Tiling of rectangles with squares via Diophantine approximation
Combinatorics
2022-11-01 v2 Number Theory
Abstract
This article shines new light on the classical problem of tiling rectangles with squares efficiently with a novel method. With a twist on the traditional approach of resistor networks, we provide new and improved results on the matter using the theory of Diophantine Approximation, hence overcoming long-established difficulties, such as generalizations to higher-dimensional analogues. The universality of the method is demonstrated through its applications to different tiling problems. These include tiling rectangles with other rectangles, with their respective higher-dimensional counterparts, as well as tiling equilateral triangles, parallelograms, and trapezoids with equilateral triangles.
Cite
@article{arxiv.2201.11545,
title = {Tiling of rectangles with squares via Diophantine approximation},
author = {Tamás Keleti and Stephen Lacina and Changshuo Liu and Mengzhen Liu and José Ramón Tuirán Rangel},
journal= {arXiv preprint arXiv:2201.11545},
year = {2022}
}
Comments
16 pages