that was cut through by the river pregel, and right in the middle of the river was a small island, kneiphof. the island was connected by seven bridges, and the townspeople liked to ponder whether or not you could have a trip that actually used each bridge exactly once. now, this is a problemhat might trto address tively, okg for all poss phs and sny of tm woulrk but ft a problem that you could solve mathematically. and the mathematician who figured this out was leonhard euler, who actually lived in konigsberg. he realized that the problem wasn't one about geography. it had nothing to do with the lengths of the bridges or their distances from one another, but it had everything to do with connectivity, which bridges are connected to which islands or riverbanks. he got to the essence of the problem by simplifying it, turning the bridges into lines, squashing the landmasses into points, which we'll call vertices. and in the process, he formed a graph, which became the topological backbone of the problem. euler had turned his trip around town into navigating a graph of four vertices and seven ed