![]() ![]() ![]() By ignoring the parts of the maze without pac-dots the pac-graph can be created, with the paths and the junctions forming the edges and vertices respectively. This same idea can be applied to Pac-Man. Therefore the route that the residents were looking for did not exist (a route now exists due to two of the bridges being destroyed during World War II). In Königsberg, each island is connected to an odd number of bridges. This means that all of the vertices of the graph except two (the first and last in the route) must have an even number of edges connected to them otherwise there is no route around the graph travelling along each edge exactly once. The only bridge ends that do not need a pair are those at the start and end of the circuit. In this way, the ends of the bridges at each island can be paired off. Euler represented Königsberg in this way as he realised that the shape of the islands is irrelevant to the problem: representing the problem as a graph gets rid of this useless information while keeping the important details of how the islands are connected.Įuler next noticed that if a route crossing all the bridges exactly once was possible then whenever the walker took a bridge onto an island, they must take another bridge off the island. This type of diagram has (slightly confusingly) become known as a graph, the study of which is called graph theory. ![]() Dog leads, mirrors and Hermann Minkowski.Significant figures: David Singmaster (1938–2023).Do the shuffle: finding π in your playlists.Penguins: the emperors of fluid dynamics.Chalkdust issue 14 – Coming 22 November. ![]()
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