Tiling a circular disc with congruent pieces

Kurusa, Árpád and Lángi, Zsolt and Vígh, Viktor (2020) Tiling a circular disc with congruent pieces. MEDITERRANEAN JOURNAL OF MATHEMATICS, 17 (5). ISSN 1660-5446

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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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