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Recovered from the browser cache of: Pieter

**The author writes:**

This may need some extra information...

There once was a city, Königsberg (the current Kaliningrad), that had seven bridges over the Pregel river. The people were wondering if there was a walk through the city that crossed each bridge once.

The mathematician Euler proved that such a route was not possible. His proof made the problem abstract, making *nodes* of each land mass, and *edges* of each bridge. A combination of nodes and edges is called a *graph*. He then figured that, except for the first node and the last node, the number of edges should be even, because every time you enter a land mass, you should also leave the land mass. In the Köningsberg problem, all nodes had an odd number of edges, so this was not possible.

This was the birth of graph theory, the mathematical study of edges and nodes.

One important class of graphs is the *tree*. A graph is called a tree if (1) you can "travel" from each node to each other node by edges (it is connected) and (2) there is no route that takes you back to your starting point (it has no cycles).

One more thing you might need to know for this joke is that the "banana tree" is not really a tree.