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quadratic surfaces

Defines: 
elliptic paraboloid, hyperbolic paraboloid, parabolic cylinder, ellipsoid, one-sheeted hyperboloid, two-sheeted hyperboloid, cone surface, hyperbolic cylinder, elliptic cylinder
Synonym: 
surfaces of second degree
Major Section: 
Reference
Type of Math Object: 
Topic

Mathematics Subject Classification

51N20 no label found

Comments

I'm sorry I broke this entry, pahio, I wanted to add illustrations for the graphics, but it's behaving weirdly page iamge vs html mode
(image misplaced, colors wrong, no equations being displayed)

y the way, a possible cause for all these pstricks and graphics problems might be that tetex version installed on planetmath is waytoo old (and thus breaks things dealing with new xkeyval package), but that's just a conjecture
f
G -----> H G
p \ /_ ----- ~ f(G)
\ / f ker f
G/ker f

I'll try to get the picturesi n EPS as soon as possible, to make your entry work again
f
G -----> H G
p \ /_ ----- ~ f(G)
\ / f ker f
G/ker f

The first picture is fine! I believe that fitting of such pictures is rather difficult.

Best regards,

Jussi

I meant when yo uview the entry in html mode, the graphic for a)
shows besides b) (and I can't figure out why)
and the white background becomes black
f
G -----> H G
p \ /_ ----- ~ f(G)
\ / f ker f
G/ker f

And, in page image mode, "setgray" stuff appears on the top of the page and the last line is cut off.

By the way, I actually like the black background. I think it looks really nice and makes the picture stand out better.

Also, this must be some kind of record on Planet Math --- the entry went up within a day of the request!! Usually these things take months. In fact, it went up so fast that there was no time to move it down to the fulfilled list. I'll move it there so you can erase it from the requests list.

Ray

;)
all I know is that I had to upload like 10 differnet files o make the entry render due the tetex version pm uses has very old packages.
I think that somehow make it break the background, but hey, I also like better the black background

on the other hand, the picture that should go below a) still moves around (perhaps the \item is acting weird, I don't know)
f
G -----> H G
p \ /_ ----- ~ f(G)
\ / f ker f
G/ker f

Hi, isn't the double plane a degenerate case? A straight line cannot intersect it in exactly two points.

Of course it is a degenerate case. I only included it so as to be complete. Maybe it would be better to make a separate heading for degenerate cases and move it there.

Also, the case of two planes (which could be subdivided into the case of two parallel planes and case of two intersecting planes) is usually classified as a degenerate case in most of the algebraic geometry books I am used to because of the fact that, even though a generic line intersects it in two points, it can be expressed as the union of two first degree surfaces (planes). I suppose that there are different ways of defining degenerate. Maybe some algebraic geometers in the mebership could add their opinions on how they understand the word "degenrate". I know we have a lot of differential goemeters around here, but maybe not so many algebraic geometers.

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