Joint Graduate Student Colloquium

John Sawatzky, Department of Pure Mathematics, University of Waterloo

"The Banach-Tarski Paradox"

A famous theorem of Banach and Tarski states that a sphere can be cut into finitely many pieces that can be rearranged into two identical copies of the original sphere. This result, known as the Banach-Tarski paradox because of its unintuitive nature, has become very well-known in popular mathematics circles in recent years. In this talk we will work through a proof similar to Banach and Tarski's original argument with an emphasis on the importance of the usage of the axiom of choice in the proof.

MC 2054