Cutting polygons composed of equal rectangles into similar rectangles
type: Item
instance of: scholarly article
title: Cutting polygons composed of equal rectangles into similar rectangles
zbMATH Open document ID: 1484.51009
DOI: 10.1134/S0001434621110092
author: I. V. Novikov
published in: Mathematical Notes
publication date: 2022-01-11T00:00:00Z
review text: \textit{M. Dehn} [Math. Ann. 57, 314--332 (1903; JFM 34.0547.02)] proved his famous result that a rectangle can be cut into squares if and only if the ratio of the sides of the rectangle is a rational number. One can consider the general and very complicated problem of cutting a polygon into similar rectangles. The author treats the particular case of cutting a polygon all of whose sides belong to \(\mathbb Q[\sqrt{p}]=\{a+b\sqrt{p}:a, b \in\mathbb Q\}\), where \(p\) is a quadratic irrationality.
reviewed by: Martin Lukarevski
Mathematics Subject Classification ID: 51M15
Mathematics Subject Classification ID: 51M04
zbMATH DE Number: 7455551
zbMATH Keywords: cutting
zbMATH Keywords: tiling
zbMATH Keywords: additive function
zbMATH Keywords: rectangle
zbMATH Keywords: quadratic irrationality
MaRDI profile type: Publication
cites work: Rectangling a rectangle
full work available at URL: s0001434621110092
OpenAlex ID: W4200114204
description: scientific article; zbMATH DE number 7455551