Talk:Sylvester–Gallai theorem

message: One should add the trivial Kelly proof using the minimality of the distance between one point and a line which does not contain it.
:Huh? The Kelly proof is in the section "Proof of the Sylvester–Gallai theorem". But I think it's longer than the projective duality one, so I don't know why you call it trivial. —David Eppstein 14:51, 24 April 2007 (UTC)
thread_title: Trivial proof

message: I don't know if Sylvester's matrix theorem is also by the same Sylvester, but since Sylvester's theorem redirects here, I'm adding a disambiguation link Cai 10:21, 24 April 2007 (UTC)
thread_title: Redirect

message: A couple comments:
* It would not take much more work to give Melchior's full derivation.  If I get time I might try to add it.
* The section on "Generalizations of the Sylvester–Gallai theorem" seems inconsequential.  Perhaps it should be removed?
Jwesley78 02:01, 29 December 2009 (UTC)
thread_title:  Melchior 

message: The following invisible comment was attached to the statement of Dirac's conjecture:
:Dirac's original paper used brackets around the n/2. (This generally implies "take the integer part".)  Thus, the "counter-examples" below are not truly "counter-examples".
What brackets "generally mean" is irrelevant, the question is what they meant to Dirac. It seems unlikely that they meant "round half-integers up" i.e. "ceiling of", since then the brackets would be superfluous (for integers, t ≥ n/2 is equivalent to t ≥ \lceiln/2\rceil).  So I would guess that it meant "floor of".  In that case the two "counter-examples" should be renamed "examples (with odd n?) where equality holds".  All the best, --Jorge Stolfi (talk) 01:58, 30 December 2009 (UTC)
replies: text: I changed the wording to not call them "counter-examples" to Dirac's conjecture.  They are simply examples for which the number of ordinary lines is less than n/2.  I'll remove that comment now. Jwesley78 02:09, 30 December 2009 (UTC)
replies: text: It is better now, good! But we still need to find out what Dirac meant by the brackets, and replace it by the proper notation (ceiling or floor).  It is not OK to use Dirac's notation in the article without defining it.  All the best, --Jorge Stolfi (talk) 14:24, 30 December 2009 (UTC)
replies: text: Floor. See Floor and ceiling functions. Kope (talk) 15:21, 30 December 2009 (UTC)
thread_title:  Dirac's conjecture 

message: It seems bizarre to call this the "Sylvester-Gallai theorem" when Sylvester merely posed the problem and Gallai's proof was 3 years later than Melchior's.  Isn't there any source that calls it "Melchior's theorem"?  All the best, --Jorge Stolfi (talk) 09:46, 31 December 2009 (UTC)
replies: text: The name "Sylvester-Gallai theorem" is well-established in the literature. I've not seen it called anything other than that. I believe Melchior's work was completely independent of Sylvester's/Erdos's question. He was concerned with polygrams (i.e. "Vielseit"). Coxeter's review of the paper is here. I suspect that the connection between Erdos's question and Melchior's result was not found until years after the name was already well-established. An interesting historical note (that my advisor told me) is that it is suspected that Melchior died in WWII during the carpet bombings of Munich, as there is no record of him after the war. Jwesley78 15:25, 31 December 2009 (UTC)
replies: text: In modern terminology polygrams are called arrangements of lines. From Coxeter's review it seems that Melchior was primarily trying to classify simplicial arrangements. —David Eppstein (talk) 17:19, 31 December 2009 (UTC)

text: Similar things happen, see, e.g., Hahn–Banach theorem.Kope (talk) 15:12, 1 January 2010 (UTC)
thread_title:  Wrong name 

message: Hi David, I see that you reverted all the references to the style Author(Year).  I really can't see the advantage of that style in Wikipedia. Among many other disadvantages, you lose the links from refs back to the text. Sigh...  All the best, --Jorge Stolfi (talk) 22:26, 1 January 2010 (UTC)
replies: text: I used Author (year) only for references that were already in the format "In year Author ...". That is, the referencing style only formalizes what was already in the text. But if the text includes a clear statement like this of which paper is being referred to, what is the point of also having a footnote pointing to the same paper? —David Eppstein (talk) 00:26, 2 January 2010 (UTC)
thread_title:  Reference style 

message: A few years ago I located the Melchior paper in the UC library and scanned it: Uber Vielseite der projektiven Ebene. From what I can tell, the article itself says that it's from "Volume 5, Issue 6", but I don't see the year printed therein. Justin W Smith (talk) 17:36, 21 October 2012 (UTC)
replies: text: The UC library catalog says that "Volume 5" was published in 1940.  (So if anyone wishes to undo my recent edit, I wouldn't protest; there appear to be conflicting sources.) Justin W Smith (talk) 17:49, 21 October 2012 (UTC)
thread_title:  1941(?) Melchior paper 

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thread_title:  External links modified 

message: While reviewing this for DYK I happened to notice that the Mandelkern source is listed in the references section but never cited anywhere in-text. Not sure if a citation was erroneously deleted or if it ought to be moved to "Further reading" or similar. GorillaWarfare (talk) 19:52, 7 September 2020 (UTC)
replies: text: Thanks for catching this. I'm not sure how it happened either but I added a little to the article about its content, citing it. —David Eppstein (talk) 20:39, 7 September 2020 (UTC)
thread_title:  Unused citation