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The city of Königsberg in Prussia (now Kaliningrad, Russia) was set on both sides of the Pregel River, and included two large islands—Kneiphof and Lomse—which were connected to each other, and to the two mainland portions of the city, by seven bridges. The problem was to devise a walk through the city that would cross each of those bridges ...
Seven Bridges of Königsberg – Walk through a city while crossing each of seven bridges exactly once. [ 6 ] Squaring the circle , the impossible problem of constructing a square with the same area as a given circle, using only a compass and straightedge .
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]
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.
Medieval Königsberg's third town was Kneiphof, which received town rights in 1327 and was located on an island of the same name in the Pregolya, south of Altstadt. The 14th-century Königsberg Cathedral. Within the state of the Teutonic Order, Königsberg was the residence of the marshal, one of the chief administrators of the military order. [15]
Trestle bridge - thrown over both branches of the Pregolya and passes over Kneiphof, is part of the Leninsky Prospekt, built in 1972, [99] to replace two of the seven Königsberg bridges - Lavochny and Zeleny. There is a pedestrian descent from the bridge to the island, an automobile exit to Moskovsky Prospekt. There is no road exit to the island.
Top: A failed attempt on a plane — the missed wall is indicated Bottom: A solution on a torus — the dotted line is on the back side of the torus Comparison of the graphs of the Seven bridges of Konigsberg (top) and Five-room puzzles (bottom).
Königsberg Cathedral rose high above the island town. Kneiphof Town Hall served as city hall for all of Königsberg from 1724 until 1927, when the administration moved to the Stadthaus . The island's secondary school, Kneiphof Gymnasium , was located north of the cathedral and later hosted the combined Stadtgymnasium Altstadt-Kneiphof .