Fibonacci mod n and Petrie polygons Seminar

Outside the MRSI at Berkely there is a beautiful sculpture called "The Eightfold Way", which is a representation of Klein's Genus 3 surface underlying Klein's quartic. Where does this sculpture get its name? After all this surface has more to do with the number seven. Its automorphism group is PSL(2,7) and it is constructed from a subgroup of the (2,3,7) triangle group.

We answer this by considering an elementary question involving the Fibonacci sequence..

We discuss Petrie polygons which are zig-zag closed paths on the surface and relate these paths to Fibonacci sequences.