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Hi Craig and all,
For counter-intuitive, you can't go past this one from the mathematicians.
It is possible to take a solid sphere S and divide it up into a finite number of pieces and then reassemble them (using only translations and rotations) into two identical copies of the original sphere. This is known as the Banach-Tarski Paradox.
In fact, ignoring the original sphere's centre, it can be divided into precisely 4 pieces S1/S2/S3/S4 that can be re-assembled into two spheres S1+S2 and S3+S4 each of the same volume as the original.
A more impressive statement of the theorem says that it is possible to take a solid sphere the size of a pea and divide it into a finite number of pieces that can be reassembled into a sphere the size of the Sun.
Regards, Rob.
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