>> I hadn't heard of that one, but it makes perfect sense in a topology
>> context.
>> In that context "split" really means a 1:2 mapping of spaces.
>> Cut the ball in half, then in the two hemispheres the new equator plane
>> is a curve from the lip that follows a 0.5*y scaled sphere, from there
>> just map the curved planes back to flat to get two spheres.
>> Since we're talking about a mapping, not a real object, there's no
>> conservation of volume, a sphere is a sphere, no matter what the size.
>
>  That doesn't work. The volume of the sphere cannot be modified by a
> simple change in topology. You cannot simply change the topology and
> then calculate the volume as if you hadn't. You have to calculate the
> volume using the *new* topology, not the old one.

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.

>  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?

>  And besides, the original setup happens in regular cartesian coordinates,
> without any change in topology.
>
>> The paradox is that the more mathematicians learn,
>> the less they are able to explain clearly.
>
>  You clearly haven't understood the theorem.

Obviously you can't cut a mathematician's brain in half and
end up with two whole mathematicians, it's against the law =P

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