C] The puzzle is called The Seven Bridges of Königsberg. In the Middle Ages, Königsberg became a very important city and trading center with its location strategically positioned on the river.
endobj Une telle promenade n'existe pas, et c'est Euler qui donna la solution de ce problème en caractérisant les graphes que l'on appelle aujourd'hui « eulériens » en référence à l'illustre mathématicien, à l'aide d'un théorème dont la démonstration rigoureuse ne fut en fait publiée qu'en 1873, par Carl Hierholzer. <>/ExtGState<>/ProcSet[/PDF/Text/ImageB/ImageC/ImageI] >>/MediaBox[ 0 0 612 792] /Contents 4 0 R/Group<>/Tabs/S/StructParents 0>> The Seven Bridges of Konigsberg • The problem goes back to year 1736. It’s based on an actual city, then in Prussia, now Kaliningrad in Russia.
La solution du problème par Euler Euler a d’abord simplifié le problème en travaillant avec un schéma de la ville plus simple que le plan habituel qui montrait toutes les rues et tous les bâtiments importants.
endobj The city is divided by a river with two islands in between and, further downstream, the river splits the city again. <>/Pattern<>/Font<>/ProcSet[/PDF/Text/ImageB/ImageC/ImageI] >>/MediaBox[ 0 0 960 540] /Contents 4 0 R/Group<>/Tabs/S/StructParents 0>> Le schéma d’Euler ne montre que les quatre régions et les sept ponts les reliant, les seules informations importantes pour résoudre le problème.
<> Artwork from the eighteenth century shows Königsberg as a thriving city, where fleets of ships fill the Pregel, and thei… In 1254, Teutonic knights founded the city of Königsberg under the lead of Bohemian King Ottoker II after their second crusade against the Prussians. 2 0 obj Solving the Königsberg Bridge Problem Introduction I d e ci d e d t o e xp l o re t h e K ö n i g sb e rg B ri d g e P ro b l e m f o r my I n t e rn a l A sse ssme n t . endobj %PDF-1.5 4 0 obj <> 2 0 obj
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View Problem 4 Solution.pdf from MATH MISC at University of Texas, Dallas. 3 0 obj endobj • In Konigsberg, a river ran through the city such that in its center was an island, and after passing the island, the river broke into two parts. regions are connected by bridges. Euler’s solution opened up an entire new branch of mathematics, now known as graph theory. The Seven Bridges of Königsberg is a historically notable problem in mathematics. Euler and the K onigsberg Bridge Problem The great Swiss mathematician Leonhard Euler (1707{1783) became interested in the K onigsberg problem around 1735 and published a solution (\Solutio problematis ad geometriam situs pertinentis") in 1741. ��'����d(�[z��)O,�Luq�R#Y ����l�Zަ��$%+�8G�r��|_ • This problem lead to the foundation of graph theory.
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