2007/01/22 by Frank R. Bernhart, Bernhart, Frank, H. Lee Price +1
Engineering · Mathematics · #11G99 #Advanced Numerical Analysis Techniques #FOS: Mathematics #History and Theory of Mathematics #Mathematics and Applications #Metric Geometry (math.MG) #Number Theory (math.NT)
paper · pdf · doi:10.48550/arxiv.math/0701624
openalex publication_date 2007/01/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.