This is Leonard Euler. Euler is considered one of the preeminent
mathematicians of the 18th century, and one of the greatest
mathematicians to have ever lived. At least that's what Wikipedia
says. His collected works fill 80 volumes, and is remembered today
for his introduction of much of modern mathematical notation
and terminology, among other things. He had 13 children, of which
only 5 survived childhood. He went blind in his 60s but his output
continued at the rate of one paper a week in 1775.
The city of Königsberg in Prussia (now Kaliningrad, Russia) was set on both sides of the Pregel River, and included two large islands which were connected to each other and the mainland by seven bridges. The problem was to devise a walk through the city that would cross each bridge once and only once, with the provisos that: the islands could only be reached by the bridges and every bridge once accessed must be crossed to its other end
First, Euler pointed out that the choice of route inside each land mass is irrelevant. The only important feature of a route is the sequence of bridges crossed. This allowed him to reformulate the problem in abstract terms (laying the foundations of graph theory), eliminating all features except the list of land masses and the bridges connecting them.
In modern terms, one replaces each land mass with an abstract "vertex" or node, and each bridge with an abstract connection, an "edge", which only serves to record which pair of vertices (land masses) is connected by that bridge. The resulting mathematical structure is called a graph.
Euler shows that the possibility of a walk through a graph, traversing each edge exactly once, depends on the degrees of the nodes. The degree of a node is the number of edges touching it. Euler's argument shows that a necessary condition for the walk of the desired form is that the graph be connected and have exactly zero or two nodes of odd degree.
undirected graph
directed graph
degree
indegree
outdegree
edge weight
Paper Graphs
Pick a short story or novel you like (or would like to learn more
about) and create a network graph on paper that represents an aspect
of it: e.g. the characters.
