# Squaring the plane

by

Year of Award: 2014

Award: Robbins

Publication Information: American Mathematical Monthly, 115 (2008), no. 1, 3-12.

Summary: (Adapted from the JMM 2014 Prizes and Awards booklet) The problem is simple. You are supplied with infinitely many square tiles, but they all have different sizes, in fact, there is exactly one $n$-by-$n$ square for each positive integer $n$. Your task is to use these squares to tile the plane, no overlaps or gaps allowed, and you must use all the squares. This article gives a complete description of such a tiling of the plane.