Given a quadrilateral inscribed in a circle, Ptolemy's Theorem relates the lengths of the diagonals and sides. In general, for an inscribed polygon, Ptolemy's relation allows one to write the length of any diagonal as a Laurent polynomial in terms of the lengths of the diagonals coming from some fixed triangulation. Schiffler and Musiker showed that these Laurent polynomials can be written in terms of perfect matchings (or "dimer covers") of some planar graph. Recently, Penner and Zeitlin defined a super-symmetric version of Ptolemy's relation, involving anti-commuting variables. In recent work with Musiker and Zhang, we showed that iterated applications of the super Ptolemy relation gives a sum over double dimer covers of the same planar graph.