Talk:Curvature

Mathematics C‑class High‑priority

	Mathematics portal This article is within the scope of WikiProject Mathematics, a collaborative effort to improve the coverage of mathematics on Wikipedia. If you would like to participate, please visit the project page, where you can join the discussion and see a list of open tasks.MathematicsWikipedia:WikiProject MathematicsTemplate:WikiProject Mathematicsmathematics articles
C	This article has been rated as C-class on Wikipedia's content assessment scale.
High	This article has been rated as High-priority on the project's priority scale.

Daily pageviews of this article

A graph should have been displayed here but graphs are temporarily disabled. Until they are enabled again, visit the interactive graph at pageviews.wmcloud.org

Archives

1

This page has archives. Sections older than 365 days may be automatically archived by when more than 5 sections are present.

(Layout problem)

The illustration and the text are interfering with each other, as viewed from Netscape. I've tried putting a colon before the "div", and I've tried putting "br" before and after it, to no avail.
Michael Hardy 20:12 Mar 14, 2003 (UTC)

This seems to be affecting a number of images that used to work correctly in Netscape (they still work as expected in IE). Was something changed in the Wiki software that is affecting this? I'll change it to using a table.
Chas zzz brown 22:50 Mar 14, 2003 (UTC)

Earth's curvature

Seeking information on the Earth's curvature, but no linkage from this page. I've read that "The earth's curvature is not visible from altitudes lower than about 20 miles.", but I'd really like a cite.
~ender 2007-08-21 12:06:PM MST —The preceding unsigned comment was added by 70.167.217.162 (talk)

Signed curvature in three dimensions

It seems noteworthy to me that the local curvature can easily be obtained by adding an obvious term. If one extends the given equation $\kappa ={\frac {|{\dot {r}}\times {\ddot {r}}|}{|{\dot {r}}|^{3}}}$ by the directional vector normalized to unit length the curvature vector becomes as signed quantity: $k_{3D}={\frac {{\dot {r}}\times {\ddot {r}}}{|{\dot {r}}\times {\ddot {r}}|^{3}}}{\frac {|{\dot {r}}\times {\ddot {r}}|}{|{\dot {r}}|^{3}}}$

Where the added term makes $k_{3D}$ consistent to the sign in the signed curvature k for the two dimensional case:

k={\frac {x'y''-y'x''}{(x'^{2}+y'^{2})^{3/2}}}.

Thus it is possible to give also a signed curvature for a three dimensional curve. Then one can integrate this and obtain, for example the 'net' curvature for a Lissajous (1:2) figure to be (0.0,0.0,0.0) instead of the unsigned case, where the curvature adds up.

I verified this 'experimentally' in Mathematica. However, can this be found in literature?
User:Aritglanor Friday, June 19, 2009 at 3:44:14 PM (UTC)

Assessment comment

The comment(s) below were originally left at Talk:Curvature/Comments, and are posted here for posterity. Following several discussions in past years, these subpages are now deprecated. The comments may be irrelevant or outdated; if so, please feel free to remove this section.

needs refs, try finding some here.

Cronholm144 15:03, 18 May 2007 (UTC)[reply]

Also deals primarily with the curvature of curves and Gauss curvature. Should offer a more generic elementary interpretation of curvature, pointing to other articles for details. Silly rabbit 19:13, 21 May 2007 (UTC)[reply]

Last edited at 22:11, 28 May 2007 (UTC). Substituted at 01:56, 5 May 2016 (UTC)

About convex and concave curvature

I have made several edits about convex and concave curvature, but those are reverted [1] [2] [3] by User:Sławomir Biały. How sad the Wikipedia only include "convex curvature" for representing "positive curvature" in terms of Gaussian curvature, but not include "concave curvature" for representing "negative curvature"! More sadly, even though the revert might be valid, Wikipedia still not explain "convex curve" nor "concave curve" in terms of Mean curvature... UU (talk) 16:22, 25 December 2016 (UTC)[reply]

You're simply wrong that convex/concave surfaces can have negative curvature. A (smooth, strictly) locally convex surface, by definition, is a surface that locally lies on one side of its tangent plane. A neccesary and sufficient condition for local convexity is positive Gauss curvature. Sławomir Biały (talk) 16:58, 25 December 2016 (UTC)[reply]

Need revision for "Curvature of Plane curves"

Please see the latest edits by Lichinsol (reverted by some editor) in history. The section "Curvature of plane curves "lacks clear mathematical illustrations and things are written in an unsynchronized manner. Also suggestion for a derivation of" Local expressions " formula on my edit. Need suggestions! (The editors who are repeatedly reverting my edits are edit warring. I am not. Without looking into the edit and simply reverting just because it is bold is not the reason to revert as suggested by BRD. BRD too is not the reason to revert. I eant to re revert, but then I would be warring.) Lichinsol (talk) 01:36, 2 October 2019 (UTC)[reply]