Talk:Parametric equation

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Needs layman introduction

This article could use the addition of an initial introduction for the laymen before it goes into more technical discussion. For example it might say something like this:

"Parametric equations are a set of small mathematical formulas or equations created on the spot to make an original complex problem equation more manageable by temporarily replacing it. Usually, the original complex equation is cumbersome because it has more than one variable within one side of the equation (left or right of the equal sign). An example of this is y^2+x^2=r. This is the formula for the graph of a circle but is often difficult to conceptualize the relationship. (see below for the two derived parametric equations).

The process typically involves the introduction of a third variable on the spot in a way such that the existing variables can be seperated from each other. The consequence of this is that two new equations are created representing two new graphs. But this is often helpful in various fields of endeavor like physics and chemistry etc."

Please remember the composition of your audience. The accuracy of the semantics of this example explanation can obviously be picked apart by the elite but then only the elite can read it. The more technical stuff can come after this type of intro within the article. —Preceding unsigned comment added by 99.147.240.11 (talk) 15:03, 5 September 2010 (UTC)[reply]

Parametric equations, CAD, CADD, and CAGD

CAD software developers have been making extensive use of parametric equations for decades. I felt this deserved at least some treatment. Mburdis (talk) 02:19, 3 October 2010 (UTC)[reply]

Mathematicians have been making use of parametric equations for centuries :-).

I agree that this article should mention that most spline (mathematics) are parametric equations, and that they are useful to CAD software developers, typographers, etc., not just mathematicians. --DavidCary (talk) 07:04, 16 February 2013 (UTC)[reply]

Parametric equation is compression?

I believe it is a compression in terms of computer science. Instead of specifying all the points of a set you specify few parameters and some variable, usually t. The set of all points is infinite, but in the computers science it is practically finite (computers are finite machines), for example You have raster, all the points on the monitor screen, it is finite set of points. I belive the relation is there but I do not know if it is ok to mention it. Should it be noted? — Preceding unsigned comment added by Daemonicky (talk • contribs) 12:32, 31 August 2011 (UTC)[reply]

Yes, I agree that it is often useful to "compress" an image into a small file that contains parametric curves and other geometric shapes rather than storing a raw bitmap of points. But perhaps vector graphics or curve-fitting compaction would be a better article to mention this insight. --DavidCary (talk) 07:04, 16 February 2013 (UTC)[reply]

Need a definition

The article fails to either define the term "parametric equation" or explain that it is not a rigidly defined term while giving a description of the general sorts of equations that might or might not be considered parametric.Dfeuer (talk) 18:30, 29 January 2012 (UTC)[reply]

I agree. The article is unclear on whether a parametric equation is a parametrization of a function or the equations that make up the parametrization themselves. – FenixFeather ^(talk)^(Contribs) 05:37, 15 April 2014 (UTC)[reply]

The first line of the article gives an accurate definition: "In mathematics, a parametric equation of a curve is a representation of the curve through equations which express the coordinates of the points of the curve as functions of a variable, called a parameter." Maybe one should change "parametric equation of a curve" into parametric equation of a curve. As far as I know, there no other definition of "parametric equation"; in fact, "parametric equation" alone has no meaning. One may add that that "parametric equation of a curve" is somehow an abuse of language, because a parametric equation of a curve consists in two equations. Personally, I would have titled this article "Parametric curve", but "parametric equation" is standard in low level courses of analytic geometry. D.Lazard (talk) 08:09, 15 April 2014 (UTC)[reply]

I agree that it is an abuse of language to say that a parametric equation is two equations. Perhaps the passage in the lead

"For example,

x = cos t

y = sin t

is a parametric equation for the unit circle"

could be changed to

"For example,

(x, y) = (cos t, sin t)

is a parametric equation for the unit circle."

That way an equation is defined as one equation. 208.50.124.65 (talk) 20:32, 11 July 2014 (UTC)[reply]

Alternatively, it is common to see, say, x = cos t and y = sin t referred to individually each as a parametric equation, and together as the parametric equations of the curve. So the opening sentence could be replaced by "In mathematics, the parametric equations of a curve express the coordinates...."

I like this approach. I'll be bold and put it in. 208.50.124.65 (talk) 23:55, 11 July 2014 (UTC)[reply]

Please don't: Even if formally incorrect, the singular is standard, and cannot be changed without reliable source. Without this historical background, the correct formulation would be "parametric representation". As this wording is commonly used (although I have no reference at hand), I would suggest "In mathematics, a parametric equation or parametric representation of a curve expresses..." (note the indefinite article, as there are many different parametric representations for the same curve). D.Lazard (talk) 00:09, 12 July 2014 (UTC)[reply]

From Thomas, George B., and Finney, Ross L., Calculus and Analytic Geometry, Addison Wesley Publishing Co., fifth edition, 1979, p. 91: "The equations x=f(t), y=g(t), which express x and y in terms of t, are then called parametric equations, and the variable t is called a parameter."

I'm not sure why you say the use of the singular to refer to the two equations is "standard". I've never seen it, and you don't provide a source. The singular is standard for referring to the single vector equation I mentioned above. 208.50.124.65 (talk) 15:24, 12 July 2014 (UTC)[reply]

And from Math world, "Parametric equations": "Parametric equations are a set of equations that express a set of quantities....one set of parametric equations for the circle are given by...."

In the absence of any sources for the assertion that conventional usage is nongrammatical, I'm putting in the correct usage with sources. 208.50.124.65 (talk) 18:07, 13 July 2014 (UTC)[reply]

Animated Parametric helix

I find it misleading that the curve is drawn with varying velocity. It starts slow, accelerates, then slows down. This may imply that t (time) is progressing as a cosine. --Felix Tritschler (talk) 12:18, 4 September 2020 (UTC)[reply]

Explanation of Parametric Form

Parametric form is described nowhere in wikipedia (as far as I am aware), and it is not described in this page. However, "Parametric Form" redirects to this. Can someone who understands this page add an explanation of parametric form to it, or if it is not needed here, at least remove the redirect and add the parametric form explanation to the "Vector notation" article. I would add the explanation here, except I don't adequately understand parametric equations, and I am afraid that I would put the explanation in the wrong spot. Thank you!! Jarfuls of Tweed (talk) 07:05, 10 January 2023 (UTC)[reply]

I don’t see anything in vector notation about “parametric form”. Can you link to where you saw this? In my experience, the term “parametric form” refers to a parametrization of a curve, often explicitly in contrast to “implicit form”. For example, we might say that the circle

x^{2}+y^{2}=1

is in implicit form, while the circle

t\mapsto (\cos t,\sin t)

is in parametric form. –jacobolus (t) 08:24, 10 January 2023 (UTC)[reply]

I agree that "parametric form" is sometimes used colloqually. So, I have added a sentence in the article. D.Lazard (talk) 11:09, 10 January 2023 (UTC)[reply]

Is the "Parametric Vector Form" part what you were talking about before? Did you copy that from another article or is that new text? I am finding the whole section very confusing. What is the motivation/context? Does the block math really need all of that business about "if x1 is the leading entry", etc.? –jacobolus (t) 00:18, 11 January 2023 (UTC)[reply]

Yes, that was what I was talking about. I used poor terms before when saying "if x1 is the leading entry". Let me know if my changes to the bottom of this page make more sense now. I also added links to videos on the same topic so that you can learn it if I still explained it poorly. Jarfuls of Tweed (talk) 02:20, 11 January 2023 (UTC)[reply]

What is the purpose of this section? What is it trying to communicate? I feel like I am missing the most basic context. In my opinion there are too many formulas here and not enough prose. –jacobolus (t) 02:42, 11 January 2023 (UTC)[reply]

@Jacobolus the purpose is to explain how to convert a system of equations into parametric vector form (a process that is required to learn in many intro linear algebra courses) Jarfuls of Tweed (talk) 02:56, 11 January 2023 (UTC)[reply]

it is used when finding the kernel in linear algebra and it is used a couple other times, but I can't remember exactly when (I finished that course just over a year ago) Jarfuls of Tweed (talk) 03:06, 11 January 2023 (UTC)[reply]

I agree with the concerns of {u|Jacobolus}} about the new section § Parametric Vector Form. This section has other issues:

It is presented as a subsection of § Examples with vectors, while vectors are not mentioned in it.
It is sourced only with You Tube videos, while these are not WP:reliable sources (see WP:YOUTUBE) and there are a lot of textbooks on the subject.
Most of it is out of the scope of this article, as being (badly) described in System of linear equations#Describing the solutions. Nevertheless a part of it is relevant here, namely that the solutions of a underdetermined system can be parametrized by taking as parameters the variables corresponding to some columns of a row reduced form of the matrix of the system.

So, I'll replace this new section by a short paragraph focused on this parametrization. D.Lazard (talk) 10:45, 11 January 2023 (UTC)[reply]

Thanks. Can we find an introductory linear algebra textbook that describes this (ideally using the term "parametric form") as a source? –jacobolus (t) 17:05, 11 January 2023 (UTC)[reply]

The textbook from which I originally learn linear algebra is called "linear algebra and its applications" (5th edition) by David C Lay. The section that teaches it in this book starts on digital page 62 (equivalent to physical page 45) of https://www.cartagena99.com/recursos/alumnos/temarios/210609113348-Linear%20Algebra%20and%20its%20applications.pdf. Jarfuls of Tweed (talk) 19:59, 11 January 2023 (UTC)[reply]

Sophisticated functions

I’ll remove the section § Some sophisticated functions for the following reasons:

WP:PEACOCK title
No indication that any of the curves in this section is notable
This section has been recently used for for adding more WP:original research, and for edit warring

D.Lazard (talk) 11:15, 19 March 2023 (UTC)[reply]

user:JOSEP MARIA BATLLE FERRER is a newcomer to Wikipedia, so let's try to be nice please. Cf. WP:BITE.

Hi JOSEP MARIA BATLLE FERRER and welcome to Wikipedia; sorry it’s been a bit abrupt, with people repeatedly removing your contributions and not much welcome or conversation yet.

This article, though it is currently pretty disorganized and mediocre, is nonetheless not a good venue for the new interesting graphs of parametric functions you have found. They are pretty interesting looking, but it would be better to publish those on some other website. What this page needs is someone to go read the existing mathematics/science literature about parametric functions and then more comprehensively summarize what is out there. Research into new parametric functions belongs first somewhere else. –jacobolus (t) 15:45, 19 March 2023 (UTC)[reply]

Introduction needs replacement

The introduction, without being incorrect, manages to convey nothing to someone who doesn't already know what a parametric equation already is.

I hope someone familiar with this subject can write a clear introduction and remove the current one.— Preceding unsigned comment added by 2601:204:F181:9410:10AD:61E0:72E5:372D (talk) 19:21, 8 December 2024 (UTC)[reply]

What would you suggest instead? Can you find a clear and gentle introduction somewhere else which we can take ideas from? Which parts of the current text do you find particularly difficult to make sense of? –jacobolus (t) 03:41, 9 December 2024 (UTC)[reply]

The lead looks fine to me. Parametric equations and other related terms are defined in terms of functions, but I don't know how anyone can understand parametric equations without first understanding functions.—Anita5192 (talk) 03:45, 9 December 2024 (UTC)[reply]

Something comprehensible to many readers, maybe beginning like this:

A parametric equation defines a mapping from one mathematical space to another, thereby creating a curve or surface in the second space. — Preceding unsigned comment added by 2601:204:F181:9410:10AD:61E0:72E5:372D (talk) 15:49, 9 December 2024 (UTC)[reply]

I agree that "defines a group of quantities" is meaningless for everybody. Moreover it is mathematically incorrect since a parametric equation is not a definition and a "group of quantities" has no mathematical meaning. On the other hand, "a mapping from one mathematical space to another" seems too technical for many readers, and an equation does not "creates" anything. Nevertheless, I'll try to boldy resolves this issue. D.Lazard (talk) 16:14, 9 December 2024 (UTC)[reply]

I changed the lead, hoping that this will be considered as better than the previous version. Nevertheless this can certainly be further improved. D.Lazard (talk) 16:47, 9 December 2024 (UTC)[reply]

The definition of a parametric equation should not be tied to a space or surface or curve.—Anita5192 (talk) 16:16, 9 December 2024 (UTC)[reply]

This is the introduction, not a formal definition. — Preceding unsigned comment added by 2601:204:F181:9410:10AD:61E0:72E5:372D (talk) 17:24, 9 December 2024 (UTC)[reply]