Talk:Reflection group
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Creation of the article
editI could find no group-theory article in Wikipedia that gave detailed background information for my kaleidoscope puzzle. An article on reflection groups that included such groups defined in spaces over finite fields might have suited my purely egocentic purpose, but there was no such article, so I wrote a stub, including a lengthy quotation from the home page of Anne V. Shepler, a mathematician who specializes in this area. I wrote Shepler about the article, and she replied with an expanded and simplified version of the quote I had taken from her home page. The new version is now the main (first) section of the article on reflection groups. Cullinane 22:35, 10 August 2005 (UTC)
Editing of the article
editThis is to note that the first section of the article is no longer an exact quotation from Shepler. See the article's history section. Cullinane 02:50, 25 August 2005 (UTC)
Regarding some of the recent edits:
The fact that every rotation in 3D Euclidean space is the product of two reflections is perhaps best conveyed in Chapter 7, "The Cartan-Dieudonne Theorem," of Geometric Methods and Applications for Computer Science and Engineering, by Jean Gallier. This seems too special a result to discuss in detail in the article, since the article is intended to cover reflection groups in spaces over arbitrary fields, not just Euclidean spaces. (For Euclidean spaces, see Coxeter group.) Cullinane 03:38, 25 August 2005 (UTC)
- I added that because there was a logical gap between the first sentence and the rest.--Patrick 14:44, 25 August 2005 (UTC)
- You were right. The details of the Cartan-Dieudonne(-Scherk-Hamilton) theorem are not relevant to the main article, but the basic result that you added was called for. I just thought the discussion section, rather than the main article, should have a link to further details, for the few readers who might be interested. Cullinane 17:10, 25 August 2005 (UTC)
As noted today on my user page, a link to the kaleidoscope puzzle was the original motivation for my creation of the article on reflection groups. That link, deleted on Oct. 2, 2006, should, I would contend, be restored, but I fear any attempt on my part to restore it would only lead to an edit war. Cullinane 03:07, 12 November 2007 (UTC)
Another link that might be added: Reflection Groups in Finite Geometry. Cullinane (talk) 14:34, 10 December 2007 (UTC)