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Ken Pledger  
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 More options May 18, 9:11 pm
Newsgroups: sci.math
From: Ken Pledger <ken.pled...@mcs.vuw.ac.nz>
Date: Mon, 19 May 2008 13:11:28 +1200
Local: Sun, May 18 2008 9:11 pm
Subject: Re: curves on quadrics
In article
<92887ab2-0d8a-4296-8034-114c86aae...@56g2000hsm.googlegroups.com>,
 Mariano Suárez-Alvarez <mariano.suarezalva...@gmail.com> wrote:

> On May 18, 7:04 pm, Ken Pledger <ken.pled...@mcs.vuw.ac.nz> wrote:
> > In article
> > <f4b27853-16cf-45fb-8559-3df2021bf...@d1g2000hsg.googlegroups.com>,
> >  Dmitry Sustretov <dmitry.sustre...@gmail.com> wrote:

> > > .... By the way, are hyperboloid and hyperbolic paraboloid (that
> > > have been mentioned) the only quadric surfaces that are ruled?

> >       Your geometry here is presumably affine or Euclidean, not purely
> > projective.

> Why? ....

      In projective geometry there's only one kind of proper quadric.  
To switch to affine geometry you choose an absolute (plane at infinity);
then a hyperboloid meets that plane in a real proper conic and a
hyperbolic paraboloid meets it in a real line-pair.

            Ken Pledger.


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