On Sun, Jun 17, 2001 at 08:58:35PM +0100, Greg McCarroll wrote:
> * Chris Benson ([EMAIL PROTECTED]) wrote:
> > On Sun, Jun 17, 2001 at 06:58:03PM +0100, Roger Burton West wrote:
> > > On Sun, Jun 17, 2001 at 06:52:04PM +0100, Greg McCarroll wrote:
> > > 
> the main problem is for low values of N, i.e. the ones you can imaginine
> in your head, you can figure out regular convex polyhedra whose points 
> lie of the sphere and whose sides are all the same shape (i.e. a triangular
> pyramid, a cube or diamond, etc. however i'm not convinced you can 
> construct such shapes for all values of N

_Some_ low values are OK.  I visualise an ocean covered planet with two
water lilies: one leaf grows to cover the N-hemisphere, the other S.
This works for the Platonic solids 4,6,8,... faces (assuming the leaves 
will become triangles, squares, ...) but has gaps: 3 is never going to 
look right.
> > and that page also has a link to "Easy method for a fairly good point
> > distribution " at http://www.math.niu.edu/~rusin/known-math/97/spherefaq
> yes, but it leaves an unpleasant taste in your mouth afterwards,
> or is that just me?

I'd like to see how it works ... but I can't be bothered working out how
to plot a sphere with Perl.  It seems a complex solution for something
that *seems* simple: but I suspect anything simpler would be worse.
And nothing will make 3 points look good.

Mmmm, so if there are 3 water lilies with circular leaves, what is the
largest they can grow on the surface of a sphere without overlap?  
On a circle it's easy to see it's just less than the radius of the 
circle.  Not so easy with a sphere.
Chris Benson

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