On Mar 20, 6:13=A0pm, Tim Little <t...@[EMAIL PROTECTED]
>
wrote:
> On 2008-03-20, Alexm <amcwill...@[EMAIL PROTECTED]
> wrote:
>
> > If the curves consist of 3 points (i.e., triangles) then the
> > computer calculations would be not very difficult and would consist
> > of choosing the three vertices randomly and then scaling so that the
> > perimeter =3D L.
>
> First, how do you choose 3 points "randomly"? =A0Do you take (X,Y)
> coordinates chosen independently from a Gaussian distribution?
> Uniform within some range or other? =A0Equal-area choice from within a
> unit circle? =A0Do you throw out any triangles that do not include the
> origin? =A0Do you choose uniform angles and some distribution on radii
> instead? =A0If so, which distribution?
>
> > Would working with n-polygons (polar coordinates with n angles and
> > radii randomly chosen) give a good approximation to the answer if n
> > is taken larger and larger?
>
> I don't think there is any such thing as "the" answer to be
> approximated. =A0There are only answers that vary with the initial
> distributions.
>
> - Tim
Yes, there are difficulties both practical and, more im****tantly,
conceptual. Thanks for bringing me down to earth.
AlexM
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