Tiling a circular disc with congruent pieces

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...

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Bibliographic Details
Main Authors: Kurusa Árpád
Lángi Zsolt
Vígh Viktor
Format: Article
Published: 2020
Series:MEDITERRANEAN JOURNAL OF MATHEMATICS 17 No. 5
doi:10.1007/s00009-020-01595-3

mtmt:31407382
Online Access:http://publicatio.bibl.u-szeged.hu/19353
Description
Summary: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.
Physical Description:Azonosító: 156-Terjedelem: 15 p
ISSN:1660-5446