Talk:Upper half-plane

Discussion until 2005-02-10 before major rewrite of linas
Isn't the first sentence:


 * In geometry, the Half-plane model of hyperbolic geometry is described by hyperbolic motions.

reduntant? It looks to me that that info is contained in the second paragraph:


 * In mathematics, the upper half plane H is the set of complex numbers x + iy such that y > 0. It is the domain of many functions of interest in complex analysis, especially modular forms.  It is also a model of the hyperbolic plane.

And the second paragraph should be the first either way, as it is a more general description of the subject. Comments? Oleg Alexandrov 18:29, 7 Feb 2005 (UTC)


 * Actually, I want to split this article into three. One part would be called Poincare metric, and would have the metrics for D and H in it.  One would be Half-plane model as a special case of fuchsian model and would hold the mobius-transformation group SL(2,R) and H=SL(2,R)/U(1) formulas in it; and finally, there would be a very very simple page called Upper half plane which just says x+iy>0 and maybe links off to these other topics. Could you hold off on major edits until after this split, or take a stab at making this split yourself? I was hoping to make this edit sometime over the next week or two. linas 19:24, 7 Feb 2005 (UTC)


 * And finally, Schwarz-Alhfors-Pick theorem would be its own page also. Does this split make sense to you? would it be agreeable? If it is, I'll make the split later tonight. linas 19:35, 7 Feb 2005 (UTC)
 * I am going to say the same thing here that I want to say at Talk:Adjoint endomorphism. How about this for the order of things: instead of splitting short articles in the hopes that one day they will become long, let's write stuff in the short articles, make them long, and once they have become long and have enough independent material, then splitting sections off into separate articles makes sense -Lethe | Talk 04:39, Feb 9, 2005 (UTC)
 * My comment was more about layout than actual math. I don't know enough about this topics to have an opinion. So feel free to do whatever you think is necessary, but sooner or later please change the introduction to this article to make it reflect the contents of the article. Oleg Alexandrov 20:01, 7 Feb 2005 (UTC)


 * Awesome! This is exactly how I think this article should look like. As stated, the half plane is just a set. Many things can be done with it, and they are explained in their corresponding articles. Oleg Alexandrov 05:56, 10 Feb 2005 (UTC)

Well, I split up the article; not so much because it was long, but because there were several articles that were talking about almost the same thing, but in different ways, and it all seemed a mess. So I shuffled things into several places:
 * Hyperbolic geometry provides an overview
 * Poincaré_half-plane_model provides particular details
 * Poincaré metric provides the formulas for the metric
 * Mobius transform, Fuchsian group and Kleinian group and modular group provide specific geometries.

Anyway, I think the new structure is cleaner than the old warren it used to be. I'm going to try to clean up modular forms and elliptic integral to tie in correctly into this structure as well. Ugh. And Riemann surface too ... it doesn't even link to these pages. Go figure. linas 08:03, 10 Feb 2005 (UTC)

Open set or closed set?
According to the article Half-space (geometry), a half-space can be either open or closed. The present article uses the definition corresponding to an open half-space. But according to Mathworld, the upper half plane includes the x-axis, making it a closed half-space.

Since there is apparently no consensus on the meaning of the unqualified term "upper half-plane," the article ought to mention both definitions. Dratman (talk) 04:33, 31 October 2012 (UTC)

Assessment comment
Substituted at 02:40, 5 May 2016 (UTC)