Can You Tile A4 Paper with Squares?

We prove that A4 paper cannot be tiled (covered) with finitely many, non-overlapping squares. The squares can be of any size. This is true for any rectangle whose ratio of the height to the width is irrational; for A4, the ratio is the square root of 2. Interestingly, the idea of the proof is linear algebraic (although we don’t assume you know linear algebra). We prefix the proof with a brief explanation of the A series papers. This is an entry for the 3Blue1Brown the Summer of Math Exposition. #SoME1 #3b1b