|
![](/i/fill.gif) |
Tim Attwood <tim### [at] comcast net> wrote:
> Well, the volume is half for the new spheres, but there is a 1:1 mapping
> from each of the new spheres to the original.
But the thing is, the Banach-Tarski paradox states that you can slice
the sphere into a finite amount of pieces and then, using translations
and rotations only you can construct two spheres of the same size.
Everything in cartesian coordinates. No topology changes.
Besides, your "1:1 mapping" doesn't double the volume of the sphere.
The Banach-Tarski paradox does.
> > Besides, if what you say was true, the same trick would work with a
> > 2-dimensional circle, but it has been proven that it doesn't.
> The same slicing should work with circles, what did who
> disprove where?
Just read the theorem.
--
- Warp
Post a reply to this message
|
![](/i/fill.gif) |