Abstract / résumé
Name / nom: Andrew James Critch
School / école: Memorial Unversity
Length / durée: 50 min
Title / titre: Two Balls for the Price of One: The Banach-Tarski Paradox
Abstract / résumé:
The following theorem due to Hausdorff, Banach, and Tarski begets an entire class of paradoxical results: Given any two bounded sets A and B in 3D space (R3), each having nonempty interior, one can partition A into finitely many disjoint parts and rearrange them by rigid motions to form B.
I will present a rigorous proof of this theorem which I believe to be more understandable than previous, similar proofs, by deconstructing a solid ball into 10 rigid pieces and reassembling them into two complete balls of the same volume. Time permitting, the proof will be examined in epistemic detail as a paradox, considering the axiom of choice among other less obvious intuitive leaps: a single additional intuitive condition makes the paradox apparently impossible!
Prerequisites / choses nécessaires: Not listed.
PDF format / format PDF: critch.pdf