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Konigsberg3

A bridged history of Königsberg

To mathematicians, they are the most famous bridges in the world. Spanning the river Pregel as it flows into the Baltic Sea, the Seven Bridges of Königsberg are today virtually synonymous with the field of topology, the mathematical study of shapes.

Their immortality was assured in 1735 when Leonhard Euler, the great Swiss mathematician, became intrigued by the city’s unique geometrical configuration. In addition to settlements on the north and south banks of the river Pregel, 18th Century Königsberg also included two large islands known as Kneiphof and Lomse. These islands were connected to the mainland as well as each other by seven bridges that were central to the city’s life.

Konigsberg_bridges

Euler wanted to know the answer to a comparatively simple question: would it be possible for a visitor to cross each and every one of Königsberg’s seven bridges once and only once? Being a mathematician and not a tourist, it didn’t matter to him whether the visitor started in the same place as she finished.

Such a path, Euler eventually concluded, would not be possible. The visitor (let’s call her Doris) would either find herself stranded on Kneiphof or else forced to angrily patrol the riverbank waiting for the authorities to build her another bridge. Needless to say, Euler refused to consider either jumping or swimming as valid options.

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