Hanna Mularczyk, The Banach-Tarski Paradox, March 5, 2019
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Hanna Mularczyk Title: The Banach-Tarski Paradox
Tue, March 5, 6pm - 7pm, Science Center 507. Abstract: Ever thought volume preservation was a sham? Well, you might have been onto something. The Banach-Tarski paradox is a result in math that defies all geometric intuition: given a ball in three-space, there is a way to break it apart into finitely many (as few as five!) pieces and rearrange those pieces to create two balls identical to the first. You could try it at home with a baseball and a saw, but you'll probably be better off just coming to this Math Table. Together we'll use a mix of concepts from geometry, group theory, and set theory, including the Axiom of Choice, to piece together one of the most absurd theorems of all time. While the overarching argument of the proof should not be too hard to grasp for those with little math background, experience in some of these topics will be useful for details. |