Four -- square, colors, theorem, poem

During my doctoral study days at the University of Oklahoma I knew several mathematicians who were working on graph theory problems -- and a couple of them worked on problems related to the Four Color Conjecture -- a conjecture (dating back to around 1850) that became a theorem in 1976 with a proof by Kenneth Appel and Wolfgang Haken verifying (using many hours of computer time).  It asserts that four colors are sufficient to color any plane map so that no pair of adjacent regions have the same color.  This theorem has been again on my mind since reading the obituary of Kenneth Appel, who died on April 19.
Here is a link to an earlier posting (5 November 2011) on the Four Color Problem with a poem by Frank Bernhart.  And here, repeated from that post, is my poetic version of the Four Color Theorem:

        F O U R
        F O U R
        F O U R
        F O U R

Following Euler in Koenigsberg

     The Köenigsberg Bridges have an important link to mathematics -- for mathematician Leonhard Euler (1707-1783) took a legendary Köenigsberg puzzle-pastime as the seed for development of a new branch of mathematics, graph theory (which is now generally included under the umbrella of combinatorics).  As the story goes, Köenigsberg residents made a Sunday recreation of trying to tour their city, crossing each of its seven bridges exactly once.  This problem is perhaps particularly fascinating because of its impossibility -- a dilemma cause by the existence of odd (rather than even) numbers of bridges between the parts of this water-separated city.