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Abstract:
In 1924, S. Banach and A. Tarski published a paper (Fundamenta
Mathematicae 6: 244–277) which put forward an astonishing, one might say
paradoxical result: that one can break a ball in euclidean 3-space into
a finite number of pieces, then by rigid motions reassemble the pieces
into two disjoint copies of the original ball. The object of this
lecture is to describe the historical context of the paper, to describe
the presumptions and the arguments upon which it is based, and to
discuss its implications.
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