Transforming Solids...

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Posted by Matthew Brown on October 31, 19100 at 05:37:27:

I'm not sure whether this is relevant to 'Extra Dimensions', but I'll post it anyway!...

Me and my... Associates were discussing something whilst wasting time in our Key Skills lesson (6th form). We were wondering whether or not it would be possible to inverse a solid sphere, ie. turn inside-out.
This should be easy enough for a shell (hollow sphere) - the two surfaces would simply swap over. However, we were more concerned with a SOLID sphere...

My thoughts and reasoning are thus:
A sphere can be thought of as containing two faces. A two dimensional plane on it's surface, and a zero-dimensional 'surface' at it's center (ie. a point). This point-surface is required to turn the sphere inside out:
Such a transformation would put that point on the outside, and the 2D surface on the inside. This results in a transformed-sphere comprising of a point (zero dimensional object) CONTAINING a two dimensional plane...
Is this right? I appreciate that this probably could not occur physically, I'm just talking about theoretically... Am I correct, or is it something... else...

I also thought - if the solid sphere contains mass, and through the transformation, it is turned into a point like object, it would therefore have - effectively - zero volume. This would mean its density would be infinite - a black hole.
Is this correct?

Does anybody know? - is this correct, wrong, or indifferent...? Please RSVP!!

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