Heron's Formula, Descartes Circles, and Pythagorean Triangles

Details Heron's Formula, Descartes Circles, and Pythagorean Triangles Heron's Formula, Descartes Circles, and Pythagorean Triangles

2007-01-22

arxiv.org/abs/math/0701624v1

Mathematics

Metric Geometry

29 pages, 12 figures, 1 table, LaTex

Scientific paper

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.

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