Talk:Curve

message: I added French curve to the 'See also' section. Perhaps trivial and obsolete, but certainly curve-related.  —Preceding unsigned comment added by Moris JM (talk • contribs) 17:49, 7 February 2010 (UTC)
thread_title: Addition to 'See also'

message: I can not stand these last changes,
there is Diff geom subsection, if you feel something should be added do it there or make new page, 
call it curves in euclidean space or so.
Tosha 02:13, 7 May 2004 (UTC)
thread_title: last changes "focussing on differential geometry"

message: The redirect for uc seems too specific. Perhaps an abstract here would be a good idea? -MagnaMopus 18:57, 18 January 2006 (UTC)
thread_title:  [[universal curve]] 

message: I've created Mechanical curve as redirect to this page, but if there's someplace better for it to redirect please edit it. From the page at Archimedes: "the first Greek mathematician to introduce mechanical curves (those traced by a moving point) as legitimate objects of study". Is that like  Spirograph or something? Thanks! Ewlyahoocom 20:20, 11 May 2006 (UTC)
replies: text: Yes, a spirograph is one example, but a simpler one might be an astroid, an involute, or really any continuous function if the moving point is taken to be an abstract and not necessarily a concrete object whose movement is being measured by the curved function. LokiClock (talk) 20:11, 25 June 2009 (UTC)
thread_title:  Mechanical curve 

message: Mechanics, engineering and applied geometry are somehow related although, here, isn't it that the surface lines are only called curved lines for example, I dont understand why the addition of "curved" to a line is needed here even for nonstraight plane objects since it is obviously a line, anyway. --Mathstrght (talk) 09:10, 4 November 2022 (UTC)
thread_title:  Curved lines in applied geometry 

message: I say that a straight line is a curve with an undefined radius.--Luke Elms 20:25, 22 November 2006 (UTC)
replies: text: This sounds true to me, but I would use the term radius of curvature. We have \rho = \frac{1}{\kappa} where \rho is radius of curvature and \kappa is the curvature. Since \kappa = 0 for a straight line, \rho is undefined. FionaLovesCats (talk) 23:54, 21 April 2022 (UTC)
thread_title:  I would like to put my two cents in 

message: Consider the following two plane curves:
:\gamma_1 : [0, 2] \rightarrow \mathbb{R}^2, ~\gamma_1(t) = (t, t^2),
:\gamma_2 : [0, 1] \rightarrow \mathbb{R}^2, ~\gamma_2(t) = (2t, 4t^2).
Clearly, viewed as functions, these two are different. Are they also different when viewed as curves? Or are they different representations of the same curve? The present text equates the curve and the function, and thus appears to make them different. Most people (and, I suspect, most mathematicians) would consider them the same curve, just like 0.5 and 1/2 are different representations of the same number.
Is anyone aware of a (reliable, published) source that pays attention to this issue? If so, what do they have to say about it?  --LambiamTalk 20:33, 27 December 2006 (UTC)
replies: text: This topic is discussed at the end of section Curve#Differential_geometry. 88.73.158.80 14:24, 3 May 2007 (UTC)
thread_title:  Same curve or not? 

message: Is something that is very easily applied with projections of curved lines into straight plane or planes. --Mathstrght (talk) 09:08, 4 November 2022 (UTC)
thread_title:  Comparative geometry of curved lines 

message: What about curves in civil engineering??? Peter Horn 02:43, 19 July 2008 (UTC)
thread_title:  [[Curve (civil engineering)]] 

message: The text treats “Jordan curve” and “Jordan arc” as synonyms. I believe this is wrong; a Jordan curve is a homeomorphic image of a circle, as stated, but a Jordan arc, as far as I know, is a homeomorphic image of a closed interval. In other words, a Jordan curve is closed, a Jordan arc is not. Isn't that how the terms are used in the literature? Hanche (talk) 02:26, 10 November 2009 (UTC)
thread_title:  Jordan curve vs Jordan arc 

message: The text starting "Another way to think about a curve..." and ending "by Frank Ayers, Jr." is incorrect. First let me note that I have Ayers book (I'm presuming it's his Schaum's book on DE's). On page 41 he gives the correct formulae for the equations of the tangent line and it's x and y intercepts for a general curve F(x, y) = 0. The equation given in the text for the tangent is incorrect and should have parentheses around the X-x part, i.e. it should read Y-y = (dy/dx)(X-x). The equation given for the y intercept is correct. The equation for the x intercept is incorrect and should be X = x-ydx/dy. The statement "...but this case we will use it to find the X and Y intercepts which are when x and y equal to 0" should read "...but this case we will use it to find the x and y intercepts which are when X and Y respectively are equal to 0". These are minor mistakes and easily fixed. A bigger problem is that the whole concept is wrong. It is not true to say that the sum of the x and y intercepts has to be equal to 2 for a curve. This is easily seen by considering the curve y=3 whose tangent line is itself and which has no x intercept and y-intercept 3. Another problem is that the two equations being combined are only simultaneously true when the tangent line passes through the origin in which case they again do not add up to 2. Recommend that the entire text be removed. Psmythirl (talk) 19:27, 6 January 2010 (UTC)
replies: text: I don't understand this part or how it relates to the rest of the Differential geometry section. I think it uses X in a different sense to the rest of the section, but it doesn't make that explicit or define its terms. It seems to have more to do with the "Graph of a function" sense. But if it's mistaken as well as confusing, I agree it should go. (In fact, seeing as no one has offered a defence of it since your comment in January, I've decided to remove it for now.) Dependent Variable (talk) 11:12, 30 August 2010 (UTC)
thread_title:  Incorrect details in Differential geometry section 

message: There a few issues with this article that lead me to the opinion that it still requires much work and is not of B class quality. First, there is an almost complete lack of references given for the material. The St Andrews and 2dcurves.com are good resources and make good external links, but they are mainly catalogs of individual curves, not a resource for the definition of a general curve or its properties. That leaves a single note and a single reference to support one section out of the entire article. Second, several of the sections are much to long considering the material is covered in another article. I brief introduction to the idea should be given only and details should merged with the other article. Finally, the article attempts to give a single definition of a curve when really there are several definitions depending on the context; a curve in topology is very different from a curve in algebraic geometry. I will try to address some of these issues myself, but the article should not be marked B class in its present state.--RDBury (talk) 19:17, 26 January 2010 (UTC)
replies: text: It seems I have missed something vital here. What does B class mean? Where do I look for more info? Hanche (talk) 02:34, 5 February 2010 (UTC)
replies: text: See the math rating banner at the top of the page, it has links to more information.--RDBury (talk) 07:14, 24 February 2010 (UTC)
thread_title: Demoting to Start class

message: The section "Conventions and terminology", after defining a path to be a continuous map from R into a manifold, says that the word "curve" is used in diff.geom. & vect.calc. for a path, but that it is used in topologoy for the image of a path. This contradicts the definition given in the immediately preceding section, "Topology". What gives?
Also, the lead defines a "curve" as a space which is locally homeomorphic to a line, i.e., a one dimensional manifold. Is this wrong? I mean, it works for a simple curve that doesn't ever cross over itself, but in general the image of a curve may include (infinitely many) points that are not locally homeomorphic to a line. Is there a definition without this problem (without referencing paths, as they brings in the issue of multiple paths having identical images). Also, is a single point supposed to qualify as a topological curve (since it is the image of the path whose map function happens to be just a trivial constant)?
I think the different approaches and terminology should be given more priority in the article (ie. explained earlier and making the distinctions more clearly). Cesiumfrog (talk) 01:01, 3 May 2011 (UTC)
thread_title:  path-image, alternate definitions, dubious 

message: The section "Algebraic curve" says
:Algebraic curves can also be space curves, or curves in even higher dimension, obtained as the intersection (common solution set) of more than one polynomial equation in more than two variables. 
Would it be correct to make this more specific by saying the following?:
:Algebraic curves can also be space curves, or curves in even higher dimension n, obtained as the intersection (common solution set) of n–1 polynomial equations in n variables. 
Loraof (talk) 15:12, 15 October 2015 (UTC)
replies: text: This is not correct. However, I agree that we need to be specific. I'll edit the page for fixing this. D.Lazard (talk) 11:42, 16 October 2015 (UTC)
thread_title:  Space curves 

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thread_title:  External links modified 

message: Because of several non-equivalent definitions of a curve, this article must be structured as a broad-concept article. I have done the job, except for the sections on differentiable curves. 
IMO,  should redirect to Differential geometry of curves (this latter title is confusing, as I do not understand why this article is not named "Differentiable curve" and what is the difference between "Differentiable geometry of curves" and "Study of differentiable curves"). The part of Curve devoted to differentiable curves should be reduced to a summary of Differential geometry of curves, whose size should be of the same order as that of the two other sections. If some content would be lost by this reduction, it should be added to Differential geometry of curves.
Also, the two articles must be made coherent: presently, a eight-shaped curve is a differentiable curve in one of the articles, and not in the other.
I could probably do these modifications, but it would be much better if they would be done by an expert. D.Lazard (talk) 16:36, 1 May 2019 (UTC)
thread_title:  Sections on differentiable curves 

message: Also it is segments that maybe used in differential geometry calculus and these are actually used. --Mathstrght (talk) 09:06, 4 November 2022 (UTC)
thread_title:  Differentiatial geometry and calculations for curved lines 

message: Hello curve enthusiasts! Here's what I think should change here.
In the section Curve#Differentiable_arc it is stated that "Arcs of lines are called segments or rays, depending whether they are bounded or not". I think that the whole line should also be considered an arc to itself. I propose that it instead say "Arcs of lines are segments, rays, or lines depending how they are bounded". This issue comes down to whether we require a strict subset relation or not in the definition of arc, and I think we should be explicit about that either way.
In the section Curve#Length_of_a_curve a formula is written
:
\operatorname{Length}(\gamma)
~ \stackrel{\text{def}}{=} ~
\sup \!
\left( \left\{
\sum_{i = 1}^{n} d(\gamma(t_{i}),\gamma(t_{i - 1})) ~ \Bigg| ~ n \in \mathbb{N} ~ \text{and} ~ a = t_{0} < t_{1} < \ldots < t_{n} = b
\right\} \right).
I think we should lose the parentheses because it's common to see \sup A where A is some set, and we don't lose any information by doing this. I would prefer
:
\operatorname{Length}(\gamma)
~ \stackrel{\text{def}}{=} ~
\sup \!
\left\{
\sum_{i = 1}^{n} d(\gamma(t_{i}),\gamma(t_{i - 1})) ~ \Bigg| ~ n \in \mathbb{N} ~ \text{and} ~ a = t_{0} < t_{1} < \ldots < t_{n} = b
\right\}.
Within that same section is the formula
:
{\operatorname{Speed}_{\gamma}}(t) ~ \stackrel{\text{def}}{=} ~ \limsup_{[a,b] \ni s \to t} \frac{d(\gamma(s),\gamma(t))}{|s - t|}.
I think that [a,b] \ni s \to t is unnecessarily confusing. I would use the \substack LaTeX command like in this article to stack s \to t and s \in [a,b] but that doesn't seem to be supported by Wikipedia. At least I get errors when I try :(. I would even just consider
:
{\operatorname{Speed}_{\gamma}}(t) ~ \stackrel{\text{def}}{=} ~ \limsup_{s \to t} \frac{d(\gamma(s),\gamma(t))}{|s - t|}.
as the domain of \gamma has already been specified.  FionaLovesCats (talk) 01:03, 22 April 2022 (UTC)
replies: text: These seem good suggestions. Be WP:BOLD and edit the article yourself. D.Lazard (talk) 10:01, 22 April 2022 (UTC)
thread_title:  A few complaints 

message: I think curved line is very rear to use but curve simply never in mathematics, this is some jargon that is not acceptable. --Mathstrght (talk) 09:04, 4 November 2022 (UTC)
thread_title:  Straight lines, functions, bend spaces with curves 

message: An editor has identified a potential problem with the redirect :Curved line and has thus listed it for discussion. This discussion will occur at Wikipedia:Redirects for discussion/Log/2022 November 16#Curved line until a consensus is reached, and readers of this page are welcome to contribute to the discussion.  Steel1943 (talk) 17:29, 16 November 2022 (UTC)
thread_title:  "Curved line" listed at [[Wikipedia:Redirects for discussion|Redirects for discussion]]