Reptiles with Holes

Francis Jordan; Sze Man Ngai

doi:10.1017/S001309150400001X

Reptiles with Holes

Francis Jordan, Sze Man Ngai

Mathematical Sciences

Georgia Southern University

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

Croft, Falconer and Guy asked: what is the smallest integer n such that an n-reptile in the plane has a hole? Motivated by this question, we describe a geometric method of constructing reptiles in ℝ^d, especially reptiles with holes. In particular, we construct, for each even integer n≥4, an n-reptile in ℝ² with holes. We also answer some questions concerning the topological properties of a reptile whose interior consists of infinitely many components.

Original language	American English
Journal	Proceedings of the Edinburgh Mathematical Society
Volume	48
DOIs	https://doi.org/10.1017/S001309150400001X
State	Published - Oct 1 2005

Keywords

Holes
Reptiles

DC Disciplines

Education
Mathematics

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https://doi.org/10.1017/S001309150400001X

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title = "Reptiles with Holes",

abstract = "Croft, Falconer and Guy asked: what is the smallest integer n such that an n-reptile in the plane has a hole? Motivated by this question, we describe a geometric method of constructing reptiles in ℝd, especially reptiles with holes. In particular, we construct, for each even integer n≥4, an n-reptile in ℝ2 with holes. We also answer some questions concerning the topological properties of a reptile whose interior consists of infinitely many components.",

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N2 - Croft, Falconer and Guy asked: what is the smallest integer n such that an n-reptile in the plane has a hole? Motivated by this question, we describe a geometric method of constructing reptiles in ℝd, especially reptiles with holes. In particular, we construct, for each even integer n≥4, an n-reptile in ℝ2 with holes. We also answer some questions concerning the topological properties of a reptile whose interior consists of infinitely many components.

AB - Croft, Falconer and Guy asked: what is the smallest integer n such that an n-reptile in the plane has a hole? Motivated by this question, we describe a geometric method of constructing reptiles in ℝd, especially reptiles with holes. In particular, we construct, for each even integer n≥4, an n-reptile in ℝ2 with holes. We also answer some questions concerning the topological properties of a reptile whose interior consists of infinitely many components.

KW - Holes

KW - Reptiles

UR - https://digitalcommons.georgiasouthern.edu/math-sci-facpubs/598

UR - https://doi.org/10.1017/S001309150400001X

U2 - 10.1017/S001309150400001X

DO - 10.1017/S001309150400001X

M3 - Article

SN - 0013-0915

VL - 48

JO - Proceedings of the Edinburgh Mathematical Society

JF - Proceedings of the Edinburgh Mathematical Society

ER -

Reptiles with Holes

Abstract

Keywords

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