Heron's Formula, Descartes Circles, and Pythagorean Triangles

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dc.creatorBernhart, Frank
dc.creatorPrice, H. Lee
dc.date2007-01-22
dc.date.accessioned2026-07-07T07:42:38Z
dc.date.available2026-07-07T07:42:38Z
dc.descriptionThis 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.
dc.description29 pages, 12 figures, 1 table, LaTex
dc.identifierhttps://arxiv.org/abs/math/0701624
dc.identifierhttp://arxiv.org/abs/math/0701624
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/122518
dc.subjectMetric Geometry
dc.subjectNumber Theory
dc.subject11G99
dc.titleHeron's Formula, Descartes Circles, and Pythagorean Triangles
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