On Sat, 18 Apr 2009, Jon wrote:

> A sphere of large radius becomes a plane, reverses curvature and converges
> on a new center.

If the center is not moved then the infinite radius sphere is the plane at 
infinity, which though non-existing in Euclidean geometry, does exist in 
projective geometry.

Since a naive person like you doesn't know about projective geometry but 
only some vague notions of Euclidean geometry, you are forced to admit 
that as the radius r, increases to infinity, the center will move.  In 
this event the center will be a point at infinity which again does not 
exist in Euclidean geometry but only projective geometry.

What do you mean by reverses curvature?  A plane has zero curvature.
Since the curvature went from 1/r to 0, to reverse that would mean that 
the curvature went from -0 to -1/r?  That is incorrect.  Spheres do not 
have negative curvature.

A plane can be considered as a sphere with zero curvature.
A point can be considered as a sphere with infinite curvature.
Is that the convergence of the centers that you expected?

Throw your trash away, it's not recreational nor does it show any 
knowledge of math except for some worthless artsy-feely sort of pseudo 
math.  Are you an example of a new math educated student?