This is a project that uses Graph Theory, and Euler Circuits and Paths to solve an updated version of the Konigsberg Bridge Problem. The city of Konigsberg in Prussia (now Kaliningrad, Russia) was set on both sides of the Pregel River, and included two large islands, which were connected to each other and the mainland by seven bridges. The problem was to find a walk through the city that would cross each bridge once and only once. The islands could not be reached by any route other than the bridges, and every bridge must have been crossed completely every time.
This classic problem has been updated by using the NYC metro area (Manhattan, The Bronx, Brooklyn, Queens, Staten Island and New Jersey) in conjunction with the 19 trans-Hudson/East River bridges and tunnels. Students use Graph Theory (counting edges, vertices and degrees) to establish if all bridges and tunnels can be traversed in a way that makes metro NYC an Euler Path or an Euler Circuit.