The Banach-Tarski Paradox

Tom Wieting
Department of Mathematics, Reed College

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.