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 | The contents of the Invariant interval page were merged into Line element on July 2012. For the contribution history and old versions of the redirected page, please see its history; for the discussion at that location, see its talk page. |
 | Text and/or other creative content from Invariant interval was copied or moved into Line element with this edit. The former page's history now serves to provide attribution for that content in the latter page, and it must not be deleted as long as the latter page exists. |
What is the purpose of this stub? edit
I am not sure I see the point, but I have given a few suggestions for improvement in the todo list. ---CH 19:27, 3 March 2006 (UTC)
improvement edit
I think this article might need some more information, like the article [1]. I find that one more descriptive. I myself cannot write much since I'm only a beginner. -I got scammed 11:35, 2 October 2006 (UTC)
Oops, sorry the article meant the Riemannian metric for 2D manifolds, not the full thing. Just got a bit confused (prove I'm a beginner)
square root of metric edit
Line element should apparently be the element of length i.e. square root of the metric tensor, rather than the metric itself. Tkuvho (talk) 04:14, 4 August 2010 (UTC)
- I second that. First, line element is described as ds, then ds² is called as line element. Very typical terminological inconsistency, a second example could be plain noun `metric` referring to metric tensor, not metric as in mathematics. --91.152.67.177 (talk) 14:51, 26 July 2014 (UTC)
Rewritten completley... edit
also, I intend to add some images later (but it takes me a long time, even for something simple). F = q(E+v×B)⇄ ∑ici 09:55, 27 June 2012 (UTC)
- Will also add some (not extensive) info linking classical mechanics and differential properties of curves, i.e. the position vector, velocity as a tangent vector, acceleration as curvature etc, which all require the line element dr, so that we don't bias general relativity all the time, in doing so the links to the Frenet–Serret formulas.
- I can't write about Riemann manifolds or advanced tensor calculus, differential geometry and topology etc., as suggested by the TODO list above, but I think the article is fine without so will not add this info. That's on anyone who feels so inclined. F = q(E+v×B)⇄ ∑ici 10:04, 27 June 2012 (UTC)
Very Wrong... edit
The opening paragraph starts by talking about affine space, and then talks of spaces with curvature, apparently not aware that affine space is flat. Also not aware that the line element is a simple generalisation of Pythagorean formula to curvilinear coordinates, and hides ignorance behind an irrelevant reference to the Frenet–Serret formulae95.150.154.10 (talk) 21:04, 21 September 2014 (UTC)
Terrible edit
The article is terribe. It wasn't written by a mathematician. I would it all delete Tim Ocean (talk) 11:00, 17 March 2016 (UTC)