Talk:Ellipsoid

message: An IP user has set a question in section "Plane sections" of the article, about the proof that planes sections of an ellipsoid are circles, single points of empty point. I have put it in the field "reason=" of a template . As I am not sure wether a detailed proof deserves to appear in the article. I'll answer here.
Let  be an ellipsoid,  be a plane,  be an affine transformation that maps the unit sphere onto , and  be the inverse transformation. The image by  of the intersection of  and  is the intersection  of the unit sphere  and the plane . It is thus either a circle, a point, or the empty set. Thus the intersection of  and  is , that is an ellipse, a point or the empty circle.
I do not know if such a proof deserve to be put in the article. Therefore, I leave to the community to decide what should be done. D.Lazard (talk) 14:57, 18 September 2017 (UTC)
replies: text: This is good, but my immediate impression is that it is a bit too verbose and far afield for the main text of this article.  Perhaps it could be encapsulated into the note that you just inserted, or inserted as an example in Affine transformation and linked from this article.—Anita5192 (talk) 19:54, 18 September 2017 (UTC)
replies: text: I agree with Anita. I'll also add a reference for the result in this article. --Bill Cherowitzo  (talk) 04:47, 19 September 2017 (UTC)
thread_title:  Plane sections 

message: the  edit 858602570 is correct, Geoid, an important object modeled by an elipsoid. It is not an elipsoid, it is modeled as an elipsoid (instead a sphere). The most used elipsoid-Goid model in nowadays, is the WGS84 elipsoid.  --Krauss (talk)
:First of all, "important" is your personal opinion. I agree that the geoid is an important concept and that working with the geoid requires to know about ellipsoids. However this is a mathematical article, not an article about geodesy, and importance should be estimated relatively to readers of this article. As they are probably interested primarily to mathematics and specifically to geometry, a link to Geoid seems unimportant for them. In any case, the link will not help them to better understand the article and its context.
:Also, the body of the article provides links to Earth ellipsoid and Reference ellipsoid, which, for this article, are more appropriate than Geoid. Thus, adding Geoid in See also section, would be against the recommendations of WP:NOTSEEALSO: . D.Lazard (talk) 11:19, 8 September 2018 (UTC)
replies: text: I agree.  This existing links to Earth ellipsoid and Reference ellipsoid suffice for readers to make the connection.  There's no need to add a link for geoid; this is more likely than not to be confusing. cffk (talk) 12:16, 8 September 2018 (UTC)
replies: text:  I disagree. The presented arguments justify adding the link to geoid. cffk (talk)'s confusion is his own private problem. Cocorrector (talk) 13:19, 19 November 2018 (UTC)

text: Hi  thanks. Now I see that Earth ellipsoid and Reference ellipsoid are links in the article, that is good (Earth model is important and is comtemplated). I see also that Geoid article is not citating the term ellipsoid... It is because in my mind I do a "jump" over the intermediary concept, that is Geodetic datum... Now the "see also" section is correct. PS: of course, the 3 concepts are similar, perhaps one day some articles will be merget to the "most important"...  The "importance of the article" is not personal opinion, is a collective behaviour of pageviews, see statistics. Geoid and Geodetic datum are the most "important" in this objective facet of the Wikipedia's articles.  Krauss (talk) 13:53, 19 November 2018 (UTC)
thread_title:  Important link, explanation 

message: An editor as inserted in the list item about Poinsot's ellipsoid a comment about a so called "Mac Cullagh ellipsoid". I have reverted this edit, and I'll revert it again for the following reasons:
* The term "Mac Cullagh ellipsoid" is not used in the literature. A Scholar Google search on these words results only in Mac Cullagh's articles and some articles of 19th century citing Mac Cullagh work. The searches of "Mac Cullagh ellipsoid", "MacCullagh ellipsoid", "McCullagh ellipsoid" (between quotes) provides only two hits. Thus this terminology is definitively not notable and not reliably sourced. Therefore it does not belong to Wikipedia per the policy WP:OR.
* From the given description, it seems that the so-called Mac Cullagh ellipsoid is exactly the Poinsot's ellipsoid. As Poinsot's work is earlier that Mac Cullagh's, there is no for mentioning Mac Cullagh in this article. This would give WP:UNDUE weight to this work, which deserves only a mention  in the history section of Poinsot's ellipsoid.
Thus I'll revert again the mention of "Mac Cullagh ellipsoid" in this article. If you disagree, please, read carefully WP:BRD and do not start WP:Edit warring.
I'll also revert the insertion of Geoid in section "See also", as the linked article does not contain the word "ellipsoid", and is linked in other articles appearing in this see also section. It thus not useful for any reader to link this article. D.Lazard (talk) 19:11, 16 November 2018 (UTC)
replies: text: I agree, even a novice reading of Poinsot article shows it is the same formula (it uses T instead of 2E). Maybe you should put a mention there of the alternative name. Geoid instead of being a "see also" should probably be in this use list.Spitzak (talk) 19:54, 16 November 2018 (UTC)
replies: text:  Glad to see D.Lazard and Spitzak clarifying the problem. Let me further clarify it to them both: МасCullagh ellipsoid IS NOT ths same as Poinsot's ellipsoid. Not to worry though since there are many things that would be obvious to novices although they are not true. So, a formula using 2E instead of T IS NOT the same. Cocorrector (talk) 12:21, 19 November 2018 (UTC)

text:  With some luck Spitzak can learn the difference between Poinsot's ellipsoid and MacCullagh ellipsoid in Zhuravlev Foundations of Theoretical Mechanics (Fizmatlit, Moscow, 2008)) [in Russian], whereas D.Lazard displays little ability to do the same. Our sorrow for him should not preclude us from neutralizing him. By the way, his objection to Geoid seems to be consistently stupid. Cocorrector (talk) 12:49, 19 November 2018 (UTC)
thread_title:  Mac Cullagh ellipsoid 

message: I think the formula in this section for e_1 is incorrect by setting its z-coordinate to 0. If so, after inverse affine transformation, the corresponding z-coodinate is still 0, which is not necessary.— Preceding unsigned comment added by 24.188.214.97 (talk) 07:27, 3 December 2018 (UTC)
thread_title:  e_1 

message: The equation for the surface normal in the Parametric Representation section appears to be incorrect for non-spherical ellipsoids. When I try to replicate, the normals point roughly outward but do not match the surface curvature except at the poles and the equator. It is as if the map from the isotropic sphere to the anisotropic ellipsoid is not taken into account. 98.69.156.214 (talk) 03:20, 10 April 2020 (UTC)
replies: text: The parametric representation is regular only for \theta\ne\pi/2. I added this restriction. It is \vec x_\varphi \times \vec x_\theta= \vec n \cos\theta.--Ag2gaeh (talk) 07:58, 10 April 2020 (UTC)
thread_title:  Incorrect surface normal parametric form 

message: The volume of an ellipsoid is 2/3 the volume of a circumscribed elliptic cylinder, and π/6  the volume of the circumscribed box.
These do not circumscribe uniquely; our preferential embedding in at least the box case can likely be specified as the one having minimum volume. — MaxEnt 00:45, 26 May 2020 (UTC)
thread_title:  The circumscribed box 

message: The top of article describes ellipsoid as an affine image of a sphere.  Since the position of the sphere is not fixed, linear transformations (if understood as homogeneous degree 1 maps) suffice.  This is better for introduction as not everyone shares the mathematics terminology that linear transformations must be homogeneous or involve a choice of origin, and "linear" is more intuitive.  "Affine" is a more math-specific term and the Wiki link to a page about transformations preserving "an affine structure" is ridiculous as an explanation for people who may not know what is an ellipsoid.  It is more of a definition for purists that can be elaborated inside the article. 73.89.25.252 (talk) 04:39, 14 June 2020 (UTC)
replies: text: Ellipsoids are considered in the Euclidean space. The concept of a linear transformation is not defined in a Euclidean space. So, it is wrong to use "linear transformation" here. It is not pedantry to use the only existing correct term. Nevertheless, I agree that the first sentence of Affine transformation was much too technical. I have fixed it. D.Lazard (talk) 14:31, 14 June 2020 (UTC)
thread_title:  Affine vs linear image of sphere : unnecessary pedantic distinction