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  • The Seven Bridges of Königsberg

    Ah Königsberg, Ah Königsberg, how sweet thy bridges cross
    the four land masses peacefully, but I admit, I’m at a loss.
    How do I go on each bridge once and on each land mass too?
    A puzzle, for which I have struggled so and now I have the flu.

    ...I’m a math major, not a’s a much better poem to introduce you to the Seven Bridges of Königsberg:

    Like mice in mazes, locals scampered forth
    and back, around and through the town, traversed
    and re-traversed the central island, bent
    on crossing each of seven bridges once
    and only once.

    You alone declined to join the briskly questing citizenry.
    Knowing the elusive route would not
    be found on foot, in chance meandering
    (some providential Spaziergang)
    you proceeded without stirring from
    your chair to take a different sort of trip.

    With pen and paper first you razed the place,
    demolished houses, Marktplatz, terraces
    and domes. You rid it of shrubbery and trees.
    Walls fell. Cathedrals crumbled. Squirrels, ducks
    and hedgehogs vanished. Not a lamppost was spared,
    not a Denkmal stood. No cobblestone escaped
    your ruthlessly obliterating hand.

    And when you’d sheared away particulars,
    trimmed Königsburg to the bone, you saw
    a skein of penstrokes, luminous patterns
    of points and lines, necessary sequences:
    where trails of connecitivity led, and where
    they failed, and why – no matter time or place,
    terrain or weather.

    Ineluctably you built and crossed a single, Ideal Bridge
    to reach a quiet Kneiphof of the mind,
    an island of essences. Stripped stark. Clean.
    Bare bedrock of a new geometry.

    The Königsberg Bridge Poem “Homage to Euler” by Judith Saunders

    ...Okay, so that wasn’t much better...sorry Ms. Saunders...Well let’s talk about the bridges of Königsberg. As the poem eluded to, Königsberg was a place that had a four different land masses and a seven bridges, arranged as shown below:

    The people who lived there wanted to know if there was any way to start on one land mass, traverse each bridge exactly once, and end up on the same land mass you started on. Leonhard Euler took on the challenge. He drew points on each land mass and possible paths over each bridge: