Heron's Formula, Descartes Circles, and Pythagorean Triangles
Metric Geometry
2007-05-23 v1 Number Theory
Abstract
This article highlights interactions of diverse areas: the Heron formula for the area of a triangle, the Descartes circle equation, and right triangles with integer or rational sides. New and old results are synthesized. We show that every primitive Pythagorean triple (PPT), furnishes a Descartes quadruple of tangent circles with integral curvatures, and so generates an integral Apollonian packing (IAP) containing a rectangle of centers. Thus Pythagorean triples serve to generate a large number of in-equivalent integral packings.
Keywords
Cite
@article{arxiv.math/0701624,
title = {Heron's Formula, Descartes Circles, and Pythagorean Triangles},
author = {Frank Bernhart and H. Lee Price},
journal= {arXiv preprint arXiv:math/0701624},
year = {2007}
}
Comments
29 pages, 12 figures, 1 table, LaTex