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:Konigsberg_bridges.png|frame|right|{{w|Königsberg}}, Prussia in Euler's time, showing the Pregel river and its seven bridges. Two of the original seven bridges no longer exist,[https://goo.gl/maps/ChdBoeQMr3AQPi446] although there are three new bridges. The Baltic port city is now Kaliningrad, a Russian exclave.]] | [[File:Konigsberg_bridges.png|frame|right|{{w|Königsberg}}, Prussia in Euler's time, showing the Pregel river and its seven bridges. Two of the original seven bridges no longer exist,[https://goo.gl/maps/ChdBoeQMr3AQPi446] although there are three new bridges. The Baltic port city is now Kaliningrad, a Russian exclave.]] | ||
| − | 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 whether a path through the city crossing each of the seven bridges just once exists, without crossing the river forks any other way. In 1736, Euler proved that no such path | + | 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 whether a path through the city crossing each of the seven bridges just once exists, without crossing the river forks any other way. In 1736, Euler proved that there is no such 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. {{w|Graph (discrete mathematics)|Graphs}} are a data structure common in many algorithmic problems in computer science. |
[[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. The use of the word "tried" implies failure, which is probably a good thing since his success would create a {{w|Temporal_paradox#Grandfather_paradox|paradox}}. [[:Category:Time travel|Time travel]] is a recurring topic on xkcd and examples where attempts to change the past fails has also been used before like in [[1063: Kill Hitler]]. | [[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. The use of the word "tried" implies failure, which is probably a good thing since his success would create a {{w|Temporal_paradox#Grandfather_paradox|paradox}}. [[:Category:Time travel|Time travel]] is a recurring topic on xkcd and examples where attempts to change the past fails has also been used before like in [[1063: Kill Hitler]]. | ||
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An alternative modification allowing an easy solution is to remove bridges. During World War II, two bridges to the central island connecting it to the north and south banks were destroyed by bombing, so today there is an Eulerian trail across the five remaining bridges. | An alternative modification allowing an easy solution is to remove bridges. During World War II, two bridges to the central island connecting it to the north and south banks were destroyed by bombing, so today there is an Eulerian trail across the five remaining bridges. | ||
| − | 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}} | + | 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#Aluminum_apex|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. The value of aluminum and the use of it as the tip of the Washington Monument was also mentioned in [[1608: Hoverboard]] where a heist to steal the tip is [https://www.explainxkcd.com/wiki/images/6/6f/1608_0995x1083y_Tip_of_Washington_monument.png depicted]. |
==Transcript== | ==Transcript== | ||
