.08903

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