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Conundrum Inspires Topology

Known as the birthplace of the philosopher Immanuel Kant, the City of Königsberg (now Kaliningrad, Russia) is more famous in math and computer science circles for its seven bridges problem. The Pregel River runs through the town and flows on either side of the island of Kneiphof. Seven bridges were built to access the island and either shore as shown in the accompanying diagram. The townspeople wanted to know if it was possible to devise a route that would visit each section of the City but would involve crossing each bridge exactly once.

The Swiss mathematician Leonhard Euler addressed this problem by replacing the landmasses in the city with vertices and the bridges with arcs connecting those vertices as shown in the diagram in Figure 2. The paper he published in 1736, "The Seven Bridges of Königsberg," not only demonstrated that a solution was not possible for the seven bridges problem but also provided a criterion that allows one to quickly determine whether there is a solution for any similar problem with any number of bridges. This paper laid the foundation for the branch of mathematics known as topology.