Talk:Curvature

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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)


Is the curvature for a circle really 1/r? I would guess this is something someone writing an article on curvature wouldn't get wrong, but it doesn't work out for me...

f = x2 + y2 − r2
\nabla f = \begin{pmatrix} {2x} , {2y} \end{pmatrix}^T
\kappa_f = \nabla\cdot\left(\frac{\nabla f}{\|\nabla f\|}\right) =
\nabla \cdot \frac{\begin{pmatrix} {2x} , {2y} \end{pmatrix}^T}{\sqrt{4x^2 + 4y^2}} \not= here it is
\frac{(2+2)}{2 \sqrt{r^2}} =
\frac{2}{r}  !
Yep, the curvature of a circle is 1/r! The mistake in your algebra is where you calculate the divergence - you have assumed the denominator is constant, when it isn't. Kaplin 21:14, 19 July 2006 (UTC)

Contents

[edit] Intrinsic and extrinsic curvature

As it stands, the article is almost entirely about extrinsic curvature, derived from paths in a two or three dimensional space. I think this article needs more material relating to intrinsic curvature which is of great importance in differential geometry and its applications in physics such as general relativity. The distinction is a major one. An extrinsic curvature may be calculated for the orbit of a planet at a particular point in its path, but the intrinsic curvature of space-time due to the gravitational field causes the orbit to have the form it does (including things like the precession of the orbit of mercury). Elroch 00:48, 13 February 2006 (UTC)

Agree that we could do with a treatment of intrinsic curvature and that the distinction is a major one. Maybe, a distinction made upfront with some emphasis throughout. --Eddie | Talk 10:27, 13 February 2006 (UTC)
It is elementary article, there is something about Gauss curvature, and if someone needs more there are refs. Tosha 00:13, 16 February 2006 (UTC)
I agree. I added a more general introduction after I made my comment. I hope this helps. Elroch 22:57, 16 February 2006 (UTC)

[edit] Curature in polar coordinates

The given expression for curvature when using polar coordinates is confusing. If we are using polar coordinates, then generally the curve will have the form r = r(θ) so one should expect an expression for the curvature to be in terms of the derivative of r with respect to θ. Writing it in terms of F(y) is confusing.

--81.153.87.195 15:37, 30 January 2007 (UTC)

Corrected this. --Bob The Tough 13:10, 12 February 2007 (UTC)

[edit] Numerical evaluation of curvature

I was looking for a method to compute surface curvature at a point on a surface in 3D, given a number of points in the neighborhood. I couldn't find any. Should this be added to this article, or should it link to some more general article on numerical methods for e.g. numerical differentiation / integration ?

Mauritsmaartendejong 20:26, 19 June 2007 (UTC)

Maybe it would be enough to add something like "Here y' is derivative of function y." after the first equation? Then one would find link to "Numerical differentiation" in the article "Derivative". --Martynas Patasius 12:56, 20 June 2007 (UTC)
This might be the case where you have to go to the research litrature. I've seen several techniques used: for example fitting a patch and then calculating it from the equations from the patch, there are several other techniques[1]. I'm not aware of any one method which is superiour to others and they can vary depending on the type of data you have.
For this reason I don't think it wise to explicitly mention any one method. --Salix alba (talk) 17:43, 20 June 2007 (UTC)

[edit] 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)

[edit] Curvaton in Physics

Please, may someone explain what is a Curvaton in physics. I've been trying to reach information about the Curvaton in Wikipedia, but I was unable to find it. According the dictionary, a Curvaton is:

1. (cosmology) an scalar field that can generate fluctuations during inflation, but does not itself drive inflation; it generates curvature perturbations at late times after the inflaton field has decayed and the decay products have redshifted away, when the curvaton is the dominant component of the energy density

In someone in physics could create a full article, I think is very interesting.

You could try Wikipedia:Reference desk/Science, which is the best place for science questions. --Salix alba (talk) 22:19, 2 January 2008 (UTC)

[edit] arclength parametrisation

When parametrising using arclength, the formulas for curvature become nice. Maybe this should be added. Randomblue (talk) 13:41, 4 February 2008 (UTC)

A more immediate issue is the redlink arclength parametrisation (or arclength parametrization). Anyway, I think much of the article should be moved out to curvature of a curve, and much more detail should be supplied there. A survey of various kinds of curvature should remain here. I tried to do this at one point, but became very badly stuck trying to discuss curvature in general in a way that would cover all cases. Silly rabbit (talk) 13:47, 4 February 2008 (UTC)

[edit] Osculating circle picture

It's nicely done (in colors!), but is quite misleading: it shows the osculating circle at a vertex of the curve, where one of them is contained inside the other. At a generic point of non-zero curvature, the osculating circle will actually cross the curve in a bent version of the cubic parabola meeting the x-axis at the origin. Is there anyone knowledgeable about graphics generation who can fix the picture? Arcfrk (talk) 23:33, 22 February 2008 (UTC)

[edit] Article needs to split

One of the big differences between a dictionary and an encyclopedia is that each topic has its own page. The three different definitions of curvature in the article are from pretty different domains.

I'm of the opinion that this article should become 3 articles, maybe Curvature (space) Curvature (surfaces) and Curvature (curves).- (User) WolfKeeper (Talk) 05:06, 27 April 2008 (UTC)

No, the concept is the same, what if one wants to understand "what curvature is". --Tosha (talk) 05:01, 29 April 2008 (UTC)