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Mariano Suárez-Alvarez  
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 More options May 18, 6:31 pm
Newsgroups: sci.math
From: Mariano Suárez-Alvarez <mariano.suarezalva...@gmail.com>
Date: Sun, 18 May 2008 15:31:11 -0700 (PDT)
Local: Sun, May 18 2008 6:31 pm
Subject: Re: curves on quadrics
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?

>       The hyperboloid of one sheet and the hyperbolic paraboloid are the
> only proper (non-degenerate) quadrics with real rulings, yes.  Cones,
> cylinders and plane-pairs also have real rulings, and if you allow
> complex coordinates then even ellipsoids are ruled.

Mostly because when working over the complex numbers
there is no difference between an ellipsoid and an
hyperboloid! ;-)

-- m


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