Talk:Seven Bridges of Königsberg

message: The "Bridge 8" part speaks about Blue prince wanting to go from his castle to the guesthouse, "Bridge 9" says the Red prince wants to stop the Blue prince from going doing a circuit. 2.64.220.235 (talk) 20:20, 27 December 2012 (UTC)
thread_title: The extra problems are not consistent 

message: I think this shouldn't be in the category of "Localities with numbers in their names". There is no locality named "Seven Bridges of Königsberg". There is only a locality named Königsberg, and it has seven bridges in it. The bridges by themselves are famous because of this problem, but don't constitute a locality.
Discuss.  — JIP | Talk 10:37, 9 Mar 2005 (UTC)
thread_title:  Category removal 

message: This article, at the moment, seems to me to be more suited to a text book than an encyclopaedia. Specifically, there are problems given (which I have no problem with in this context, since the article is essentially /about/ those problems), but I don't think the answers should be given separately, but rather worked into the explanation of the problems. Also, the tone of the 'solutions' article is exteremely textbooky (it speaks directly to the reader, whereas an encyclopaedia generally uses the neutral voice). 
Perhaps it should be re-worded, and/or some of the extra problems moved to a Wikibook on Graph Theory? LVC 05:56, 15 October 2005 (UTC)
thread_title:  Textbook style 

message: I think that the wording in the most recent version (modified by 12.104.57.3) is less clear than the previous one.  In particular, I think the phrase "and is thus the complete opposite of what is required" is not mathematically precise, and misses the point, which is that the existence of any node of odd degree forbids the existence of an Eulerian circuit.  Accordingly, I am going to revert to the version modified by Icairns, 09:24, 24 January 2006.  I hope this is OK; I am a Wikipedia novice and don't mean to step on any toes.JLeander 05:20, 28 January 2006 (UTC)
thread_title: Phrasing issues

message: Someone told me once that after the Russians took over the city in 1945, they built a bridge (the joke was that it was to spite Euler) which now makes an Eulerian circuit possible.  Can anyone confirm this and/or add details? --Saforrest 02:54, 30 May 2006 (UTC)
replies: text: Here is a link to Google Satellite view of the area today:  https://www.google.com/maps/@54.7034274,20.5163074,2217m/data=!3m1!1e3 SlowJog (talk) 03:21, 22 May 2015 (UTC)
replies: text: I don't know what the actual state was in 2000, but the article says there were 5 bridges, and the map in that section shows 8. Also, if today's map were to be zoomed out a little more than the one in that section, there would be 9.  It isn't clear from the map where the city boundaries are, so it could be that 5 of the bridges are within the city limits. In either case, that section, the image, or both need updating. SlowJog (talk) 03:48, 22 May 2015 (UTC)
thread_title:  State of the bridges now? 

message: Removed this copy of article text; see history for old versions. John Reid ° 20:38, 16 November 2006 (UTC)
thread_title: Variations

message: Q: It is possible to walk with a route that crosses each bridge exactly once, and return to the starting point?
A: Yes, if you do it in winter when the rivers are frozen over. (LOL, Am I right or what?)
~Mix. —The preceding unsigned comment was added by Mix Bouda-Lycaon (talk • contribs) 09:47, 25 January 2007 (UTC)
thread_title:  A Solution: 

message: What is general name for puzles in which you have to redraw a figure without picking your pensil off the paper, retrace a line, or folding a piece of the paper?--Anthonynow12 17:20, 4 February 2007 (UTC)
replies: text: A topology problem. I dunno if there's a nick-name for it. I Haven't seen many. Though i know how to connect a 3x3 grid with 4 connected lines. —The preceding unsigned comment was added by Mix Bouda-Lycaon (talk • contribs) 06:41, 6 February 2007 (UTC)
thread_title:  Puzzle Name 

message: the puzzle is possible if the nodes have 0, 2 OR 3 odd nodes, the article only says 0 or 2, i will fix this  —Preceding unsigned comment added by 220.253.81.58 (talk) 11:36, 21 August 2008 (UTC)
replies: text: Only 0 or 2.  Either you start and end at different vertex (then the endpoints are of odd degree and every vertex is even), or you have a circuit (and then every vertex including the starting point is of even degree). WLior (talk) 20:54, 22 August 2008 (UTC)
replies: text:  It is impossible for a network to have 3 odd nodes, or any other odd number for that matter. A simple proof of this is that an odd number of odd nodes would give an odd total number of endpoints, but every segment must have exactly 2 endpoints, so the total must be even. 91.105.48.118 (talk) 21:51, 27 December 2010 (UTC)
thread_title:  node mistake 

message: Two of the seven original bridges were destroyed by bombs  during World War II. Two others were later demolished and replaced by a modern highway. The three other bridges remain, although only two of them are from Euler's time (one was rebuilt in 1935).[2]  Thus, there are now five bridges in Königsberg (modern name Kaliningrad).
In terms of graph theory, two of the nodes now have degree 2, and the other two have degree 3.
Two demolished, two replaced by one, and the remaining three, makes four.
The next line says "five", and the next paragraph mentions only four again.--WPaulB (talk) 17:48, 28 February 2010 (UTC)
replies: text: (1) If two bridges are replaced by one highway, the highway still has to cross the river in both places so there are still two bridges (which plus the three remaining ones makes five as stated). (2) The "nodes" in the problem are the landmasses, not the bridges. 91.105.48.118 (talk) 21:54, 27 December 2010 (UTC)
replies: text: In an article about graph theory, telling me that two edges between a pair of nodes can't be replaced by one edge is absurd.  It is entirely possible to remove two bridges and replace it with one wider bridge that holds a highway.  That's the essence of flow diagrams, no - weighted edges?  Second, highways have a beginning and end.  It is entirely possible that a highway can start or end on one landmass, and not cross a river twice.  if you want to make this unambiguous, display it on a map. --WPaulB (talk) 13:46, 7 February 2012 (UTC)
thread_title:  Confusing Text 

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thread_title: File:Konigsberg bridges presentstatus.png Nominated for Deletion

message: It is (as of 26 February 2006) possible to walk the (six or seven) bridges, starting from the northern shore and ending on the island in the middle (the Kneiphof).  Double sharp (talk) 07:40, 18 March 2012 (UTC)
thread_title:  Outdated 

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replies: text: Checked, working - DutchTreat (talk) 11:08, 9 July 2017 (UTC)
thread_title:  External links modified 

message: I added a hatnote that links to the article's own section on present-day, bcz 
# even tho it seems clear the problem is of much wider interest than the physical bridges, there seems little point in splitting out the p-d info, which will interest many readers (and is of much more value than an abstract diagram in introducing the math topic to students who aren't ready for more complex topology topics), 
# tho our coverage of the problem is a better candidate for primary topic than is the physical bridges, access to the available p-d section should be as easy as possible to those with no interest in the tpl'y problem, whose short name is almost synonymous with it rather than with the architectural features, and
# it's well established that duplication of content in between articles is generally a bad idea.
   There're reasonably good hints that little need has been found for Hatnotes targeting a section within the same page where a H-N Dab appears, but this improvised extension that so far seems unobjectionable should be harmless.--Jerzy•t 11:20, 17 December 2016 (UTC)
thread_title:  Hatnote 

message: Can anyone add a section about the origin & history of the problem? Jonathan Williams (talk) 15:52, 19 July 2017 (UTC)
replies: text: It seems to have originated as a challenge or idle question among people strolling around the streets and bridges of the city at the time... AnonMoos (talk) 14:17, 23 July 2017 (UTC)
replies: text:    We got any hint of a ref supporting that? Hard to know where to start in looking for one.--Jerzy•t 16:43, 28 July 2017 (UTC)
replies: text:   ... i guess math geniuses tend to under-document their own idle thots....--Jerzy•t 16:47, 28 July 2017 (UTC)
replies: text: That's what it says in the 1963 book Life Science Library: Mathematics by David Bergamini: "It had been a tradition among the townspeople that the seven bridges could not all be crossed in a continuous walk without recrossing the route at some point, but no one knew the explanation" (p. 188).  It's a very popularizing book, without further references of its own... AnonMoos (talk) 01:24, 30 July 2017 (UTC)

text: If you want a slightly more academic source, James R. Newman says the following in his preface to a translation of Euler's writing that was published in the July 1953 issue of Scientific American: "The townsfolk had long amused themselves with this problem: Is it possible to cross the seven bridges in a continuous walk without recrossing any of them?" -- AnonMoos (talk) 13:52, 30 July 2017 (UTC)
thread_title:  History of problem? 

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thread_title:  External links modified 

message: The bridge problem inspired the Bristol Bridges Walk. Like Konigsberg Bristol spans the two banks of a river and two river islands.
The Bristol Bridges walk is an Eulerian cycle crossing all 45 major bridges in the city. It has been the subject of the several articles in newspapers and magazines, and there is a book about the walk. It also featured in several charity events including being the headline event for Bristol Giving Day 2019 (a major event). Is it worth mentioning this somewhere? Fzbristol (talk) 19:19, 18 September 2022 (UTC)
thread_title:  Bristol Bridges Walk 

message: The title of Euler's article uses the Latin term for topology, 'geometria situs' - that maybe hadn't been fully formalized by this stage, but it's possibly misleading to say it 'prefigured' it, when the terminology was already set up and at least some of the core ideas established? 2.204.255.32 (talk) 10:16, 9 April 2024 (UTC)
thread_title:  "prefigured the idea of topology"