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The Seven Bridges Of Königsberg Essay

1014 words - 5 pages

Around the date 1763, a problem arose in Königsberg, Germany (Diestel). This problem began with a few curious citizens but soon spread to scientists and other intellects, and eventually became known as the Königsberg Bridge Problem. The town of Königsberg was cut into four separate land masses by the river Pregel (Green). At the time, Königsberg was a large trading city, valuable because of its position on the river. The prosperity of the city allowed the people to build seven bridges so citizens could traverse through these four separate land masses with ease. Each bridge had a name, which included Connecting Bridge, Honey Bridge, High Bridge, Blacksmith’s Bridge, Merchant’s Bridge, Wooden ...view middle of the document...

Furthermore, it was a simple problem of evens and odds. For a traveler to come to and leave a piece of land without crossing the same bridge twice, there had to be two separate bridges connecting to the same piece of land. Euler provided the answer to a problem that had challenged many minds, old and young, for many years, and in doing so, laid the foundation for the graph theory (Green).
Simply put, the graph theory is the mathematical theory of the properties and applications of graphs. It is the relationship between lines and points and the graph that consists of the lines and points among them. As said in the “Introduction to the Graph Theory” and as shown in Fig. 1, the graph theory states that the two graphs shown are the same. According to Jun-ichi Yamaguchi, “No attention is paid to the position of the points and length of the lines” (Yamaguchi). There are many graphs and special graph names that are used when speaking of the graph theory, but the only one that needs to be focused on is the Eularian graph. An example of this graph, following his theory on the bridges of Königsberg, is shown in Fig. 2. A Eularian graph, as described by Jin-ichi Yamaguchi, is “a graph [that] has way of getting from one vertex to another [and] includes every edge exactly once and ends at the initial vertex” (Yamaguchi). The Eularian graph is what was initially used to describe the impossibility of traversing each of the seven bridges of Königsberg only once in a path to all four land masses, which is why it remains an important concept in the graph theory to this day (Yamaguchi).
The relationship between the graph theory and the bridges of Königsberg is seen in almost every book written on the graph theory. Teo Paoletti, in his “Leonard Euler's Solution to the Konigsberg Bridge...

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