Talk:Conic section

Again this page really needs a visual and should be written in a way accessible to all readers. This is not complex material. And a revision should be fairly easy...before this whole topic becomes esoteric.

I recommend the following link for graphics on conics (http://xahlee.org/SpecialPlaneCurves_dir/ConicSections_dir/conicSections.html).

User:Dick Beldin

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Very good visuals, thank you. RoseParks

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I moved this:

Finally, if the following determinant,

                 | a h g | 
                 | h b f |
                 | g h e |

equals zero, it represents a pair of straight lines, that may not coincide.

This is incorrect. There probably is a determinant like this, but it would be preferable to use the correct one. AxelBoldt 18:32 Oct 23, 2002 (UTC)

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I hate to complain when someone puts a lot of work into creating images, but it would be nice if the image of the hyperbola made it visually apparent that a hyperbola has two asymptotes. (A common error committed by students asked to draw graphs showing the asymptotes is to draw the lines in the right places and then draw a curve that does not at all appear to approach the lines; a good image could help them understand that that is an error.) Michael Hardy 21:23 17 May 2003 (UTC)

I came here to point out that the picture of the hyperbola does not appear to be very hyperbolic; then I saw that Michael Hardy had a similar complaint. Is that picture really a hyperbola? Dominus 02:44 12 Jun 2003 (UTC)

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Surely conic sections are one-dimensional? Rvollmert 17:02, 19 Apr 2004 (UTC)

A conic section is one-dimensional in the sense of being locally homeomorphic to R¹, but two-dimensional in the sense of being a subset of the plane that is not a subset of any line. This latter sense is much closer to the conventional meaning of "two-dimensional". Even topologists recognize that a statement like "the sphere is a two-dimensional manifold" requires additional explanation for a general audience. As a geometric object, the sphere is three-dimensional, because it is a subset of R³ but not of R²; the conic section, analogously, is a two-dimensional geometric figure, even though it is topologically a one-dimensional manifold. -- Dominus 20:30, 19 Apr 2004 (UTC)

Hmm. I see what you mean, sort of. This "conventional" meaning of dimension is not what the linked article on dimension specifies, though. When the term is used in an incompatible sense, that should at least be noted. Maybe dimension should be updated to cover this meaning, too? I'll remove the note on dimension for now, but feel free to readd it if you think it's not generally confusing. Rvollmert 13:40, 26 Jul 2004 (UTC)

Image

The first image has been replaced, original didn't have a verified copyright. I also made an alternative at Image:Conic_sections_2.png, based on a suggestion at Wikipedia:Image recreation requests. Take your pick. Duk 20:37, 18 Feb 2005 (UTC)

Semi-latus rectum and polar coordinates

Can anyone explain the origin of the term ? It's clearly half of the "latus rectum"; and my dim memory of Latin says "latus" means "carried" and I suppose "rectum" is saying the line is at right angles to the major axis. Is each line parllel to the directix called a "rectum" ? Why is the one through a focus called "carried" ? comment from user:80.203.35.66 moved from article to here