Euler and the bridges of Konigsberg.

The recent edition of NUMB3RS carried a passing mention of the bridge of konigsberg problem. As always no more details a brief mention and couple of graphics.

One of Euler’s popular triumphs was the solution to the problem of bridge of konigsberg. The river Pregel, known now as Pregolya runs through Konigsberg, which in Euler’s day was in Prussia (It’s now in Russia and called Kaliningrad)

The river divides, creating two islands in centre of the town and Konigsberians built seven bridges to span it. It had be a challenge among the citizen to see if any one could walk around the town, crossing each bridge once and only once and return to starting point.

Euler proved in 1735 that the task was impossible. His proof is often cited as the birth of topology where the actual physical distance between points is irrelevant. It was the network of connections between different paths of the town that was important to Euler’s solution.

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