Talk:Radius of curvature (applications)

Different definitions

Note that the usages of this term discussed at radius and intrinsic coordinates#Radius of curvature are technically distinct. The former is either the radius of a surface with circular cross-section, or (in engineering, at least) is the radius of the largest circle that circumscribes the part. The latter is the radius of a circle, tangent to a curve at a point, with matching curvature at that point. These are not the same thing.--Srleffler 15:34, 3 July 2006 (UTC)

Curvature confusion

I find it extremely confusing that this article starts by talking about two-dimensional surfaces and moves on from there. My understanding (and the article at Mathworld agrees) is that the "radius of curvature" of a curve at a point P, when used by itself, refers to the radius of a circle with curvature equal to that of the curve at the point P. While this article addresses that with the statement "the radius of curvature of a curve at a point is the radius of the osculating circle at that point," this is difficult for a non-mathematician to decipher, particularly since it seems from the first sentence that the radius of curvature must have something to do with spheres or ellipsoids. Furthermore, the fact that a huge fraction of this article deals with spheroids and elliptic coordinates seems highly inappropriate for an article titled "radius of curvature." (Although it was certainly very useful to me since I'm trying to solve for the stress in a thin-walled oblate spheroid pressure vessel.) Wouldn't it be more appropriate to discuss that in Spheroid? The organization in general is pretty weird too -- how come the fact that the radius of curvature is the inverse of the curvature isn't stated until halfway through the article, and then under the heading "Principle radii of curvature"? Like many math-related articles on Wikipedia, this one really needs some work. I'll tackle it when my grad school applications are done if no one else has by then. Geoff 05:47, 16 November 2006 (UTC)

Yeah, I'm probably the guilty party, as I took it from a simple stub (see previous edit)! P=)

Part of it is I was thinking "curvature" and "curve" are just different forms of the same word (like "verify" vs. "verification"), thus I thought "radius of curvature" and "radius of a plane curve" (or "radius of arc" or just "arcradius") are the same thing. I plan on expanding the Arc (geometry) stub (though the title is still tentative), and then fixing this article up some——though, right now, I'm working on a few supporting articles (that is, after I finish up a major revamping of ellipsoid I'm working on! P=).

I had a productive discussion here regarding curvature, that you may find useful.  ~Kaimbridge~ 15:17, 16 November 2006 (UTC)

Requested move

The following discussion is closed. Please do not modify it. Subsequent comments should be made in a new section.

Radius of curvature (applications) → Radius of curvature — This article appears to have been moved without consensus. Nontrivial page moves must be discussed first. The new name is not good, and it makes little sense to have an article on applications of radius of curvature rather than an article on radius of curvature itself. The change seems to be ill-conceived. —Srleffler (talk) 03:27, 22 February 2008 (UTC)

Survey

Feel free to state your position on the renaming proposal by beginning a new line in this section with *'''Support''' or *'''Oppose''', then sign your comment with ~~~~. Since polling is not a substitute for discussion, please explain your reasons, taking into account Wikipedia's naming conventions.

• Comment. See my comment at Wikipedia talk:WikiProject Mathematics#Radius of curvature. See also the long-standing comments in a similar vein from Geoff under "Curvature confusion", above. Matt 11:32, 22 February 2008 (UTC).

• Comment. There is already an article on radius of curvature itself: Curvature. The present article is a weird fusion of basic maths of the radius of curvature (inferior to "Curvature" and other math articles dealing with the subject) and a section on very peculiar applications to curvature of sections of ellipsoids. Presumably, they are were forked out from other specialized articles, but both their significance and the content are highly unclear. I've created a disambiguation page at radius of curvature, since we already have at least three different articles dealing with the subject, and one of the typical uses of the term in science and engineering (as the synonym of radius) is drastically different. Arcfrk (talk) 22:11, 22 February 2008 (UTC)

• Comment. This is a content fork of the main curvature articles: curvature (for plane curves), Frenet-Serret formulas and Differential geometry of curves (for space curves), Principal curvatures and Darboux frame for surfaces. There is no need for this kind of content fork from the existing curvature articles. Keep the stuff related to applications, and summarize the rest. The whole Category:Curvature (mathematics) could do with an overhaul, actually. This article isn't alone in being a content fork. Silly rabbit (talk) 02:37, 23 February 2008 (UTC)

Discussion

Any additional comments:

Outcome

N Since there doesn't seem to be consensus to move, I'm closing this request. -- SatyrTN (talk / contribs) 04:16, 16 March 2008 (UTC)

The discussion above is closed. Please do not modify it. Subsequent comments should be made on the appropriate discussion page. No further edits should be made to this discussion.

Picture request

A picture would do wonders. Could someone please, please make one? Thanks in advance. —Preceding unsigned comment added by 86.25.176.175 (talk) 21:47, 20 March 2010 (UTC)

There already seems to be an adequate diagram in the article. I'm closing this request for now. If anyone has a suggestion for an additional diagram just let me know. --CheCheDaWaff (talk) 23:23, 14 April 2016 (UTC)

New section: curvature of the earth

I've added a section that gives just the formulas needed for the Earth; this article comes up as the second result for the search "earth radius of curvature", so might as well make it easy for people to find the few formulas needed for that. Tim Zukas (talk) 18:07, 30 August 2010 (UTC)

This new section seems to have evaporated and in its stead there is a scatter-shot discussion of the curvatures on an ellipsoid. A lot of this is flaky and, in any case, it's better to have this material in one place here Earth_radius#Radius_of_curvature. So I've replaced the material on this page by a link. cffk (talk) 15:51, 3 July 2013 (UTC)

Application to Semiconductors

This appears to be good information and well-written, so it would be nice to have it somewhere. Unfortunately, I feel this is far too much detail on aspects of semiconductors beyond the application of radius of curvature, and should be trimmed to something concise and resembling the other applications mentioned. Anybody else? BillHart93 (talk) 15:44, 8 January 2014 (UTC)