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Map of Königsberg in Euler's time showing the actual layout of the seven bridges, highlighting the river Pregel and the bridges. The Seven Bridges of Königsberg is a historically notable problem in mathematics. Its negative resolution by Leonhard Euler, in 1736, [1] laid the foundations of graph theory and prefigured the idea of topology. [2]
That is, we proceed as if a solution exists and discover some properties of all solutions. These put us in an impossible situation and thus we have to conclude that we were wrong—there is no solution after all. [3] Imagine that there is an "observer" in each "room". The observer can see the solution line when it is in his room, but not otherwise.
comparison 7 bridges of Konigsberg 5 room puzzle graphs: Image title: Comparison of the graphs of the Seven bridges of Konigsberg (top) and Five-room puzzle (bottom) by CMG Lee. The numbers denote the number of edges connected to each node. Nodes with an odd number of edges are shaded orange. Width: 100%: Height: 100%
The Bristol Bridges Walk is a circular hiking route that is linked to the Königsberg bridge problem, a mathematical puzzle, which laid the foundation for graph theory, the mathematical study of networks. [2] [3] [4] The Bristol Bridges Walk presents a solution of the puzzle for the city of Bristol. [5]
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Multigraphs of both Königsberg Bridges and Five room puzzles have more than two odd vertices (in orange), thus are not Eulerian and hence the puzzles have no solutions. Every vertex of this graph has an even degree. Therefore, this is an Eulerian graph. Following the edges in alphabetical order gives an Eulerian circuit/cycle.
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[1] 1464 – Georg Steinhaupt becomes mayor. [3] 1465 – Landing force from Polish-allied Elbląg destroyed the shipyard near the Old Town, preventing the Teutonic Knights from rebuilding their fleet until the end of the Thirteen Years' War. [9] 1466 – Second Treaty of Thorn: the city becomes a part of Poland as a fief held by the Teutonic ...