Talk:Conformal map

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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)

Why mapping is better then map? Tosha

Is this page consistent in talking about preservation of orientation? Charles Matthews 08:54, 14 Sep 2004 (UTC)

[edit] conjugate

A map of the extended complex plane (which is conformally equivalent to a sphere) onto itself is conformal if and only if it is a Möbius transformation or its conjugate.

If 'conformal' means 'preserves angles', then conjugates mobius tranfomations are not conformal - they reverse all the angles.

[edit] Example of use

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)

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 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)