Editing 2694: Königsberg

[[File:Konigsberg bridges.png|frame|right|{{w|Königsberg}} in Euler's time, showing the river Pregel and its seven bridges]]

This comic is about the {{w|Seven Bridges of Königsberg}}, a seminal {{w|graph theory}} problem addressed by the famous mathematician {{w|Leonhard Euler}}. A popular pursuit, beforehand, was to attempt 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 actual solution possible. 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, granting it a trivial solution that would remove much impetus for mathematical 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 create a path that crosses each bridge exactly once, starting at the north bank and ending on the eastern island (or vice-versa). However, there would remain no way to traverse each bridge exactly once and return to your starting point, because the altered graph would have an {{w|Euler trail}} but not an {{w|Euler cycle}}. Thus, the problem might still have been sufficiently interesting to spark Euler's curiosity. Adding a ninth bridge connecting the north bank to the east island would render the problem completely trivial.

There is, of course, the possibility that without the Bridge Problem, the curiosity and genius of Euler would have refocussed upon yet another obscure theory, and developed it into a far more fiendish field of study to make for an even harder examination in Cueball's time.

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}}. Aluminium itself was a highly priced metal before the 1880s, when methods were developed to cheaply refine it. Famously, the {{w|Washington Monument}} was constructed with a tip made of pure aluminum due to its great value and conductive capacity. Aluminum had not even been extracted in its pure form at the time of Euler, and was only known in compounds such as {{w|alum}}, so it would have been rare and exotic indeed.

{{clear}}

:[Cueball, standing next to two men wearing wigs, pointing with a pointer at a map showing the 7 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.

:[Caption below the panel]

:I tried to use a time machine to cheat on my algorithms final by preventing graph theory from being invented.