Tiling by incongruent equilateral triangles without requiring local finiteness
type: Item
instance of: scholarly article
title: Tiling by incongruent equilateral triangles without requiring local finiteness
zbMATH Open document ID: 1264.51009
DOI: 10.4171/EM/205
author: Christian Richter
published in: Elemente der Mathematik
publication date: 2013-03-13T00:00:00Z
review text: A family \(\mathcal{T}=\{T_i\;|\;i\in I\}\) of subsets of \(\mathbb{R}^2\) is called a \textit{tiling} of a certain set \(S\subseteq\mathbb{R}^2\) provided \(S=\bigcup_{i\in I}T_i\) and the interiors of any two different elements of \(\mathcal{T}\) are disjoint. A tiling will be called \textit{perfect} if, for any different \(T_i\) and \(T_j\), they are similar but incongruent. This paper deals with the construction of perfect tilings for certain sets \(S\subseteq\mathbb{R}^2\), where the elements of the family \(\mathcal{T}\) are equilateral triangles. In particular, it is proved that every open subset of \(\mathbb{R}^2\) admits one such tiling.
Mathematics Subject Classification ID: 51M04
Mathematics Subject Classification ID: 52C20
zbMATH DE Number: 6144255
zbMATH Keywords: tiling
zbMATH Keywords: equilateral triangle
zbMATH Keywords: local finiteness
reviewed by: Antonio M. Oller Marcén
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 6144255