Euler and the Bridge Problem

Why would Euler concern himself with a problem so unrelated to the field of mathematics?  Why would such a great mathematician spend a great deal of time with a trivial problem like the Königsberg Bridge Problem?  Euler was obviously a busy man, publishing more than 500 books and papers during his lifetime.  In 1775 alone, he wrote an average of one mathematical paper per week, and during his lifetime he wrote on a variety of topics besides mathematics including mechanics, optics, astronomy, navigation, and hydrodynamics.  It is not surprising that Euler felt this problem was trivial, stating in a 1736 letter to Carl Leonhard Gottlieb Ehler, mayor of Danzig, who asked him for a solution to the problem:

. . .  Thus you see, most noble Sir, how this type of solution bears little relationship to mathematics, and I do not understand why you expect a     mathematician to produce it, rather than anyone else, for the solution is based on reason alone, and its discovery does not depend on any mathematical principle.  Because of this, I do not know why even questions which bear so little relationship to mathematics are solved more quickly by mathematicians than by others. [quoted in Hopkins, 2]

Even though Euler found the problem trivial, he was still intrigued by it.  In a letter written the same year to Giovanni Marinoni, an Italian mathematician and engineer, Euler said, “This question is so banal, but seemed to me worthy of attention in that [neither] geometry, nor algebra, nor even the art of counting was sufficient to solve it." [quoted in Hopkins, 2]  Euler believed this problem was related to a topic that Gottfried Wilhelm Leibniz had once discussed and longed to work with, something Leibniz referred to as geometria situs, or geometry of position.  This so-called geometry of position is what is now called graph theory, which Euler introduces and utilizes while solving this famous problem.