  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.
