Venn Symmetry and Prime Numbers: A Seductive Proof Revisited

An n-Venn diagram is a Venn diagram on n sets, which is defined to be a collection of n simple closed curves (Jordan curves) C1, C2, ..., Cn in the plane such that any two intersect in finitely many points and each of the 2n sets of the form Ë Cie is nonempty and connected, where ei is one of "interior" or "exterior". Thus the Venn regions are all bounded except for the region exterior to all curves; the finite intersection property means that each bounded region is the interior of a Jordan curve. See [6] for much more information on Venn diagrams. An n-Venn diagram is symmetric if each curve Ci is riHC1L, where r is a rotation of order n about some center (we use O for the fixed point of rotation r).