Talk:Parametric equation

message: 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)
thread_title:  Needs layman introduction 

message: 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)
replies: text: 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)
thread_title:  Parametric equation is compression? 

message: 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)
thread_title:  Animated Parametric helix 

message: 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)
replies: text: 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)
replies: text: 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)

text: 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)
replies: text: 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)
replies: text: 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)
replies: text: @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)
replies: text: 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)

text: 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)
replies: text: 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)
thread_title:  Explanation of Parametric Form