space-filling circles

3D Model

Going shell by concentric shell, we can fill up all of 3D space with disjoint (non-intersecting) circles. Start with the row of vertical red rings, and at each shell make a family of circles that avoid the two points at the intersection of a shell and its ring. Inspired by Andrzej Szulkin’s American Math Monthly article (Nov 1983, pp 640-41).