Dual Rectangles
Number Theory
2009-06-18 v1
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.
Cite
@article{arxiv.0906.3096,
title = {Dual Rectangles},
author = {Graham Everest and Jonny Griffiths},
journal= {arXiv preprint arXiv:0906.3096},
year = {2009}
}
Comments
6 pages, 2 figures