Editing 2694: Königsberg
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==Explanation== | ==Explanation== | ||
+ | {{incomplete|Created by a WOLF, TWO GOATS, AND THREE BAGS OF GRAPH NODES. Do NOT delete this tag too soon.}} | ||
− | [[File: | + | [[File:Konigsberg bridges.png|frame|right|{{w|Königsberg}}, Prussia in Euler's time, showing the Pregel river and its seven bridges. The Baltic port city is now Kaliningrad, a Russian exclave. Only five of the bridges remain.[https://goo.gl/maps/ChdBoeQMr3AQPi446] ]] |
− | This comic is about the {{w|Seven Bridges of Königsberg}}, a seminal {{w|graph theory}} problem solved by the famous mathematician {{w|Leonhard Euler}}.[https://www.maa.org/press/periodicals/convergence/leonard-eulers-solution-to-the-konigsberg-bridge-problem] The problem was | + | This comic is about the {{w|Seven Bridges of Königsberg}}, a seminal {{w|graph theory}} problem solved by the famous mathematician {{w|Leonhard Euler}}.[https://www.maa.org/press/periodicals/convergence/leonard-eulers-solution-to-the-konigsberg-bridge-problem] {{w|Graph (discrete mathematics)|Graphs}} are a data structure common in many algorithmic problems in computer science. The problem was to devise a path through the city that would cross each of the seven bridges exactly once, without crossing the river forks any other way. In 1736, Euler proved that there was no such possible path. This result is considered to be the first theorem of graph theory and the first proof in the theory of networks[http://www-personal.umich.edu/~mejn/courses/2004/cscs535/review.pdf] — a subject now generally regarded as a branch of {{w|combinatorics}} — and presaged the development of {{w|topology}}. Combinatorial problems of other types had been considered since antiquity. |
− | [[Cueball]] attempts to cheat on the final exam in his algorithms class by traveling back in time to commission the construction of an eighth bridge before Euler could learn of the problem, allowing a trivial solution that would remove the rationale for further analysis. He hopes that this would alter his present-day timeline in such a way that the test becomes easier because graph theory might never have been developed | + | [[Cueball]] attempts to cheat on the final exam in his algorithms class by traveling back in time to commission the construction of an eighth bridge before Euler could learn of the problem, allowing a trivial solution that would remove the rationale for further analysis. He hopes that this would alter his present-day timeline in such a way that the test becomes easier because graph theory might never have been developed. |
− | With the addition of the eighth bridge, it becomes possible to cross each bridge exactly once, starting at the north bank and ending on the larger eastern island, or vice-versa. However, there is still no way to traverse each bridge exactly once and return to the starting point, because the altered graph would have an {{w|Eulerian trail|Euler trail}} but not an Euler cycle. Thus the problem might still have been interesting to Euler. | + | With the addition of the eighth bridge, it becomes possible to cross each bridge exactly once, starting at the north bank and ending on the larger eastern island, or vice-versa. However, there is still no way to traverse each bridge exactly once and return to the starting point, because the altered graph would have an {{w|Eulerian trail|Euler trail}} but not an Euler cycle. Thus the problem might still have been sufficiently interesting to spark Euler's curiosity and develop a nearly identical general principle on the way to demonstrating that locals could indeed find no route that ended at its initial starting point. Adding a ninth bridge connecting the north bank to the east island would render the problem completely trivial and the locals may then have developed entirely different obsessions, never drawing Euler into the issue and leaving him to focus upon different problems entirely. This could backfire on Cueball, and result in an even harder topic arising in his examination, that was never even taught to him in his original timeline experience. |
− | + | The title text alludes to the fact that ordinary {{w|aluminum foil}}, which was not commercially available until 1911, would have been a tremendously valuable curiosity in the 18th century, which didn't even have {{w|tin foil}}. Aluminum was a highly priced metal before the 1880s when inexpensive methods were developed to refine it. The {{w|Washington Monument}} was constructed with a tip made of pure aluminum due to its value and conductive capacity. Aluminum had not been extracted in its pure form at the time of Euler, and was known only in compounds such as {{w|alum}}, so the metal would have been unique and exotic. | |
− | + | ==Transcript== | |
+ | {{incomplete transcript|Do NOT delete this tag too soon.}} | ||
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:[Cueball, standing next to two men wearing wigs, pointing with a pointer at a map showing the seven bridges problem, with an extra bridge added in dashed lines] | :[Cueball, standing next to two men wearing wigs, pointing with a pointer at a map showing the seven bridges problem, with an extra bridge added in dashed lines] | ||
:Cueball: Lord Mayor of Königsberg, I will reward you handsomely if you construct this bridge before my friend Leonhard arrives. | :Cueball: Lord Mayor of Königsberg, I will reward you handsomely if you construct this bridge before my friend Leonhard arrives. | ||
:[Caption below the panel:] | :[Caption below the panel:] | ||
− | :I tried to use a time machine to cheat on my algorithms final by preventing graph theory from being invented. | + | :I tried to use a time machine to cheat on my algorithms final by preventing graph theory from being invented. |
{{comic discussion}} | {{comic discussion}} | ||
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[[Category:Comics featuring Cueball]] | [[Category:Comics featuring Cueball]] | ||
[[Category:Comics featuring real people]] | [[Category:Comics featuring real people]] | ||
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[[Category:Math]] | [[Category:Math]] | ||
[[Category:Programming]] | [[Category:Programming]] |