Talk:Four color theorem
This is the talk page for discussing improvements to the Four color theorem article. This is not a forum for general discussion of the article's subject. 
Article policies

Find sources: Google (books · news · scholar · free images · WP refs) · FENS · JSTOR · NYT · WP Library 
Archives: 1, 2, 3, 4 
Four color theorem has been listed as a level5 vital article in Mathematics. If you can improve it, please do. This article has been rated as BClass. 
Four color theorem was a Mathematics good articles nominee, but did not meet the good article criteria at the time. There are suggestions below for improving the article. Once these issues have been addressed, the article can be renominated. Editors may also seek a reassessment of the decision if they believe there was a mistake.  
 
Current status: Former good article nominee 
This article is of interest to the following WikiProjects:  



Sections older than 90 days may be automatically archived by Lowercase sigmabot III. 
Contradiction in proof section?[edit]
The last paragraph in Four color theorem#Proof by computer: 'They responded that the rumors were due to a "misinterpretation of [Schmidt's] results" and obliged with a detailed article'  without further comment it looks like Schmidt was wrong. But then we learn that their book later " explained and corrected the error discovered by Schmidt [...]", so Schmidt was right? Related question: Why was it "a rumor" years after the master thesis was published? mfb (talk) 07:22, 16 May 2019 (UTC)
Requested move 22 August 2020[edit]
 The following is a closed discussion of a requested move. Please do not modify it. Subsequent comments should be made in a new section on the talk page. Editors desiring to contest the closing decision should consider a move review after discussing it on the closer's talk page. No further edits should be made to this discussion.
The result of the move request was: not moved. (closed by nonadmin page mover) Jerm (talk) 03:18, 30 August 2020 (UTC)
Four color theorem → Fourcolor theorem – Punctuation Electricmaster (talk) 08:39, 22 August 2020 (UTC)
 Oppose on grounds given. Most of the scholarly, reliable sources don't punctuate this. See the references section, with titles like "The Four Color Theorem: History, Topological Foundations and Idea of Proof." There do appear to be a few sources that punctuate this, but we should follow the preponderance of the sources here. SnowFire (talk) 16:25, 22 August 2020 (UTC)
 Oppose per argument above, but Move to Four colour theorem for harmonize the grammar. 114.125.232.69 (talk) 16:48, 22 August 2020 (UTC)
 That would involve switching from American English to English English. As Appel is American and Haken taught in America I think color is the most appropriate spelling to use.Salix alba (talk): 16:57, 22 August 2020 (UTC)
 Indeed, and since the article title has used the American spelling since its creation, MOS:RETAIN applies. Favonian (talk) 17:01, 22 August 2020 (UTC)
 That would involve switching from American English to English English. As Appel is American and Haken taught in America I think color is the most appropriate spelling to use.Salix alba (talk): 16:57, 22 August 2020 (UTC)
 Oppose  it's a theorem about four colors, not a theorem being fourcolor. 16:55, 22 August 2020 (UTC) — Preceding unsigned comment added by CiaPan (talk • contribs) 16:55, 22 August 2020 (UTC)
Oppose because this article tells about a theorm about four colors, which IMO the correct title should be Four colour theorm for more NPOV title. 182.1.13.112 (talk) 16:59, 22 August 2020 (UTC)
 Oppose. Hyphen is not needed and therefore should be omitted. —David Eppstein (talk) 17:15, 22 August 2020 (UTC)
 Oppose both hyphenation and Britishification per the arguments by SnowFire, Salix alba and others above. XOR'easter (talk) 22:33, 22 August 2020 (UTC)
Oppose hypernated is not needed for that article and thw title should be remained as this, thought IMO, the correct title of Four color theorem shouldn't be color but Colour. 36.77.93.106 (talk) 23:54, 22 August 2020 (UTC)Oppose. Hyphen is not needed and the correct title should be four colour theorem. 110.137.165.233 (talk) 00:39, 23 August 2020 (UTC)
 Now four IPs from Sumatra, with even more participating on the same request at Talk:Five color theorem. —David Eppstein (talk) 05:44, 23 August 2020 (UTC)
 I've taken the liberty of striking out all but the first of the Sumatran IPs, on the principle that they're obvious puppetry of some sort (meat or socks, don't care which). —David Eppstein (talk) 22:16, 23 August 2020 (UTC)
 Oppose hyphenation (and "colour"), per WP:COMMONNAME. Paul August ☎ 14:20, 23 August 2020 (UTC)
Move to four colour theorem hypernation is not necessary for the article. 180.245.102.250 (talk) 00:07, 26 August 2020 (UTC)
OP here. While I personally disagree on keeping the title without hyphenation, I respect the counterarguments and the current democratic consensus. This reminds me of the debate regarding air superiority fighter vs airsuperiority fighter. It seems to be a matter of stylistic preference. Thanks for your input. Electricmaster (talk) 10:34, 26 August 2020 (UTC)
 The discussion above is closed. Please do not modify it. Subsequent comments should be made on the appropriate discussion page. No further edits should be made to this discussion.
Simple Proof[edit]
Discussion closed because it is not about improvements to the article based on reliablypublished sources; see WP:TALK 

The following discussion has been closed. Please do not modify it. 
On a square grid start with a single square. Add a layer of squares around it so that it becomes a 3x3 square. Each square you add will touch at most 3 other squares, so will only require at most 4 colors to map it. Add layer after layer to infinity, similarly the criterion for 4 colors is met. Is this what was said to be the proof?GuildCompounder (talk) 03:14, 15 December 2020 (UTC)
It recently occurred to me that layers can be added inwards instead of outwards. Start for example with a 9x9 layer, add a 7x7...3x3. All the squares in the layers touch at most 3 other squares making them 4 colorable. The exception is the 1x1 centre square which touches 4 squares. However, if opposite sides of the centre square touch each other, that would separate the other opposite sides of the centre square which could then be the same colour. That is why what works out for the 2 dimensional map does not work for the 3 dimensional map (which has no limit to the number of colours required).GuildCompounder (talk) 17:59, 13 March 2021 (UTC)
THe "opposites cutoff" theorem I mentioned above is valid for convex objects like spheres and cylinders, but is blown for toroids. We can visualize 6 colours for the toroid by applying a diagonal slash through the failed theorem rectangle. Then delete the original 5 colour region allowing a 2 colour loop to touch in 2 places when it only needs 1 connection. This allows a gap at the far end of the loop. Now the 3 five colour regions all touch each other, requiring 7 colours. GuildCompounder (talk) 20:43, 15 March 2021 (UTC) 
 Wikipedia level5 vital articles in Mathematics
 Wikipedia BClass vital articles in Mathematics
 Wikipedia BClass level5 vital articles
 Former good article nominees
 Old requests for peer review
 BClass mathematics articles
 Toppriority mathematics articles
 Featured articles on Mathematics Portal
 CClass Maps articles
 Topimportance Maps articles
 BClass geography articles
 Highimportance geography articles
 WikiProject Geography articles