Talk:Sphere

message: Spherical product redirects to Sphere but it is not mention anywhere in the article, is it? --RokerHRO (talk) 12:20, 31 March 2014 (UTC)
replies: text: Came here to say the same thing. I still don't know what a spherical product is (I think I've worked it out but that's not what an encyclopedia should be making me do) Andybak (talk) 22:53, 14 July 2021 (UTC)
replies: text: Is it actually a recognized term? The history is brief with the redirect created by long departed User:Xp54321 who does not look like a mathematician. No obvious mathematical use in a brief search? --Salix alba (talk): 05:49, 15 July 2021 (UTC)
replies: text: "Spherical product" shows up in a browser search; for example, https://www.cs.mcgill.ca/~dudek/SQ/spherical_products.html, but I don't know how accurate or practical this source is.—Anita5192 (talk) 18:21, 15 July 2021 (UTC)
replies: text: Thats a useful link, the key paper seems to be Superquadrics and Angle-Preserving Transformations (free copy). We have a paper on Superquadrics which seems like a better target of the redirect. I'll change it, and maybe add a brief section on the spherical product there. --Salix alba (talk): 19:16, 15 July 2021 (UTC)
thread_title:  Spherical product? 

message: In the Terminology section, it states that you can take any arbitrary point of the sphere as a pole, take its antipodal point as the opposite pole and the line between the two points is the axis of rotation.
This is only true in the case where a) The sphere is rotating and b) the two poles are chosen such that their positions on the sphere are unchanged by the rotation - ie. not arbitrary.
:The article correctly states (although in a very awkward way) that any diameter of a sphere may be an axis of rotation. This is a mathematical property of spheres and has nothing to do with spinning physical objects. Please sign your comments and put new ones at the end of the page. Thanks. Bill Cherowitzo  (talk) 20:32, 27 July 2015 (UTC)
replies: text: Then they shouldn't use the word 'rotation.' And frankly, mathematicians are totally incompetent in the domain of quality and effective use of language. Which is fine, but they ought to be kept on shorter leashes in regard to terminology and naming conventions. The 'ball/sphere' distinction is another ridiculous example. Although, the latter seems to have been the result of faulty reasoning, while the former seems to be just poor use of language. Firejuggler86 (talk) 22:14, 4 October 2020 (UTC)
thread_title:  Dubious definition of axis of rotation 

message: I have calculated the the numbers of small sphere in alarge sphere by my formulaدکترغلامعلی نوری  Dr  Goal.A. Newray 09:05, 12 September 2015 (UTC)
replies: text: This looks like Sphere packing in a sphere, your results seem to differ. We cannot publish results here which have not been peer reviewed, please see WP:OR.--Salix alba (talk): 18:01, 12 September 2015 (UTC)
thread_title:  numbers of small sphere in a large sphere 

message: Substituted at 02:36, 5 May 2016 (UTC)
thread_title: Assessment comment

message: I'm not 100% sure, but it looks like the n in the surface are and volume formulae refers to the lowest-dimensional Euclidean space in which the sphere can be embedded, not the dimension of the sphere itself as it's used elsewhere.  In particular, it seems to me that the surface area should be proportional to r^n (e.g., that of a circle proportional to the radius), and the volume of the ball to r^(n+1). 50.252.247.245 (talk) 19:11, 15 July 2020 (UTC)
thread_title:  Formulae for surface area and volume, n? 

message: As previous editors commented, it's circular for this page to define a sphere as the surface of a ball and for Ball (mathematics) to define a ball as the region enclosed by a sphere. The ball-sphere distinction is important but not so important that it needs to be in the lead, as another commenter complained. Definition as the set of points at a given radius from a center seems more common: see , , . Given previous lengthy battles over the lead I thought I'd leave a note just in case. Feel free to disagree with me as long as you don't start a multi-page flame war like in .
In general I'd like to rearrange this page so that the grade school material comes first and the grad school material comes later. I will work on combing out the knots in this hairy ball as I have time. -Apocheir (talk) 04:28, 29 December 2021 (UTC)
thread_title:  Lead v2 

message: In the section on Eleven Properties of the Sphere, it is claimed that "Any closed surface will have at least four points called umbilical points." However, if we click to read the hyperlinked article about umbilical points, we read that "A torus can have no umbilics"; this contradicts the claim that any closed surface has at least four umbilical points. Moreover, again according to the article about umbilical points, "An unproven conjecture of Constantin Carathéodory states that every smooth topological sphere in Euclidean space has at least two umbilics" - and it is strange that a claim in one article should be stronger than an unproven conjecture in another article. 
Assuming I'm not missing something here, I recommend deleting the sentence "Any closed surface will have at least four points called umbilical points." The paragraph also needs some copy editing (example: "...because the sphere these are the lines..."), and it could be briefer. Proposal:
At any point on a surface, the normal direction is at right angles to the surface. The intersection of a plane that contains the normal with the surface is a curve that is called a normal section; the curvature of this curve is called the normal curvature. For a typical point on a typical surface, different normal sections at the point will have different curvatures; but there may exist points on the surface at which all normal curvatures are equal. Such points are called umbilical points. Umbilical points can be thought of as the points where the surface is closely approximated by a sphere. For any point of the sphere, the curvatures of all normal sections are equal, so every point is an umbilical point. The sphere and plane are the only surfaces with this property. --Jzimba (talk) 20:21, 11 February 2022 (UTC)
thread_title:  Inconsistent claim about umbilical points