The Banach-Tarski Paradox seems patently false. The authors explain it and its implications in terms appropriate for an undergraduate.
Grzegorz Tomkowicz is a self-educated Polish mathematician who has made several important contributions to the theory of paradoxical decompositions and invariant measures. Stan Wagon is a Professor of Mathematics at Macalester College, Minnesota. He is a winner of the Wolfram Research Innovator Award, as well as numerous writing awards including the Ford, Evans, and Allendoerfer Awards. His previous work includes A Course in Computational Number Theory (2000), The SIAM 100-Digit Challenge (2004), and Mathematica(R) in Action, 3rd edition (2010).