How boundless is our world?
An orange can be chopped into a finite number of chunks, and these chunks can then be put together again to yield two oranges, each of which has the same size as the one that just went into pieces.
A pea can be split into a finite number of pieces, and these pieces can then be reassembled to yield a solid ball whose diameter is larger than the distance of the Earth from the Sun.
These two illustrations are from the Volke Rundel's article on the Banach-Tarski paradox.
Monday, March 19, 2007
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