Dual Rectangles

This article has been written for an educational magazine whose target audience consists of students and teachers of mathematics in universities, colleges and schools. It concerns a notion of duality between rectangles. A proof is given that only finitely many integral sided pairs of dual rectangles exist. Then a geometrical group law is shown to hold on the set of all rational self-dual rectangles. Finally, the arithmetic of a cubic surface is used to construct new pairs of rational dual rectangles from old, a technique inspired by the theory of elliptic curves.