### 抄録

We consider a tiling of a square by finitely many tiles each of which is a rectangle. We do not assume that the tiles are mutually congruent. Such a tiling is called irreducible if for any two tiles the union of them is not a rectangle. A tiling is called generic if no four tiles meet in a point. A tilling is trivial if it has only one tile. A tile r in a generic tiling of a square is called a spiral if it is contained in the interior of the square and for each edge e of r there is a tile s adjacent to r such that the straight line containing e intersects the interior of s. We show that a nontrivial generic irreducible tiling of a square has a spiral.

元の言語 | English |
---|---|

ページ（範囲） | 175-184 |

ページ数 | 10 |

ジャーナル | Journal of Geometry |

巻 | 90 |

発行部数 | 1-2 |

DOI | |

出版物ステータス | Published - 2008 12 |

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### ASJC Scopus subject areas

- Geometry and Topology

### これを引用

*Journal of Geometry*,

*90*(1-2), 175-184. https://doi.org/10.1007/s00022-008-1923-5

**An irreducible rectangle tiling contains a spiral.** / Motohashi, Tomoe; Taniyama, Kouki.

研究成果: Article

*Journal of Geometry*, 巻. 90, 番号 1-2, pp. 175-184. https://doi.org/10.1007/s00022-008-1923-5

}

TY - JOUR

T1 - An irreducible rectangle tiling contains a spiral

AU - Motohashi, Tomoe

AU - Taniyama, Kouki

PY - 2008/12

Y1 - 2008/12

N2 - We consider a tiling of a square by finitely many tiles each of which is a rectangle. We do not assume that the tiles are mutually congruent. Such a tiling is called irreducible if for any two tiles the union of them is not a rectangle. A tiling is called generic if no four tiles meet in a point. A tilling is trivial if it has only one tile. A tile r in a generic tiling of a square is called a spiral if it is contained in the interior of the square and for each edge e of r there is a tile s adjacent to r such that the straight line containing e intersects the interior of s. We show that a nontrivial generic irreducible tiling of a square has a spiral.

AB - We consider a tiling of a square by finitely many tiles each of which is a rectangle. We do not assume that the tiles are mutually congruent. Such a tiling is called irreducible if for any two tiles the union of them is not a rectangle. A tiling is called generic if no four tiles meet in a point. A tilling is trivial if it has only one tile. A tile r in a generic tiling of a square is called a spiral if it is contained in the interior of the square and for each edge e of r there is a tile s adjacent to r such that the straight line containing e intersects the interior of s. We show that a nontrivial generic irreducible tiling of a square has a spiral.

KW - Spiral

KW - Tiling

UR - http://www.scopus.com/inward/record.url?scp=58149201140&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=58149201140&partnerID=8YFLogxK

U2 - 10.1007/s00022-008-1923-5

DO - 10.1007/s00022-008-1923-5

M3 - Article

AN - SCOPUS:58149201140

VL - 90

SP - 175

EP - 184

JO - Journal of Geometry

JF - Journal of Geometry

SN - 0047-2468

IS - 1-2

ER -