# Pappus Chain

Pappus Chain

The Pappus chain extends across at least two millennia of mathematics. Its origins trace back to the ancient Greek mathematician Archimedes and his studies of circles inscribed within the figure of an arbelos (or shoemaker's knife). The inversive geometry trick for efficiently computing the positions of pairwise tangent inscribed circles, or a Pappus chain, is apparently a modern invention. The Apollonian gasket or curvilinear Sierpinski sieve is constructed by the same iterative process of inscribing a circle in triplets of tangent circles. Thus the Pappus chain construction anticipates the class-2 nested behavior of many elementary cellular automata.