Talk:Quadric/Archive 1

Archive 1

Dimension

A quadric in n-dimensional space has dimension n-1 as it is determined by one equation. --MarSch 12:04, 16 September 2005 (UTC)

affine

the definition given here is for affine quadrics in the next weeks i may perhaps add some pages about geometry to wikipedia, but i think this should be changed

Hmmm. You may first want to research those funny Shift keys on your keyboard. And complement your writing skills by finding a co-author who knows about punctuation… <wink/>
—Herbee 20:38, 15 August 2006 (UTC)

when you work in a projective space, you have no linear terms, everything is quadratic

a lot can be said about projective quadrics, over finite fields, about the subspaces on it, about the number of quadrics and the number of projective equivalent classes

you see? actually the projective case is more often treated in courses and is easier (User:Evilbu on 4 feb 2006)

Hi, yes, you are right, but you should not remove the current material. WP articles have multiple audiences. This article will have an audience consisting of high-school students (well-served by the existing article), college students, grad students and working mathematicians. While "grownups" may find projective spaces easier, the young'uns won't have a clue as what that is, nor what a number field is, etc. So, it is important to start with affine over reals definition. (You may find twisted cubic or Veronese surface more to your liking). linas 18:11, 4 February 2006 (UTC)

But I completely agree with all that, until I was all grown up I also thought of quadrics of affine. I certainly won't remove any of this. I am just looking for an idea how I could start a page only devoted to projective quadrics and how it could fit in with this. (User:Evilbu on 4 feb 2006)

First, can you sign your posts with four tildes? Like so: ~~~~.

You can either start a new section in this article, or you can create new articles such as projective quadric or quadric over a general field or something like that. It is usually better to expand an existing article: when it gets too long, it can be split up. Another possibility might be to rename this article to affine quadric, and start from scratch here. linas 05:04, 5 February 2006 (UTC)

So I made an article quadric (projective geometry)

Please check it out, and then we probably must decide how we move on from here? Sorry about the nonsigning Evilbu 15:00, 11 February 2006 (UTC)

Hmm, OK. A few style points: all non-trivial formulas should be indented by single-colon. Long formulas should be busted into multiple lines. linas 01:57, 14 February 2006 (UTC)

The indices in the summation of the first eqn should go from 1, no? And it is a (D-1)-dimensional surface (that is, a hypersurface) in D-dimensional space. (Please accept my apology and correct me for any mistakes of my first wp post.) Ckhung 01:52, 14 May 2006 (UTC)

Link with German page

The link to the German page of "Quadric" should be "Quadrik" and not "Quadratische Form". —Preceding unsigned comment added by 140.77.141.2 (talk) 09:40, 20 December 2007 (UTC)

Incorrect Matrix Equation

I'm not an expert, but I believe the general matrix equation for a quadric given at the top of the page is incorrect. There is no need to use the "SigmaPx" term, nor the "R" term, as the point of these (to provide linear terms and constants) is already achieved by the "SigmaQxx" term. The quadric equation is most simply expressed as x^T * Q * x = 0 where x^T = [x y z 1], and Q is a symmetric matrix. Linear terms are provided with the fourth row/column of Q, and constants are provided with the lower-right entry in Q. There is no need for the "SigmaPx" or "R" terms. In addition, the source you cited does not contain the equation you gave. Please check:

86.165.29.7 (talk) 16:42, 10 September 2008 (UTC)Dan

Well you are right in that a quadric can be expressed as you state. The article is also correct as well as here the vectors are [x y z]. You may like to look at Quadric (projective geometry) where a similar matrix to the one you give us used. --Salix alba (talk) 18:21, 10 September 2008 (UTC)

References

Commons:Deletion requests/Category:Quadrics

All the images on this page seem to be copy-vios from [1]. I've created a deletion request on commons commons:Commons:Deletion requests/Category:Quadrics. --Salix alba (talk) 18:24, 10 September 2008 (UTC)

Added Superquadrics to the list

The See Also section was incomplete, so I added the Superquadrics which also contains other interesting quadratic shapes based in ellipsoids. —Preceding unsigned comment added by 88.12.169.12 (talk) 01:45, 24 April 2009 (UTC)