In mathematics, the pentagram map is a discrete dynamical system on the moduli space of polygons in the projective plane. The pentagram map takes a given polygon, finds the intersections of the shortest diagonals of the polygon, and constructs a new polygon from these intersections. Richard Schwartz introduced the pentagram map for a general polygon in a 1992 paper though it seems that the special case, in which the map is defined for pentagons only, goes back to an 1871 paper of Alfred Clebsch and a 1945 paper of Theodore Motzkin. The pentagram map is similar in spirit to the constructions underlying Desargues' theorem and Poncelet's porism. It echoes the rationale and construction underlying a conjecture of Branko Grünbaum concerning the diagonals of a polygon.
