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...
Elmentve itt :
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| Dokumentumtípus: | Cikk |
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2020
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| Sorozat: | 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 |
| Tartalmi kivonat: | 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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| Terjedelem/Fizikai jellemzők: | Azonosító: 156-Terjedelem: 15 p |
| ISSN: | 1660-5446 |