Euler and the Seven Bridges of Königsberg

As I was told by Google, and reminded again by Bradley Alicea at Synthetic Daisies, April 15 was Leonhard Euler’s 309th birthday.

Screen Shot 2013-04-15 at 11.28.23 PM

While Euler is known for a great deal of spectacular mathematical work, I want to focus on one little thing he did that is of particular interest to me. Specifically, Euler is one of the the first people to utilize graph theory, the mathematics that we have adopted today to study complex systems (networks, in my case food webs!).

The problem of the bridges of Königsberg is a famous mathematical problem originating in the town of Königsberg, Russia. In this town, there is an island formed by two branches of a river. The island is connected to three adjacent landmasses by seven bridges. The problem asked whether it was possible to cross all seven bridges without crossing the same one twice.

Euler used graph theory to demonstrate that there was no solution. Each land mass was a node, and each bridge was an edge. He found that in order to solve the problem, at least two nodes in the graph need to have an even number of edges.

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