The Seven Bridges of Königsberg

The bridges of the ancient city of Königsberg posed a famous and almost problematic challenge a few centuries ago. But this isn’t just about the math problem; it’s also a story about a famous Swiss mathematician named Leonhard Euler who founded the study of topology and graph theory by solving this problem. The effects of this problem have lasted centuries, and have helped develop several parts of our understanding of mathematics.

We don’t hear too much about Euler, but he is one of the most important and influential mathematicians ever, along with Archimedes and Newton. He created more published works than any other mathematician and wrote in a very understandable way. There is a fundamental part of geometry that all other mathematicians before him missed, but Euler discovered it and made the polyhedron formula: V-E+F=2

Euler stayed in Königsberg during the year 1736 while in the area of St. Petersburg. Here, he began developing a new idea called geometriam situs, later called topology. Different from topography, topology is the study of non-rigid shapes. It is about the properties of geometric figures on a surface that are unaltered when the surface is deformed.

The city of Königsberg was located in Russia on the river Pregel. Being founded in the thirteenth century by the Teutonic Knights, it was a major commercial and industrial city. During World War II it was captured and heavily ruined by communists, then had its name changed to Kaliningrad, which is its name today. Konigsberg was built around a river that created four land masses, including an island in the middle called Kneiphof Island. Euler came across this famous question during his stay in the city: “Is it possible for a pedestrian to walk across all seven bridges i...

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...önigsberg, he began to develop the beginnings of graph theory and topology. He looked past all the irrelevant detail, such as the size of land masses and width of the river, just to focus on the simple problem itself. This is a useful technique when discovering any new concept, because sometimes we do not need to keep searching for some long and complicated answer that is hard to understand. Sometimes, the answer is right in front of us.

Works Cited

1. Richeson, David. Euler's Gem: The Polyhedron Formula and the Birth of Topology. 1st. ed. Princeton, New Jersey 08540: Princeton University Press, 2008. Print. .

2. http://mathworld.wolfram.com/KoenigsbergBridgeProblem.html

3. Bram, Leon L. "Topology." Funk & Wagnalls New Encyclopedia. 23. New York: 1979.

4. Bram, Leon L. "Kaliningrad." Funk & Wagnalls New Encyclopedia. 14. New York: 1979.