Talk:Parabola

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[edit] 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.

==In the definition of a parobola, the focus is considered to be "a given point", but it is necessary


[edit] 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 放物線(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)

[edit] 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)

[edit] General Formula

I saw this:

More generally, a parabola is a curve in the Cartesian plane defined by an irreducible equation of the form

Ax2 + Bxy + Cy2 + Dx + Ey + F = 0

such that B2 = 4AC, 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)

[edit] 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)

[edit] 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. --Xplat

[edit] 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 θ is the rotation angle of the parabola in the xy plane. Evil saltine 21:22, 4 June 2006 (UTC)

[edit] Quadratic Bezier curve is a parabolic segment

Some mention should be made that a quadratic Bezier curve is a parabolic segment. -SharkD 20:06, 30 October 2006 (UTC)

[edit] 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) [1]. 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)

[edit] 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

[edit] 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) Bold text

[edit] 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.

[edit] 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)

[edit] 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)

[edit] 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)

[edit] 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)

[edit] 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)

[edit] 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)