On Tue, 18 Mar 2008, James Dow Allen wrote:
> On Mar 19, 11:15=A0am, Alexm <amcwill...@[EMAIL PROTECTED]
> wrote:
> > A closed curve C (such as an ellipse, for example) is in a plane P. C
> > is such that there exists at least one point in P from which one can
> > draw radii to every point on C without crossing C. @[EMAIL PROTECTED]
this type of
> > C have a (known)special name?
>
Notice the "@[EMAIL PROTECTED]
" above where Google
has corrupted the material it quoted.
> There is a type of "similarity" transformation in
> polar coordinates such that
> theta' =3D theta
> r' =3D r * f(theta)
> where f() is continuous. I don't know what such
> transforms are called; call them "lemon-transforms"
> for definiteness.
>
> Now, a curve satisfies Alexm's criterion iff there
> is some pole and some lemon-transform which
> makes the curve convex.
>
> Experts, is this right?
No. If C encloses a convex region, then there's a polar
projection of C. On the other hand, it is possible
that C can be a a polar projection and not enclose a
convex region.
C is a polar projection (not the usual definition) when
there's a point O and a continuous positive or prehaps
non-negative function, f:[0,2pi] -> R with f(0) =3D f(2pi)
and C is the curve in polar coordinates with O as the origin,
of the equation rho =3D f(theta).
James, get a decent news browser. One unlike Google Groups, that allows
you to filter out the spam and that will quote without changing blank
spaces to graphics, inserting format statements, or including ads. Some
people are so annoyed by Google Groups, that they block all posts from
Google Groups. Some people are so annoyed by the alterations of the
quoted material, that they don't bother to reply. So by using Google
Groups, you're missing out on the full capacity and participation of news
groups.
Get a news reader and server that work right. They're free and online
Get a full capacity news reader, you'll be glad you did.
|
