Talk:Inversive geometry

message: In the section Inversive geometry and hyperbolic geometry, does the expression "orthogonal to the unit sphere" mean that the two spheres are orthogonal at their tangent planes are orthogonal at the points of intersection?  If so, what if the spheres don't intersect?  LachlanA (talk) 06:13, 30 May 2008 (UTC)
replies: text: First question: Yes. Second question: Nonintersecting spheres are not considered to be orthogonal and aren't considered lines in the hyperbolic space.--RDBury (talk) 05:18, 13 September 2009 (UTC)
thread_title:  Orthogonality of spheres? 

message: The terms 'reference circle', 'inversion circle', and 'circle of inversion', all meaning the same thing, are used with pretty much equal frequency by various source. 'Circle of inversion' seems to be the original term and is more usual in older, more geometrical sources, while 'reference circle' seems to be used by the more trendy, computer graphics type sources. Any thoughts on what should be used here? Sticking with what's already there is a strategy too but there are other options.--RDBury (talk) 10:51, 13 September 2009 (UTC)
thread_title:  Terminology standard 

message: :I have a problem with the new version of this pic (http://upload.wikimedia.org/wikipedia/commons/thumb/8/8c/Inversion_in_circle_2.png/800px-Inversion_in_circle_2.png).  No reason is given why the triangles OPN and OP'N are similar.  It's obvious to you math wizards, and they LOOK similar to the eye, but I do not see it in any rigorous way (other than that they're both right triangles and both use the radius as a side).  
:This encyclopedia is aimed at ordinary people, not math wizards.  Even though I am profoundly, abysmally stupid; tests indicate that nevertheless, I am far less stupid than the ordinary person (for whom this article should be written).  I therefore suggest that one of you explain in the caption why the triangles are similar.
:Yes, I could go look it up myself, but we stupid people are also characteristically lazy.
:Dave Bowman - Discovery Won (talk) 11:24, 2 January 2013 (UTC)
replies: text: The caption space is getting a bit crowded. All I could do was add a hint about the proof. Perhaps it makes more sense to pull this out and write it up as a subsection. In circle with diameter OP, angles NOP and NPO are measured by half of their inscribed arcs. Since this is a semicircle, these angles are complimentary. The third angle of triangle NOP' is also complimentary to angle NOP (due to being in a right triangle) and so congruent to angle NPO ... giving the similarity of the right triangles. Bill Cherowitzo  (talk) 20:40, 2 January 2013 (UTC)
replies: text: But perhaps you were looking for something a bit simpler, such as the fact that angle NOP appears in both triangles, making them similar because they are right triangles. Bill Cherowitzo  (talk) 16:41, 3 January 2013 (UTC)
thread_title:  New pic, new problem 

message: In the section "Higher geometry" an edit was make to exclude Cayley as an originator of early models of non-Euclidean geometry. Cayley is known for the introduction of projective metrics, a method that is now standard. His "Sixth Memoir" (1859) is celebrated. As John Wesley Young wrote (pages 177–8) in Projective Geometry (1930), "That both the hyperbolic geometry of Bolyai-Lobachevski and the elliptic geometry of Riemann may be defined as geometries associatated with subgroups of the projective group was first shown by Arthur Cayley (1859), although he did not formulate his ideas on the basis of group theoretic considerations." Since attention here is on the early models, reference to Poincare is out of place. Often the Klein model is called the Cayley-Klein model, so it is not true that no model is associated with him.Rgdboer (talk) 21:27, 8 December 2011 (UTC)
replies: text: I removed Cayley since there is no model that is associated with him. It is his metric which was crucial for the development of Klein's model. Granted, Klein would not have come up with his model without Cayley's work but that does not (at least in my mind) legitimatize the attribution of Cayley-Klein to the model. They neither worked together, nor independently came to the same results – which is my criteria for combined names like this. Math history is filled with mislabeled results, so pointing to this name does not prove anything. If you want to make the claim that Cayley produced a model, find a reference that says he did ... not an ahistorical comment like Young's, nor an inference from a name. Klein's work was published in 1872, 13 years after Cayley's result and Poincaré's work follows Klein by only 10 years, so I do not see a great distinction between "early" and "not early" work. Bill Cherowitzo  (talk) 01:10, 9 December 2011 (UTC)
thread_title:  Cayley 

message: There should be some links between this topic and the pages on conformal symmetry, conformal group, conformal maps, conformal transformations etc. There is too much overlap and repetition without cross-referencing 
It would also be good to explain links with twistor theory, and why the conformal group in d dimensions is spin(d,2) Weburbia (talk) 14:11, 7 July 2013 (UTC)
thread_title:  Conformal Symmetry 

message: Could/should there be a section, "Uses of inversion" or "Usefulness of inversion" or "Applications of inversion"?  For non-mathematicians, it would be great to have a simple explanation of why and how inversion is useful, and/or why it matters.  It does say "Many difficult problems in geometry become much more tractable when an inversion is applied." but that's pretty vague.  There is an "Application" section under Circles but it's clearly written for people who already know a lot of higher-order math, and doesn't really explain anything to the lay person. Bookgrrl holler/lookee here 17:12, 12 March 2017 (UTC)
replies: text: +1. 67.198.37.16 (talk) 04:23, 8 May 2019 (UTC)
thread_title:  Why?