Talk:Parabola

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

1 This article contains a myth
2 Parable
3 General Formula
4 Gaudi's Casa Mila
5 Redundancy
6 Rotating parabolae?
7 Quadratic Bezier curve is a parabolic segment
8 Parabolae/Parabolas?
9 Parabolic arches picture
10 Area

[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 noone 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

A x 2 + B x y + C y 2 + D x + E y + F = 0

such that $B 2 = 4 A C$ , 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?