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02 July 2005

an Ancient Fairy Tale: The 7 Bridges of Königsberg

The Fairy Tale

Once Upon a Time, there was a beautiful, famous, prosperous city called Königsberg -- the King's Mountain. (That's silly. If there really was a city called Königsberg, it must still be there, right? Cities don't just disappear.)

It grew up along the banks of the River Pregel where it flows into the Baltic, around a mighty castle built by a powerful warlord prince named Otticar. Otticar chose the site with great wisdom and foresight; in time of war it was highly strategic both for soldiers and warships, but in time of peace it was a natural center for trade from every direction in Europe and beyond. Early on Königsberg joined a group of cities, the Hanse or Hanseatic League, and the treaties the cities made with each other to cooperate in trade and tariffs made all the cities rich. For centuries, Königsberg was one of the richest.

The city's docks were piled high with magnificent furs from Russia exchanged for spices and goods from the New World and the Orient. But from Königsberg itself, the world's finest amber -- Amberland was its nickname. Amber is golden-colored, translucent, fossilized, rock-hard resin from ancient forests, from trees that lived from 30 million to 90 million years ago. And with the amber itself, centuries of artisans and craftsmen who turned this rare substance into works of exquisite art bought for outlandish sums by Europe's wealthy and tasteful (a rare combination in a single person). The king of K
önigsberg's nation, Frederick William I, gave a great room entirely of precious Königsberg Amber to Tsar Peter the Great; it has recently been restored and re-opened to the public, you can see this magnificent hall today in St. Petersburg, and be stunned not just at its unique beauty, but at the miracle of history that has allowed it to survive to this moment. (The Great Hall of Amber vanished for quite a long time, with utterly no promises that it might ever come back.) History is usually not so gentle, thoughtful and kind with beautiful, fragile, irreplaceable works of art.

With centuries of such prosperity, not too often interrupted by wars (the princes of Königsberg had a knack for usually allying the city with the winning side), the wealthy merchant families and the nobility piled their wealth back into their beloved city in handsome architecture, lovely parks, great churches, palaces each one higher, greater, more spaceous than its neighbor, a magnificent synagogue -- O what a wonderful place Königsberg was to live in or to study or visit!

The great musicians of Europe made it a regular stop on their tours, and the palaces and concert halls were rarely silent; they echoed almost every night with angelic and spiritually uplifting beauty from the great singers, instrumentalists, choirs and orchestras. From his childhood, Mozart the keyboard and composing prodigy knew Königsberg well, not a year went by when his father Leopold did not bring little Wolfgang to the great port city of Königsberg.

What more do you want? A great university? Kant was born in Königsberg, studied and taught philosophy at the university his whole career, and his comings and goings from home to university and back were so regular that the Königsbergers set their clocks by them; some say he never left Königsberg, and then then he died there. Literature? A grand statue and monument to Friedrich Schiller, who lived and wrote in Königsberg, is still there. (Still there? Well, is there such a city, or not?).

Königsberg was a grand place, and for many centuries getting grander every year.

Königsberg straddled both banks of the Pregel, and in the center was an island, Kniephof. As the city grew, Seven Bridges were built to connect the island Kniephof with both banks of the Pregel and with another land region downriver. On Sundays, when the Königsbergers took a day of rest from their busy lives, they enjoyed strolling on and off Kniephof to the city's different neighborhoods over the Seven Bridges.

The flavor of Old Königsberg still lingers in the bridges' names. There was Kræmer, the Shopkeeper's Bridge; Schmiede, the Blacksmith's; Hohe, the High Bridge; Holz, the Wooden Bridge; the Green Bridge, Greune; Koettel, the Guts or Giblets Bridge (by a butcher); and Honig, or Honey Bridge, where a beekeeper kept hives.

One Sunday someone thought of a Puzzle. Could you start at one end of any particular bridge, and then stroll across all Seven Bridges, but cross each bridge only once, and somehow return to the point you started?

For centuries Königsbergers tried, trying scores, hundreds of different paths, maybe more, but no one could ever do it.

But no one could ever prove that it was impossible, either. Was there a path, a specific way to cross all Seven Bridges (each only once), that would return you to the place you started? Or was it impossible?

Word spread that this puzzle, this local oddity of the geography of the great city of Königsberg, was a real tough nut to crack.

This is a good place to pause and hope for some Comments. The Fairy Tale has a wonderful, rich, delicious Ending, with a Hero who slays the Dragon, and much more.

But the story of Königsberg and its Seven Bridges, and its proud, prosperous, curious Königsbergers, also goes on. That part of the story doesn't have so Happy an Ending.


Blogger Joana said...

I't's Euler's problem , but I can't get this silly thing to recognize the graph as it is not a sausage!!!

Blogger Bob Merkin said...

Ya got an image? If you can e-mail your image to me, I can post it to Vleeptron now! And I don't have to use that crappy free HELLO image-posting software. Did I tell you HELLO gives hemmorhoids to little children? Isn't that terrible? Someone should call the Homeland Security people on that crappy free HELLO software.

Yup yup, it's Euler's problem ... but ... well ... I am trying to see if I can coax the solution out of this Very Smart Bunch, maybe step by step, starting with that image of the map of Konigsberg and the 7 Bridges. That's all Euler had to go on. We're just as smart as Euler, aren't we?


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