Seven Bridges of Königsberg
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- | The order of the path goes 3-1-2-3-4-2. At vertex 1, we can see that this solution fails because we get in but have no way out. Since vertex 1 is neither a starting point nor an end point (since we still have to go to vertex 4), and with an odd number of lines, scraps any possible solution. | + | The order of the path goes 3-1-2-3-4-2. At vertex 1, we can see that this solution fails because we get in but have no way out. Since vertex 1 is neither a starting point nor an end point (since we still have to go to vertex 4), and with an odd number of lines, scraps any possible solution that has vertex 1 as an intermediate vertex. |
Looking back at the previous figure, we can see that all four vertexes have an odd number of lines. The existence of a path that could reach all four landmasses is impossible because it would go through more than two vertexes with odd number of lines. | Looking back at the previous figure, we can see that all four vertexes have an odd number of lines. The existence of a path that could reach all four landmasses is impossible because it would go through more than two vertexes with odd number of lines. |
Revision as of 13:29, 10 July 2009
Seven Bridges of Königsberg |
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Seven Bridges of Königsberg
- The Seven Bridges of Königsberg is a historical problem that illustrates the foundations of Graph Theory
Contents |
Basic Description
The setting of the problem is the city of Konigsberg in Prussia. The city is divided by a river with two islands. The four parts of the city are linked by seven bridges.The problem is to find a path through the city and cross each bridge once and only once. You cannot cross the rivers except on bridges and must make full crossings of a bridge (you can't go halfway across, and then walk from the other end to the midway point.)
Solution
Ideas for the Future
Make some sort of app that could allow the user to attempt to solve the problem manually. Hopefully they'll be able to trace the picture and the applet will highlight the bridge the user will not be able to go across.
Teaching Materials
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