Chris Benson
Sun, 17 Jun 2001 15:41:46 -0700
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