<p>The Seven Bridges of Königsberg is a historical mathematical problem which laid the ground for graph theory, and prefigured topology. Königsberg, in former Prussia (now Kaliningrad, Russia), set on both sides of the Pregel River, included two large islands - Kneiphof and Lomse - which were connected to the mainland by a series of seven bridges. The problem was to devise a walk through the city crossing each of those bridges once and only once.</p>
<p>The negative solution came from Swiss mathematician and physicist Leonhard Euler, who pointed out that the choice of route inside each land mass was irrelevant; only the sequence of crossings mattered. Euler created a diagram in which each land mass was represented by a <ahref="beetroot_to_p_lions_es.html#networkTopology">"vertex" or node, and each bridge became an "edge", or link</a> between them. This allowed him to consider the problem in <ahref="ciao_to_wijnhaven.html#abstraction">abstract terms</a>, in the mathematical structure of a <ahref="please_to_wijnhaven.html#graph">graph</a>.</p>
<p>The negative solution came from Swiss mathematician and physicist Leonhard Euler, who pointed out that the choice of route inside each land mass was irrelevant; only the sequence of crossings mattered. Euler created a diagram in which each land mass was represented by a <ahref="beetroot_to_p_lions_es.html#networkTopology">"vertex" or node, and each bridge became an "edge", or link</a> between them. This allowed him to consider the problem in <ahref="ciao_to_wijnhaven.html#abstraction">abstract terms</a>, in the mathematical structure of a <ahref="please_to_wijnhaven.html#graphology">graph</a>.</p>
<p>As only the connection information is relevant, the shape of the pictorial representations can be distorted in any way without changing the graph. For example, <ahref="#unravelingKnots">it does not matter if the links drawn are straight or curved, or whether a node is to the left or right of another</a>.</p>
Simon Browne
5 years ago