Tiling a circular disc with congruent pieces

Árpád Kurusa; Zsolt Lángi; Viktor Vígh

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arXiv · 1910.03836

Tiling a circular disc with congruent pieces

Árpád Kurusa·Zsolt Lángi·Viktor Vígh

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Abstract

In this note we prove that any monohedral tiling of the closed circular unit disc with $k \leq 3$ topological discs as tiles has a $k$-fold rotational symmetry. This result yields the first nontrivial estimate about the minimum number of tiles in a monohedral tiling of the circular disc in which not all tiles contain the center, and the first step towards answering a question of Stein appearing in the problem book of Croft, Falconer and Guy in 1994.

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Árpád Kurusa, Zsolt Lángi, Viktor Vígh. 2019-10-09. Tiling a circular disc with congruent pieces. https://arxiv.org/abs/1910.03836

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