>am waiting this out to see if what comes out of Mueller's investigation
The dummies are so stupid they may have confused Muller with Euler ...
http://www.storyofmathematics.com/18th_euler.htmlThe problem was to find a route through the city that would cross each bridge once and only once...
In fact, Euler proved that the problem has no solution, but in doing so he made the important conceptual leap of pointing out that the choice of route within each landmass is irrelevant and the only important feature is the sequence of bridges crossed. This allowed him to reformulate the problem in abstract terms, replacing each land mass with an abstract node and each bridge with an abstract connection. This resulted in a mathematical structure called a “graph”, a pictorial representation made up of points (vertices) connected by non-intersecting curves (arcs), which may be distorted in any way without changing the graph itself. In this way, Euler was able to deduce that, because the four land masses in the original problem are touched by an odd number of bridges, the existence of a walk traversing each bridge once only inevitably leads to a contradiction. If Königsberg had had one fewer bridges, on the other hand, with an even number of bridges leading to each piece of land, then a solution would have been possible.
