# Talk:Curvature

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## (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 ${\displaystyle \kappa ={\frac {|{\dot {r}}\times {\ddot {r}}|}{|{\dot {r}}|^{3}}}}$ by the directional vector normalized to unit length the curvature vector becomes as signed quantity: ${\displaystyle k_{3D}={\frac {{\dot {r}}\times {\ddot {r}}}{|{\dot {r}}\times {\ddot {r}}|^{3}}}{\frac {|{\dot {r}}\times {\ddot {r}}|}{|{\dot {r}}|^{3}}}}$

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

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

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 The comments may be irrelevant or outdated; if so, please feel free to remove this section.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) 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)

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)

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)