Research Article: Topology: the Mathematics of Form

Mathematics began in earliest times as a collection of practical methods for counting and measuring. In the nineteenth century a branch of geometry arose in which sizes and distances were irrelevant. Topology, sometimes called "rubber sheet geometry," deals with properties that remain the same when an object is bent or stretched. These properties include the number of times a curve intersects itself and whether a surface is open or closed.

During the lifetime of the famous Swiss mathematician Leonhard Euler (1707-1783), there were seven bridges in the Prussian town of Königsberg, where two branches of the River Pregel flowed around an island. The townspeople amused themselves by considering whether it was possible to cross all seven bridges in one continuous trip without re-crossing any of them. Eventually the so-called Königsberg Bridge Problem became a well-known puzzle, but no one was able to find a solution.

Euler approached this problem by...
(read more)