Talk:Cross-ratio

message: Isn't this all a bit technical here? 
Of course one has to really really admire its contributing editors' grasp of elementary freshman math but the fact of the matter is that the curious 'intelligent lawyer' will come away from the page absolutely none the wiser.
Rather a pity don't you think for such an attractive topic in mathematics? I wonder what the late, great (and very unassuming) H.S.M. Coxeter would have thought of it all?
Of course I can appreciate that topics like the Riemann zeta-function don't easily lend themselves to popularisation but that's (frankly) not what we're talking here and in any case their editors do try and succeed in remaining encyclopaedic as well. Would these editors had taken time off to do the same here. I've added a 'technical' template.
I'm not aware that Pappus wrote on the cross ratio and have added 'citation needed' templates. At the very least it's an uncommon assertion which should be sourced. Rinpoche (talk) 21:02, 13 September 2010 (UTC)
replies: text: Thank you for your input. As one of the contributing editors I thank you humbly for complimenting me on my excellent elementary freshman math skills. I try to stay in shape, you know, doing my morning integrals and all that. Would you care to explain why would an intelligent lawyer have any interest in cross-ratio? This is not something that comes up outside of mathematics at all. I doubt that scientists even in such quantitative fields as physics and chemistry get to see it. It is, however, an important topic in pure mathematics, and as such, it requires some background knowledge to appreciate, just as lawyers need their legal theory and doctors their anatomy. Arcfrk (talk) 04:38, 14 September 2010 (UTC)
thread_title:  A tad technical what? 

message: The cross-ratio is defined for a 4-tuple of points on a conic in the real projective plane, by replacing such a 4-tuple by the 4-tuple of lines emanating from a fixed point on the conic, and passing through the 4 points.  Does anyone know in what generality this can be done?  Does this still work in the complex projective plane?  Is there a source?  Tkuvho (talk) 00:38, 17 December 2010 (UTC)
replies: text: George Salmon (1900) A Treatise on Conic Sections, page 252. Real case.Rgdboer (talk) 03:54, 13 January 2011 (UTC)
thread_title:  4-tuple on a conic 

message: I suggest that (A,B;C,D) is defined as (AC/CB)/(AD/DB), and not as the algeraic simplification of that expression. In words, it is defined as the ratio of (the internal ratio of AC and CB) and (the external ratio of AD and DB). Algebraic simplification of the resulting experssion hides the intention and the path.  — Preceding unsigned comment added by 84.92.190.75 (talk) 00:58, 24 November 2011 (UTC)
replies: text: And what definition does that reference use?  Deltahedron (talk) 06:37, 29 September 2012 (UTC)

text: The strategy can also be seen in Dirk Struik (1953) Lectures on Analytic and Projective Geometry, page 7, a reference once used on this page but removed since by an editor. See it used currently in projective harmonic conjugate where one also sees that midpoints of segments benefit from the double ratio viewpoint. In more recent geometry, particularly the shape of a triangle is expressed as a simple ratio, such as in the work of Rafael Artzy cited there.  On the other hand, the Lester reference uses degenerate crossratio (involving ∝ ) to define the  shape of triangle. In the Lester-Artzy approach, cross-ratio is a ratio of the shapes of two triangles sharing a side.Rgdboer (talk) 02:09, 1 October 2012 (UTC)
thread_title:  Cross-Ratio Definition 

message: The elements of the group described in example 3 of the Fundamental theorem of Galois take the same form as the "six cross-ratios as Möbius transformations."  I think they should be cross referenced somehow. — Anita5192 (talk) 22:05, 8 May 2015 (UTC)
thread_title:  Cross-ratio and fundamental theorem of Galois, example 3 

message: It should be mentioned a an analoge result in more dimensions of the cross ratio involving Clifford Algebras (these are as well a generalization of quaternions), that is useful for example to know when four points in R^d belong to the same circle. (See for example: http://link.springer.com/article/10.1007/BF03041223 )  — Preceding unsigned comment added by 157.253.136.201 (talk) 22:10, 23 May 2016 (UTC)
thread_title:  Clifford Algebras 

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replies: text: Checked and removed as not an especially valuable link worth keeping.--JohnBlackburnewordsdeeds 20:05, 2 December 2016 (UTC)
thread_title:  External links modified 

message: It looks like symmetric groups are sometimes written like \mathrm{S}_3 and sometimes like S_3. Which is correct, assuming these are indeed intending to represent the same thing? -- Beland (talk) 19:01, 3 February 2023 (UTC)
replies: text: It shouldn't really matter as long as it's not internally inconsistent in an article. The italic one is probably more common. YMMV. –jacobolus (t) 00:14, 4 February 2023 (UTC)
thread_title:  Inconsistent italics?