The foundations of topology are often not part of high school math curricula, and thus for many it sounds strange and intimidating. However, there are some readily graspable ideas at the base of topology that are interesting, fun, and highly applicable to all sorts of situations. One of these areas is the topology of networks, first developed by Leonhard Euler in 1735. His work in this field was inspired by the following problem:

In Konigsberg, Germany, a river ran through the city such that in its center was an island, and after passing the island, the river broke into two parts. Seven bridges were built so that the people of the city could get from one part to another. A crude map of the center of Konigsberg might look like this:

Problem 1
Try it. Sketch the above map of the city on a sheet of paper and try to 'plan your journey' with a pencil in such a way that you trace over each bridge once and only once and you complete the 'plan' with one continuous pencil stroke. Solution

Problem 2
Suppose they had decided to build one fewer bridge in Konigsberg, so that the map looked like this:

Problem 3
Does it matter which bridge you take away? What if you add bridges? Come up with some maps on your own, and try to 'plan your journey' for each one.

to the Famous Problems Home Page
to Euler's solution to the problem