Dual Rectangles

Graham Everest; Jonny Griffiths

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arXiv · 0906.3096

Dual Rectangles

Graham Everest·Jonny Griffiths

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Abstract

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.

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Graham Everest, Jonny Griffiths. 2009-06-17. Dual Rectangles. https://arxiv.org/abs/0906.3096

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