Talk:Dessin d'enfant
WikiProject Mathematics  (Rated Bclass, Lowimportance)  


Thanks
Thanks for clarifying the connection between the riemann sphere and Dessin d'enfant; I mean the new paragraph you put in this article today.
You should make yourself an account if you want to do serious editing. Oleg Alexandrov 21:42, 10 Mar 2005 (UTC)
Glueing to create a Riemann surface
Let me start by saying "Great article! Good job!" before I offer some criticisms.
I know (or thought I knew) how to glue triangles to create Riemann surfaces, but somehow, the description in this article threw me for a loop. I'd like to see that clarified. Please note that the article on Riemann surfaces does not even hint at such a construction. In particular, I'm not sure why one wants to glue together halfspaces, instead of triangles. Yes, the jinvariant tells you how to get from triangles to halfspaces, and v.v. but, to me, "visualizing" glued triangles is easier than visualizing glued halfspaces. I feel like I'm missing some step. The only handydandy glueing article I know of on WP is fundamental polygon, which describes glueing to create compact riemann surfaces, as cribbed from a book by Jost of the same name. Compact vs. noncompact tends to be a major distinction; this article doesn't hint how that might enter. (And the WP entries on glueing to form noncompact surfaces are lacking.)
I do have to admit I only skimmed this article; perhaps I lack sufficient background, but it seems I will have to go to other sources to understand the mechanics. linas (talk) 14:18, 26 November 2007 (UTC)
 Firstly, the halfplanes being glued are compact, because they include ∞. In fact, they are triangles: triangles having 0, 1, and ∞ as their three vertices. Very big triangles, but still nice compact convex closed triangles. The reason to glue them rather than some smaller triangles is because we're not just creating a Riemann surface, but we also need to simultaneously create a Belyi function from the created surface to the Riemann sphere, and with this particular gluing construction the function is easy to describe (identity within each halfplane). —David Eppstein (talk) 16:16, 26 November 2007 (UTC)

 I'm with linas on this one: (a) this is a good and useful article; (b) I also found the reference to "halfplanes" confusing. After reading the discussion here, I think I've figured out what it means, but it's clear that "upper halfplane" as used on this page does not mean the same as upper halfplane. There must surely be a better way to describe this construction, although at the moment I can't think of a way to clarify the page without getting very verbose... Jowa fan (talk) 02:57, 28 December 2009 (UTC)
dessin a colorié —Preceding unsigned comment added by 205.237.51.207 (talk) 22:01, 21 January 2009 (UTC)
Graph drawing
Sensible, but is this really an accepted term for what I only know under the names graph or diagram? It links to the wrong article in any case. Rp (talk) 21:53, 10 October 2010 (UTC)
 A graph is an abstract structure of vertices and pairs of vertices (edges), devoid of any geometric or visual interpretation. A diagram is any visual representation of any kind of information. So neither of these is specific enough to describe what's going on here. A graph drawing is a visual representation of a graph, and that's closer. In this context, the visual part is less important than the fact that it's a graph embedded within a 2manifold, so graph embedding might be more apropos. But we already have the graph embedding link in the next paragraph, and I think for the lede the phrase graph drawing conveys the flavor of the title (which also refers in French to a kind of drawing). —David Eppstein (talk) 22:27, 10 October 2010 (UTC)