Leonard Euler's Solution to the Konigsberg Bridge Problem (2006) | Hacker News Reader

Leonard Euler's Solution to the Konigsberg Bridge Problem (2006)

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61 pointsjpelecanos12 comments

When I first saw this problem in elementary school, I went to look at an atlas to see if I could see the bridges (but couldn't because the scale in an atlas was too large). I'm just blown away that today, not only can I find the map but I can look at the aerial view and go on virtual walks through the city and the bridges -- mere seconds after reading about it:

https://www.google.ca/maps/place/Kaliningrad,+Kaliningrad+Ob...

I'm wondering what the amazing mapping advance will be 20 years from now. Real time street views of all metropolitan areas?

I visited Kaliningrad in 2007 and puzzled my hosts by asking them if I could see the famous bridges. They hadn't heard of Euler and the Bridges of Königsberg. I was astonished.

We drove around and saw a couple of what I think were the bridges dating from Euler's time. Others had been destroyed in WW2 and/or replaced with modern, larger bridges.

> Others had been destroyed in WW2 and/or replaced with modern, larger bridges.

I read a while ago that the destruction had actually rendered the bridges problem soluble (that is, that there is a modern Eulerian path); but I don't know if that was true at the time, or is still true.

From Google Maps it seem like it currently is possible to walk all the bridges, although you can't end where you started. Two of the original bridges have gone, two more have been built (not in the same locations as the destroyed ones), and there are two additional bridges that are within the city limits now but wouldn't have been in Euler's time.

I love it: the nine new bridges of Königsberg! (It would never have occurred to me to check on Google Maps; thanks!)

I grew up in Kaliningrad. I haven't heard about this puzzle until I moved to US. I think this is partly because graph theory or topology are considered too advanced to be studied in typical schools and partly because very few residents know much about Konigsberg history. It's kinda like very few Americans know much about American Indian history before Columbus.

Would traveling to the source of the river Pregel and walking around it count as a solution?

Alas! One of the Pregel's tributaries originates in a lake which is itself linked by a canal to the Baltic, forming a loop excluding Konigsberg.

Reading the post title, my first reaction was "Wow, Euler must have been really stumped if it took him until 2006 to solve the problem."

I found it kinda funny that most lectures in my Math 101 started with "the little Euler" or "the little Gauss". Like those guys did all of Math on their own when they were children, haha.

Well, Euler and Gauss knew all there was to know about mathematics at the time. That consisted of algebra up to quintic equations plus their own inventions.

You'd be unpleasantly surprised if you saw a turn-of-the century-math high school textbook (1900 or so.) Pretty advanced stuff towards the end.

That consisted of algebra up to quintic equations plus their own inventions

Well, calculus had been invented before Euler was born, and a lot of advanced math had been developed by the time Gauss appeared (a lot of it by none other than Euler).

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