  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.
