Talk:Pseudosphere

message: I think that an image of a pseudosphere would be desirable as the first image on this page. I had to go to tractrix to visualize it myself. McKay 05:06, 12 October 2006 (UTC)
thread_title:  image 

message: Pseudospherical surface redirects to this page not all Pseudospherical surfaces are pseudospheres (i know it is hard to get your head around)  
But there are many more "Pseudospherical surfaces" or "surfaces of constant negative curvature": (see for example http://virtualmathmuseum.org/Surface/gallery_o.html#PseudosphericalSurfaces )
Three surfaces of revolution:
Pseudospherical Surfaces of the parabolic type (this is the tracioid or pseudosphere)
Pseudospherical Surfaces of the hyperbolic type
Pseudospherical Surfaces of the elliptic type (called the conic type at the virtual math museum)
and also other surfaces that are not surfaces of revolution 
what to do now? (PS I am not an expert in this field, nor on wikipedia)
(I made a similar comment on https://en.wikipedia.org/wiki/Talk:Sine-Gordon_equation#Surfaces_of_constant_negative_curvature_not_always_a_pseudosphere  i am still a beginner sorry) 
WillemienH (talk) 10:19, 16 September 2014 (UTC)
thread_title:  Pseudospherical surface redirects wrongly to this page   

message: The first sentence, which is the entire introductory section, reads as follows:
"In geometry, the term pseudosphere is used to describe various surfaces with constant negative Gaussian curvature. Depending on context, it can refer to either a theoretical surface of constant negative curvature, to a tractricoid, or to a hyperboloid."
The first named section is titled Theoretical pseudosphere, and its first sentence is as follows:
"In its general interpretation, a pseudosphere of radius R is any surface of curvature −1/R2 (precisely, a complete, simply connected surface of that curvature), by analogy with the sphere of radius R, which is a surface of curvature 1/R2. The term was introduced by Eugenio Beltrami in his 1868 paper on models of hyperbolic geometry.[1]"
These sentences contain a number of errors. 
1. The word "pseudosphere" has no "general interpretation".  It means a specific surface in 3-dimensional space. (In fact, it refers to case of the tractricoid of constant negative curvature -1, not just any negative number −1/R2.)
2. First of all, the pseudosphere is a surface, not a "theoretical" surface.  It is not at all clear why the word "theoretical" was used, but it is just confusing here, since it has no meaning. 
3. The pseudosphere is a specific surface, not maybe one surface and maybe another one.  It is emphatically not a hyperboloid, and any use of the word to mean a hyperboloid is a mistake.
This word should not be used in either the first sentence or in the first (or any!) section title.
The phrase "precisely, a complete, simply connected surface of that curvature" contains three errors.  
4. The pseudosphere is not complete.  Complete means that every geodesic can be extended indefinitely, but the pseudosphere has a circle of singularities (the circle in its plane of symmetry) past which geodesics cannot be extended.
5. The pseudosphere is not simply connected.  For a space to be simply connected means that every closed curve in the space can be continuously shrunk to a point in the space.  But any closed curve on the pseudosphere that goes around its axis of revolution cannot be shrunk to a point on the surface.
(6. Any explanatory statement beginning with the word "precisely" but which contains nothing but errors has also made an error by using the word "precisely".)
I hope someone will fix this article.Daqu (talk) 19:02, 16 June 2015 (UTC)
thread_title:  Multiple major errors