An Elementary Proof that the Borromean Rings are Non-Splittable
Ollie Nanyes · American Mathematical Monthly · 1993
Linstrom and Zetterstrom [1] gave a proof that the Borromean rings (figure 1) could not consist of true circles. In this note, we give an elementary proof (sans algebraic topology) that the Borromean rings are linked though no two components are. The tool that we use is the colorability mod n of a knot or link diagram. This tool has been presented in honors undergraduate seminars. I have included a discussion of colorability mod n though the technique is well known. For example, see Kauffman, Chapter VI [2].