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Seven Bridges of Königsberg facts for kids

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Konigsberg bridges
Map of Königsberg in Euler's time showing the actual layout of the seven bridges, highlighting the river Pregel and the bridges

The Seven Bridges of Königsberg is a historically famous problem in mathematics. Leonhard Euler solved the problem in 1735. This led to the beginning of graph theory. This then led to the development of topology.

The city of Königsberg in Prussia (now Kaliningrad, Russia) was set on both sides of the Pregel River. It included two large islands which were connected to each other and the mainland by seven bridges.

The problem was to find a way to walk through the city by crossing each bridge once and only once. The islands could not be reached by any route other than the bridges. Every bridge must have been crossed completely every time. The walk need not start and end at the same spot. Euler proved that the problem has no solution.

Importance in the history of mathematics

In the history of mathematics, Euler's solution of the Königsberg bridge problem is considered to be the first theorem of graph theory. Graph Theory is a subject now generally regarded as a branch of combinatorics.

Present state of the bridges

Two of the seven original bridges were destroyed during the bombing of Königsberg in World War II. Two others were later demolished. They were replaced by a modern highway. The three other bridges remain, although only two of them are from Euler's time (one was rebuilt in 1935). Thus, as of 2000, there were five bridges in Kaliningrad.

In terms of graph theory, two of the nodes now have degree 2, and the other two have degree 3. Therefore, an Eulerian path is now possible, but since it must begin on one island and end on the other, it is impractical for tourists.

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