论文标题
通过双苯胺近似与正方形的矩形平铺
Tiling of rectangles with squares via Diophantine approximation
论文作者
论文摘要
本文阐明了使用一种新颖方法有效地用正方形的平铺矩形的经典问题。随着传统的电阻网络方法的扭曲，我们使用Diophantine近似理论为此事提供了新的和改进的结果，因此克服了悠久的困难，例如对高维类似物的概括。该方法的普遍性通过其在不同的平铺问题上的应用来证明。这些包括带有其他矩形的瓷砖矩形，以及各自的较高维度的对应物，以及带有等边三角形的平均等边三角形，平行四边形和梯形。
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.
