Talk:Parabola/Archive 1

Parable
The literary critic Hélène Cixous describes a story by the writer Clarice Lispector as a parabola. . . can anyone shed any light on her use of the term in this sense?--Mike 02:34, 4 November 2005 (UTC)


 * Perhaps parable is meant.--Patrick 12:14, 4 November 2005 (UTC)

Gaudi's Casa Mila
Gaudi's arches are described in this article as parabolic--which may well be true. However, they are also used (in fact, an identical photograph of them is used) in the article entitled "Catenary" as an example of THAT shape, which unfortunately means that one of these claims must be wrong. Anybody know the answer? (I'm leaving basically this exact post on the discussion page of that article, in the hope that someone will more likely come across this issue and clear it up.) Buck 07:43, 24 January 2006 (UTC)

Redundancy
It seems like the Cartesian equations for the parabola are introduced twice; these should probably appear only once, and after the more directly geometric definition. — Preceding unsigned comment added by 67.84.90.13 (talk) 03:31, 19 February 2006 (UTC)

Rotating parabolae?
Is there any equation for a parabola where the directrix is parallel to neither the x-axis nor the y-axis?
 * Yes; it can be found by applying a rotation matrix to the parametric curve (2pt + h, pt2 + k) from the article.

\begin{pmatrix} \cos{\theta} & -\sin{\theta} \\ \sin{\theta} & \cos{\theta} \end{pmatrix} \begin{pmatrix} 2pt + h \\ pt^2 + k \end{pmatrix} = \begin{pmatrix} (2pt + h) \cos{\theta} - (pt^2 + k) \sin{\theta} \\ (2pt + h) \sin{\theta} + (pt^2 + k) \cos{\theta} \end{pmatrix} $$, so you end up with $$ \begin{matrix} x = (2pt + h) \cos{\theta} - (pt^2 + k) \sin{\theta} \\ y = (2pt + h) \sin{\theta} + (pt^2 + k) \cos{\theta} \end{matrix} $$ where &theta; is the rotation angle of the parabola in the xy plane. Evil saltine 21:22, 4 June 2006 (UTC)

Focus
In the definition of a parobola, the focus is considered to be "a given point", but it is necessary — Preceding unsigned comment added by 130.207.237.170 (talk) 21:53, 25 October 2006 (UTC)

Parabolic arches picture
Picture with Parabolic arches in Antoni Gaudí's Casa Milà seems incorrect. See http://en.wikipedia.org/wiki/catenary with the same picture. It seems that catenary is the correct curve here — Preceding unsigned comment added by 217.150.50.194 (talk) 15:53, 21 November 2006 (UTC)

Parabolae/Parabolas?
I notice that this article seems to use "parabolae" as the plural of parabola. Can someone explain? We recently had this discussion in university, and the lecturer said that "parabolas" seems to be the most common response, also if you Google fight the two terms Parabolas comes out on top by almost 1 million more results. Also, and I should note I have very limited knowledge of lingustics, so I am happy to be corrected, isn't the ending "ae" from Latin words and "s" from Greek words? Or did I just make that up? --Aceizace 01:41, 3 November 2006 (UTC)
 * If no one objects I'd like to change "parabolae" to "parabolas" in the article. Like I said I am not majorly confident in my linguistics knowledge, but the plural of "formula" is "formulae" because "formula" is based on the Latin word "fōrma" (form) . Parabola also ends in an "a", but is from the Greek παραβολή (as the article says). If no one replies (or I only get replies in favour) then I will switch it round in a couple of weeks. --Aceizace 01:47, 22 November 2006 (UTC)


 * I agree that parabolae does not appear to be a legitimate plural. (And even if it is, changing to the more common parabolas can't do any harm.) --Zundark 09:11, 22 November 2006 (UTC)

Area
Shouldn't there be something that says that the area of a parabola is $${h \over 3} \left ( l + 4 m + r \right ) $$ where h is the distance from the endpoints to the midpoints and l, m, and r are the left endpoint, midpoint, and right endpoint respectively? I'm not sure how to fit this in the article, but it's a somewhat important todo. This Ancient Greek formula is essential to Simpson's rule. It is also not mentioned on the Simpson's rule page. Also, what about saying that three points define a unique parabola?

Dmbrown00 00:17, 12 December 2006 (UTC)

Gaudi
I've removed the picture and caption of Gaudi. Gaudi was FAMOUS for hanging chains and strings to get his curves. As you well know, this doesn't give a parabola. — Preceding unsigned comment added by 80.193.85.83 (talk) 14:46, 16 March 2007 (UTC)

Derivation of the Focus: Typo?
The rhs of the equation for the directrix appears the same as the y ordinate of the focus. This would only apply for degenerate linear parabolas, no? Both are listed as -b^2/4a + c + 1/4a. What am I missing? Kmarkus 23:47, 29 March 2007 (UTC)

---

I believe the equation for the y-coordinate of the focus should be -b^2/2a + b^2/4a + c. — Preceding unsigned comment added by 216.12.128.136 (talk) 00:42, 18 July 2007 (UTC)

Featured Article?
Upon my first review, this seems like a really good, informative article, well-written, and it doesn't appear to leave anything out. Do you think it could ever make FA status? Or is it too technical/filled with equations?

My only qualm is that the Equations section isn't written in complete sentences. Eilicea 23:02, 15 April 2007 (UTC)


 * We should try to get it rated as a "

good article" first. futurebird 16:12, 4 October 2007 (UTC)

Thanks
This page is a great help for math homework! Thanks a lot! —Preceding unsigned comment added by 68.42.170.1 (talk) 19:14, 6 January 2008 (UTC)

This article contains a myth
In the end of this article, it is mentioned that Archimedes used parabolic mirrors to set enemy ships on fire, however, Mythbusters on Discovery Science recently busted that as a myth. If no one66.8.158.58 (talk) 02:24, 8 March 2008 (UTC) rejects I remove that part.

This problem has been open for quite a well, but I checked my father's guide book from when we visited Barcelona (there's a fair section on Gaudi), and there is a very famous story of him hanging ropes and measuring the distances to produce the curves shown. As you probably know, that produces a catenary.

is it possible to generate a cnc program to generate a parabola using polar equation for a parobola where the x, y positions for the program are calucalted during runtime.#REDIRECT

I've looked up the question on if the arches of Gaudi are infact Catenaries or Parabolas, and this article is in error - the image shows Catenaries. Gaudi was noted for hanging ropes, taking measurements of the heights at which they fell, and designing according to that. This, of course, gives a Catenary.

So, what does a parabola look like? What does it have to do with a parabolic mirror? How is it different in shape from a hyperbola or one end of an eccentric ellipse?


 * Here is a parabola: U
 * Here is another one: C
 * Dietary Fiber


 * Hmm.. maybe a superimposed pic would be good. A parabola doesn't have asymptotes, a hyperbola does. An ellipse is curvy enough to close up again at the other side -- so it's a matter of curviness really. -- Tarquin 21:16 Mar 28, 2003 (UTC)

I know all that, I was very good in math. I just want someone who's good at drawing to draw a picture of a parabola! --Uncle Ed

I am! U Dietary Fiber

Q: What is the origin of the name 'parabola'? Is there something to do with 'parallel'? In Japanese, parabola is called &#25918;&#29289;&#32218;(Ho-Butsu-Sen), which means the curve(Sen) of thrown(Ho) object(Butsu). --HarpyHumming 20:54, 26 Feb 2004 (UTC)


 * It comes from the Greek words "para" (across) and "ballein" (to throw), so it's similar to the Japanese word. (Parabola is also the ancestor of "parable," the French word "parler," and its relative "parliament".) Adam Bishop 20:58, 26 Feb 2004 (UTC)

Why hasn't a simple y=x^2 been mentioned?

I agree. There should be a section discussing how/why y=x^2 forms a parabola. mpiff 03:51, 9 Dec 2004 (UTC)

User: Nobody_EDN 2004.10.22 Withdrawn because of lack of interst.

Why aren't there more ways to produce a parabola than folding paper given???

The pencil and string method seems a good one to add.

By paper folding

''Draw a straight line on a piece of paper, and a point somewhere not on the line. Then fold the paper over so that the point touches the line and crease the fold. Do this several times. The envelope formed by the creases will make a nice parabola.''

You can make an ellipse or hyperbola similarly by using a circle and a point.

These directions are hard to follow.

Anyone with graph paper or a CAD program that can handle X-Y coordinates and a little time on their hands can draw parabolae. I've written a small spreadsheet to calculate X-Y coordinates for various values of H/K/P and will make it available in Excel and/or OpenOffice format through Wikipedia if someone can tell me if this is allowable - I've never seen spreadsheets here, so I don't know if there is a prohibition against such, and I don't know how to go about uploading one to make it available. I've referenced Wikipedia many times in the past, but have never attempted to make a contribution. Pete 15:37, 2 May 2006 (UTC)

obsolete algebraic definition also?
According to dictionary.com, besides meaning a "parable" or a geometric shape, "Parabolism" can mean: "The division of the terms of an equation by a known quantity that is involved in the first term." in algebra. Maybe there should be some mention of this. Nagelfar (talk) 05:31, 28 April 2008 (UTC)

Incorrect picture
The second "parabola" in the category "Derivation of the focus" is not a parabola. It is facing the wrong way - the parabola is supposed to face opposite the directrix, no? It is obvious that FP is not the same length as PQ. Arabic Pilot (talk) 05:46, 26 June 2008 (UTC)

General Formula
I saw this:

More generally, a parabola is a curve in the Cartesian plane defined by an irreducible equation of the form
 * $$A x^2 + B xy + C y^2 + D x + E y + F = 0$$

such that $$B^2 = 4 AC$$, where all of the coefficients are real, and where more than one solution, defining a pair of points (x, y) on the parabola, exists.

The way it was phrased, you could have A, B, and C set to zero, and from what is stated, that would be a parabola, even though it wouldn't really be, because it would be a linear equation, so I added that A and or C had to be non-zero. MrVoluntarist 23:38, 5 January 2006 (UTC)


 * The new characterization is too strong. It incorrectly rules out the simple parabola $$ y = x^2 $$. 129.132.62.138 (talk) —Preceding comment was added at 16:29, 10 July 2008 (UTC)
 * Oops, wrong. Sorry. (See comment below) 129.132.62.138 (talk) 17:44, 10 July 2008 (UTC)
 * In fact, if you keep the vertex fixed and let $$p$$, the distance of the vertex to focus and directrix, go to infinity, the parabola will approach that line you are talking about. I'm removing the restriction to non-zero $$A$$ and $$C$$. 129.132.62.138 (talk) 17:10, 10 July 2008 (UTC)
 * Damn, I read "A and C non-zero" instead of "A and or C non-zero". "Or" makes sense, though still neglecting the limit case. Reverting my edit. 129.132.62.138 (talk) 17:44, 10 July 2008 (UTC)

Incorrect polar formula ?
I think the polar formula is incorrect. I think $$\ell$$ should be the distance to the directrix, not the parabola itself. Consider, for example, $$\theta=0$$. —Preceding unsigned comment added by 128.95.22.191 (talk) 18:43, 3 September 2008 (UTC)

Redundant and misleading
I paragraph last line: "Given a point (the focus) and a line (the directrix) that lie in a plane, the locus of points in that plane that are equidistant to them is a parabola." I think it should be modified to 'Given a point (the focus) and a line (the directrix), parabola is the locus of points that are equidistant to the them and it lies in the plane containing them. Earlier sentence implies that a point and a line always don't lie in the same plane. —Preceding unsigned comment added by 128.220.27.166 (talk) 02:42, 14 September 2008 (UTC)

Image: Parabolic shape formed by the surface of a liquid under rotation
Does anyone know what this image really is? It is not simply a rotating tank of liquid because it would not have a flat upper surface... Man with two legs (talk) 07:51, 15 September 2008 (UTC)
 * ...unless the tank is sealed at the top. Which it probably is.
 * Mystery solved. Man with two legs (talk) 16:36, 15 November 2008 (UTC)

equation (1)?
The text states:

"The tangent of the parabola described by equation (1) has slope"

Which is equation (1)? —Preceding unsigned comment added by Hedgehog0 (talk • contribs) 10:53, 14 May 2009 (UTC)

Another incorrect picture
The second picture at the top of the article (http://en.wikipedia.org/wiki/File:Conicas2.PNG) is showing a what appears to be (one branch of) a hyperbola, not a parabola. If you know a pointer to correct/acceptable illustration of conic section that is a parabola, please fix or leave a pointer/link here. If not, I will chase or generate one in a couple of days. —Preceding unsigned comment added by SwiftSurge (talk • contribs) 19:12, 11 October 2009 (UTC)

Replaced Conicas2.PNG with Parabel_som_keglesnit.jpg, which makes it clearer that the cutting plane is parallel to the side of the cone. --SwiftSurge (talk) 05:36, 12 October 2009 (UTC)

Uniformity in the articles on conics?
The articles on conics are apparently written by different people at different times. Is it worthwhile to try to have similar formats for all of them? Rick Norwood (talk) 14:41, 7 January 2010 (UTC)

layman
I appreciate that this is an encyclopaedia and would in no way wish to degenerate the topic, however as a reader with very poor understanding of geometry, this article is dense and unintelligible. Is there any way to include some real world scenario or information which would shed light on the subject. The introduction in particular, if you are not already well versed in the subject, is incomprehensible. Any thoughts?


 * I agree that this article is not even close to featured standard. In its current state, I think it's still "Start" class.  Some thoughts:
 * The emphasis of the article is far too heavy on the parabola as a conic section. There should be much more discussion of parabolas as graphs of quadratic equations, and as graphs of motion that represent constant acceleration.  Initially, this discussion should be comprehensible to any high-school algebra student.
 * The section on "parabolas in the physical world" should be expanded by a factor of two or three.
 * There ought to be some discussion of the role parabolas played in the history of geometry.
 * In general, this article has way too many equations, with not enough english in between. I'm not really sure what the "vertical axis of symmetry" and "horizontal axis of symmetry" sections are trying to communicate.  "Derivation of the focus" and "Reflective property of the tangent" are also extremely dense with equations, and could use more explanation. Jim 17:43, 4 October 2007 (UTC)


 * While making this information as clear as possible is important, keep in mind that Wikipedia is not a self-help guide for high-school math students. It is an encyclopedia. We should not forgo rigor or mathematical precision just to cater to people who need to see things in terms of what is, essentially, dumbed-down (no offense intended) higher-level (although not much higher) mathematics. --Cheeser1 20:47, 4 October 2007 (UTC)


 * While your comment is indented as if in response to Jim, I don't see how it addresses any failing or misunderstanding of Jim's. --Horoball 05:21, 5 October 2007 (UTC)
 * A parabola is, at heart, a conic section. "Parabolas in the real world" etc are really subsidiaries of the specific properties of this type of conic section. --Cheeser1 05:29, 5 October 2007 (UTC)
 * A conic section is one way of looking at a parabola, and it happens to be the way in which parabolas were first discovered. However, there are other ways of viewing parabolas, e.g. as the graphs of quadratic equations, or as the path taken by a projectile, that are no more or less at the "heart" of the matter than conic sections.  From my point of view, the fact that parabolas are graphs of quadratic equations is considerably more important than the fact that they are conic sections, and I think this ought to be reflected in the article.  I don't understand how this represents a "dumbing down" in any way, nor what this has to do with precision or mathematical rigor. Jim 05:55, 5 October 2007 (UTC)

Wiki has gotten worse over time. PhD wannabees toss in every possibility up front and frighten away anyone interested in the topic. Start simply and then link to more complicated stuff. Jim Foit —Preceding unsigned comment added by 71.126.7.4 (talk) 05:24, 1 August 2010 (UTC)

A parabola can be any size, but all parabolas have the same shape
This is meaningless nonsense. It may make "sense" to a non-mathematician, but it's meaningless. "Same shape" and "any size" have no meaning whatsoever, and simply regurgitate facts in an incorrect fashion that sit only a paragraph below. Also, when your addition to the article is removed, adding it back in is edit warring. --Cheeser1 (talk) 17:34, 17 November 2007 (UTC)


 * 1. It is not meaningless to say two things have the same shape.
 * 2. The version I restored was not written by me but by User:Morana.
 * 3. This is the second time you have made an unfounded accusation against me.
 * Man with two legs (talk) 00:30, 18 November 2007 (UTC)


 * Excuse me, this is not a personal issue. Don't make it one. It's a minor content dispute regarding the lead of this article. The sentence you introduced is redundant and written imprecisely (which led me to incorrectly judge it as also factually incorrect - an error I have freely and immediately admitted, and apologized for, and explained that I am not 100% at the moment). So, what is "same shape"? All cats are the same shape too. More or less. But we don't say it like that. In biology, things are the same species or genus. In math they are similar. "Same shape" and "any size" have little meaning in the context of analytical geometry - the content already in the article explains the matter correct - it's mentioned in the right place, in the right way, just an inch below. Why not stick sentences like "the derivative of a parabola is a line" and "parabolas are y={equation}" or whatever else into the lead? Yeah, it's true, and it's already in the article, and it's already written well there. --Cheeser1 (talk) 00:46, 18 November 2007 (UTC)

As a non-mathemetician (and wikipedia is written for such people) I found the information that "A parabola can be any size, but all parabolas have the same shape" to be very helpful. I can understand that. And it's better to have it near the beginning, before I get lost among all the equations!86.156.119.51 (talk) —Preceding undated comment added 09:52, 14 January 2011 (UTC).


 * The sentence "A parabola can be any size, but all parabolas have the same shape" is not "meaningless nonsense" -- it has an exact and correct meaning: "Not all parabolas are congruent, but all parabolas are similar." And it doesn't appear in more formal form "just an inch below" -- it's twelve inches below on my screen. I'm going to put in a layperson-friendly explanation of "similar" down below where it does appear, and also mention it in the lede. Duoduoduo (talk) 19:53, 27 July 2011 (UTC)

Parabolic mirrors in telescopes
The article says that "parabolic mirrors are used in most modern reflecting telescopes and in satellite dishes and radar receivers." This is incorrect as modern professional telescopes tend to be Ritchey-Chrétien reflectors, built with hyperbolic mirrors because they give a better quality result than parabolic mirrors. Amateur reflecting telescopes tend to be Schmidt-Cassegrain or Maksutov designs with spherical mirrors and correction plates, which give a better price/performance ratio. 83.104.249.240 (talk) 18:56, 5 September 2011 (UTC)

Meaning of the name
It has crossed my mind - what does the word 'parabola' mean?

I only recognize the prefix... what's 'bola'?

SuperTails1 23:18, 11 October 2007 (UTC)


 * Parabola on the Online Etymology Dictionary Jim 23:29, 11 October 2007 (UTC)


 * Now that's a useful site to know... Thanks! SuperTails1 21:38, 12 October 2007 (UTC)

It also indicates that a parabola starts out as a straight line away from the point of contact, and then varies with the removal of the same angle plane from a contact with the tip of the cone.WFPM (talk) 16:43, 28 February 2012 (UTC)

Diagram in Conic section and quadratic form
Wikipedia editor User:Kelvinsong, who excels in graphics, has drawn a nice diagram that's now in the "Conic section and quadratic form" section of this article. Great! DOwenWilliams (talk) 06:04, 22 February 2013 (UTC)

Equation in Cartesian Coordinates

 * $$y^2 = 4px\ $$
 * $$y^2 = 2px\ $$ ?

Mergememe (talk) 17:15, 23 March 2013 (UTC)

Huh? Please explain. That section of the article looks ok to me. DOwenWilliams (talk) 20:37, 23 March 2013 (UTC)

Temporary rename as: Parabola (mathematics)
To reindex the link in Google Search, I have renamed the article "Parabola" as "Parabola (mathematics)" (in the style of "Function (mathematics)") for about a one-week period. The problem, in Google Search, has been a link with prefix "https:" for a secure-server SSL protocol, which prompts some users with a security warning, and might deter them to not read the article after searching with Google, perhaps at a public library which limits access with secure websites. The new name, as "Parabola (mathematics)" will be listed in Google with a regular "http:" prefix, which any user can view without a security certificate. After about one week, the article can be renamed back to "Parabola" for access by any person with any browser. -Wikid77 (talk) 10:18, 25 April 2013 (UTC)

Links to other-language Wikipedias
I've put in an "external link" to the Parabola article in Spanish Wikipedia. I've also put a similar link into Spanish Wikipedia, pointing to this English article. Many people, such as myself, are reasonably fluent in both English and Spanish, and can benefit from reading the article in both languages. I don't think the Spanish version is as good as the English one. It isn't as complete. But it is nicely written, and gives a different perspective on the subject.

Of course, this raises the question of whether links should also be given to all other Wikipedias which cover this subject, and whether the same thing should be generally done for all subjects. What do people think?

DOwenWilliams (talk) 20:50, 1 June 2013 (UTC)

Conic section description
A few months ago, the description of a parabola as a conic section, written in the introduction of the article, read as follows:


 * the intersection of a right circular conical surface and a plane parallel to a generating straight line of that surface.

This definition is inadequate. There are many planes parallel to any generating line that are not correctly aligned to produce a parabola by intersecting the cone. Consider, for example, the plane that includes the generating line and the axis of the cone. The intersection of this plane and the conical surface looks like an inverted letter "V", with its vertex at the cone's apex. It's not parabolic. Moving this plane in a direction perpendicular to itself makes it miss the apex, but continue to be parallel to the generating line. It still doesn't generate a parabola. In fact, its intersection with the cone's surface is a hyperbola.

I've done a few edits to the description, so it now reads:


 * the intersection of a right circular conical surface and a plane which is parallel to another plane which is tangential to the conical surface.

Substituting the generating line with a parallel plane reduces the degrees of freedom. There are now no planes that fit the definition and do not produce a parabola by intersecting the cone's surface.

I have no idea how long this error was in this article. It was certainly a long time. I read the corresponding articles in French and Spanish Wikipedias, and they also had the error. I fixed them. (Someone has edited the Spanish version further, which is fine. It still does not include the original error.) I imagine that Wikipedias in languages I can't understand still have this error. There are also other descriptions of parabolas, in places other than Wikipedia, which contain the same error. I guess they all got copied from each other after the first one was written by somebody who wasn't thinking very clearly.

Maybe someone here can do the necessary editing.

Oh well....

DOwenWilliams (talk) 00:46, 23 June 2013 (UTC)

Overlapping graphics
In the introductory section to the right of the Table of Contents, two graphic images and their captions are overlapping two other graphic images and their captions. I don't know enough about page layout to fix this, but I wanted to draw it to the attention of someone that could. LBourne (talk) 00:41, 29 September 2013 (UTC)
 * Hmmm. They look all right on my screen. Two wide diagrams are on the right side of the screen, and two narrower ones are in the centre, between the wide ones and the table of contents. I've tried Internet Explorer and Chrome, and it looks ok with them both. What browser are you using?
 * Is anyone else having problems with this? If so, I guess I'll have to put the images in one long column, but that will leave a lot of blank space and look messy. DOwenWilliams (talk) 01:34, 29 September 2013 (UTC)
 * Ok. I've put it in two columns, instead of three. On my screen, it looked better before, but if it was a mess on yours, maybe this is better. DOwenWilliams (talk) 02:11, 29 September 2013 (UTC)

German, anyone?
I've been looking at Parabola articles in Wikipedias in other languages. If any of them cover aspects of the topic that aren't covered in the English version, maybe we should copy them. I've checked the versions in Spanish and French, which I can speak reasonably well, and haven't found anything that seems worth copying (apart from a couple of items that I already copied, some time ago). However, German Wikipedia does seem to have some things that might be worth having. Unfortunately, I have only a smattering of German, so I can't be sure, and certainly could not translate them reliably. But maybe there are some people here who are fluent in German and could check this out. Can anyone help? DOwenWilliams (talk) 23:28, 25 November 2013 (UTC)
 * Hi, I am the author of the new German version of the parabola-site. If You are interested in certain parts, I could try to translate them within my sandbox. So You or any one else could make the best of it. Regards ! --Ag2gaeh (talk) 09:21, 27 November 2013 (UTC)
 * Great! Maybe you could compare your German version with the English one, and make quick summaries (in your sandbox, in English) of theorems, etc., that are described in German but not in English. Then we could decide if they're worth translating fully. You may want to do the same the other way around, too. I'm sure there are some things in this English article that you don't yet have in German. Thanks a lot. DOwenWilliams (talk) 14:59, 27 November 2013 (UTC)
 * Please look at my sandbox. --Ag2gaeh (talk) 18:00, 27 November 2013 (UTC)
 * Thanks. I've looked at your sandbox, and figured out (more or less) what the theorems are about. I even looked up Pascal's theorem, with which I was unfamiliar.


 * I don't think, though, that any of that material should be put into the English Wikipedia Parabola article. Some years ago, the article was very abstract, and did not get much approval from readers. Most readers, I believe, are students in high-school, who want material which is basically simple algebra or geometry. Some readers have practical applications in mind, such as designing and constructing parabolic collectors of solar energy, and appreciate material which is helpful in that regard. Most of the article, at present, therefore fits into these two categories. Purely abstract material is given little emphasis, although some abstract theorems are mentioned. I don't think we should include any more of them.


 * But you may disagree. You have just as much right to edit the article as I do. If you want to add any of this material, go ahead!


 * Thanks again.


 * DOwenWilliams (talk) 22:40, 29 November 2013 (UTC)


 * Thanks for Your comment. I'll respect this philosophy and do not add any material to the parabola article. --Ag2gaeh (talk) 10:42, 30 November 2013 (UTC)

Origin of variables
What is the origin of the various letters in Cartesian notation (h,k,p)? Blonkm (talk) 04:23, 22 December 2013 (UTC)
 * It is quite common for p to be used to represent the focal length of a parabola, and for (h,k) to be the coordinates of the vertex, if it is not at the origin. When, where, and by whom these letters were first used, I don't know. Possibly, they relate to some language other than English. DOwenWilliams (talk) 16:12, 24 December 2013 (UTC)