Talk:Incidence geometry

Page move

I moved this page from incidence geometry to incidence geometry (structure) because otherwise it is too close in name to incidence (geometry) which is a different article. That closeness confuses my bot. I would need to fix my bot, but that could rise a host of other issues.

Please let me know if this move is an issue. Oleg Alexandrov 4 July 2005 22:04 (UTC)

• JA: Much as I believe that the world should be ruled by the needs of bots — resistance is futile — I find this usage unnatural, moreso because of the (global-havoc)-wreaking or global-(havoc-wreaking) precedent that it might set. If you can't get your bot to grok parens, then I suggest the stop-gap name Incidence geometry (mathematics). Jon Awbrey 14:00, 8 March 2006 (UTC)

• I agree with JA here, incidence geometry is the right name for this article. Paul August ☎ 22:42, 5 June 2006 (UTC)

• Sorry about the bot - Wikipedia is for its readers: the (structures) bit is inconsistent with just about everything else on the planet. I am moving it back. -- Cheers, Steelpillow (Talk) 18:47, 10 December 2008 (UTC)

Abstract polytopes

The article currently states that An abstract polytope can be regarded as an incidence geometry. Is this correct? I suspect that it is not. Polytopes have a limited connectedness, for example any line (edge) in a polygon connects to just two points (vertices). As I recall this is never true of incidence geometries (though I have no reference handy). Does anybody know for sure? -- Cheers, Steelpillow (Talk) 18:52, 10 December 2008 (UTC)

more general rewrite needed

The article currently just to list the definition of linear spaces and some of its properties. However linear spaces are just one many incidence structures you might consider in incidence geometry and the theory of linear spaces is just subfield of incidence theory. This article should certainly shortly cover (partial) linear spaces as well but it needs to cover other structures as well and give on overview/description of the field as a whole. An introduction in to the larger field can be found here:

• http://www.uwyo.edu/moorhouse/handouts/incidence_geometry.pdf

--Kmhkmh (talk) 01:18, 14 November 2013 (UTC)

P.S.: I'm seeing now that under references those lecture notes are already available. The book by Buekenhout is also good reference and guide to what should be covered by the article. I'm replacing the book by Beutelspacher/Batten by another by Batten which is more about incidence structures in general and not just restricted to linear spaces.--Kmhkmh (talk) 01:22, 14 November 2013 (UTC)

I agree with the above. Having just finished an expansion of the incidence structure page and also having been a contributor here, there is a certain amount of unavoidable overlap in the two articles due to me. I do not want to suggest a merge, rather I would like to see an expansion of this page in a direction that the other does not go. The structures page mainly talks about equivalent terminology, duality and ways to represent an incidence structure. I think that this page should deal with the different types of incidence structures and some of the more significant results concerning a type. I'm having some difficulty deciding what to do with the point-point and line-line matrices. These are rarely used tools that seem to be shoved into this article because they have no where else to go. Any ideas? Bill Cherowitzo (talk) 18:17, 2 June 2015 (UTC)

 Done Could probably use a bit more polishing. Have I left anything important out? Bill Cherowitzo (talk) 03:07, 13 June 2015 (UTC)

Fano space

To avoid the mistake I made, it would be useful to add little more detail to the following statement in the article:

In his work on proving the independence of Hilbert's axioms he worked with a three dimensional space in which each line had only three points on it. The planes in this space consisted of seven points and seven lines and are now known as Fano planes

In particular giving a little more description of the space would be helpful, such as by mentioning the number of points, lines and/or planes in the space. 15 points? 35 lines? 15 planes? —Quondum 04:21, 1 December 2013 (UTC)

OK. This must have been PG(3,2), but I've never seen it described that way. I will try to do a little research and come up with a citation which amplifies the description. Bill Cherowitzo (talk) 18:15, 1 December 2013 (UTC)

Done. Bill Cherowitzo (talk) 00:33, 3 December 2013 (UTC)

Perfect, now it is informative and illustrative. I'm sort of surprised that the numbers that I inferred seem to have been correct. —Quondum 08:06, 3 December 2013 (UTC)