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 = x 2 + y 2 - r 2

$\nabla f = \begin{pmatrix} {2x} , {2y} \end{pmatrix}^T$

$\kappa_f = \nabla\cdot\left(\frac{\nabla f}{\|\nabla f\|}\right) =$

$\nabla \cdot \frac{\begin{pmatrix} {2x} , {2y} \end{pmatrix}^T}{\sqrt{4x^2 + 4y^2}} \not=$ 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)

[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)

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Talk:Curvature

From Wikipedia, the free encyclopedia

[edit] Intrinsic and extrinsic curvature

[edit] Curature in polar coordinates

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