  This paper considers a simple geometric construction, called the Pentagram
map. The pentagram map, performed on N-gons, gives rise to a birational mapping
on the space of all N-gons. This paper finds what conjecturally are all the
invariants for this map, and along the way relates the construction to the
monodromy of 3rd order differential equations, and also to Dodgson's method of
condensation for computing determinants.
