Talk:Conformal map

message: Should we move this page to conformal mapping?  (That is now just a redirect page pointing here.) Michael Hardy 23:56, 20 Feb 2004 (UTC)
replies: text: The reason is reflected in today's reversion of an edit putting this page in the Geography project. For some reason, "mapping" connotes the mathematical context, such as conformal mapping. The substantive "map" has a strong tie to geographical study.Rgdboer (talk) 21:30, 17 April 2008 (UTC)
thread_title:  'mapping' vs. 'map' 

message: Is this page consistent in talking about preservation of orientation? Charles Matthews 08:54, 14 Sep 2004 (UTC)
replies: text: No, Charles. I don't believe this page's definition of a conformal mapping is remotely correct. As I understand it, conformal mappings are mappings that are locally complex-differentiable, i.e., mappings that locally preserve angles. I'll try to research and fix this. Norbornene (talk) 02:26, 7 September 2017 (UTC)
thread_title:  Orientation Issue 

message: I have a concern about the example recently added by 69.140.68.72: since one of the major points about a conformal map is that it preserves angles, it seems a pity to use an example which clearly changes an angle ... I don't have sufficient knowledge of applications to suggest an alternative - anyone? Madmath789 17:23, 13 June 2006 (UTC)
replies: text: I clarified what was going on. Conformal mappings preserve angles, but only for points in the interior of their domain, and not at the boundary. Thus, the map z\to z^2 from the interior of the first quadrant (x>0, y>0) to the upper half plane (y>0) converts a 90 degree angle into a 180 degree one, but this map is not conformal at the origin, which is on its boundary, as there its derivative is zero. Oleg Alexandrov (talk) 18:01, 13 June 2006 (UTC)
thread_title: Example of use

message: The phrase "conformal equivalence" is employed without giving its definition.  Can someone add this?  —Preceding unsigned comment added by 99.237.37.181 (talk) 22:19, 16 December 2007 (UTC)
replies: text: I've never heard the term used before, but conformal equivalence seems to make sense here, where stereographic projection is the conformal transformation in this case. Can I get a second opinion before adding the wikilink please? Ben (talk) 15:22, 16 January 2008 (UTC)

text: Added the wikilink. Ben (talk) 21:03, 21 January 2008 (UTC)
thread_title:  Conformal equivalence 

message: I'm having trouble with the section "Higher-dimensional Euclidean space". Isn't in addition to the types mentioned another conformal map possible? By letting an 2d-conformal map act on two of the dimensions and leaving the component perpendicalur to this plane unchanged? --Pjacobi (talk) 14:36, 16 June 2008 (UTC)
replies: text: That's not going to be conformal, unless the two dimensional map is an isometry. Think about the 1+1 dimensional case. In \R^2 if you consider a map f(x,y)=(g(x),y) where g is conformal in one dimension (which means very little), then the map f will generally not be conformal. Oded (talk) 14:42, 16 June 2008 (UTC)
replies: text:  Thank you very much. I had the wrong mental image. --Pjacobi (talk) 17:31, 16 June 2008 (UTC)
thread_title:  "Higher-dimensional Euclidean space" 

message: I like pictures in this article made by Christian.Mercat, which were removed by anonimus user. Should I revert this edit ? --Adam majewski (talk) 09:52, 21 February 2009 (UTC)
replies: text: Thx for answer. (:-) I think that images are great and shows what is very hard to understand from words/equations.  Regards--Adam majewski (talk) 06:36, 24 February 2009 (UTC)

text: Thanks talk! I liked them as well :-) Well, you know, like math should be boring, serious things are on the black board only in Finland :-) Never mind. I've put them here: Conformal pictures. Christian.Mercat (talk) 12:36, 22 April 2009 (UTC)
replies: text: I think it would be appropriate to select just one of those pictures, together with the original, and display both on this page somewhere (probably not near the top), attached together in a multiple image box with all captions and footer. That would help convey an intuitive feel for what conformal transforms look like, what is and isn't preserved. I disagree with anon, they look professional. However, I don't think it is appropriate to keep such a larger number of those pictures here, and I think the Conformal pictures article should be deleted afterward. Cesiumfrog (talk) 00:35, 23 November 2010 (UTC)
thread_title:  Pictures 

message: The transform of a solution of the Laplace equation again is a solution only in two dimensions. In general the transform must be multiplied with s-(d-2)/2 to get a solution, where s is the local scale factor. This shouldn't be swept under the carpet.radical_in_all_things (talk) 16:40, 26 May 2012 (UTC)
thread_title:  Laplace equation 

message: The following was removed but may be useful for § Complex analysis:
:A conformal map is called that because it preserves the shapes of things (at an infinitesimal scale). The term is based on the Latin prefix com- (together, with, near) and the Latin noun forma (shape, appearance)
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The contributor inserted these dictionary citations in the section dealing with alternative angles, now § Pseudo-Riemannian geometry. — Rgdboer (talk) 01:09, 7 October 2017 (UTC)
thread_title: Similar form

message: This section is not sourced. It uses concepts that are not defined here nor in linked articles. Some of these concepts are even nonsensical, such as "any [Jacobiam matrix with non-zero determinant] lies in a particular planar commutative subring and has a polar decomposition determined by parameters of radial and angular nature". 
It seems that this section has been written by a fan of the old-fashioned terminology of split complex numbers, dual numbers and other hypercomplex numbers, who do not really understand the subject of the article. 
A section on (pseudo)-conformal maps in Pseudo-Riemanian geometry would be useful here, if based on reliable sources. This gibberish is of no help for writing such a section.
So, I'll delete this section per WP:TNT. D.Lazard (talk) 11:04, 19 February 2021 (UTC)
thread_title:  Section "Pseudo-Riemannian geometry"