In this note, we prove that any monohedral tiling of the closed circular unit disc with \(k \le 3\) 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.

中文翻译：

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用等号碎片平铺圆盘

在此注释中，我们证明具有\（k \ le 3 \）拓扑圆盘作为图块的闭合圆形单位圆盘的任何单面平铺都具有k倍的旋转对称性。这一结果得出了关于圆盘单面平铺中并非所有平铺都包含中心的最小平铺瓷砖数量的第一个非平凡的估计，也是回答出现在Croft，Falconer的问题书中的斯坦因问题的第一步，和盖伊（1994）。