12:00 pm Friday, July 8, 2005
Sophex: Equidecomposable Sets and the Banach-Tarski Paradox by Alex Pekker in RLM 11.176
The notion of "sameness" pervades all areas of mathematics: homeomorphic surfaces in topology and isomorphic groups in algebra just being two examples. In this talk we will define equidecomposability, which is another notion of sameness, and show that certain sets that are the same in the usual sense are very different in this sense. We will conclude with the Banach-Tarski Theorem that shows that we can "cut" any ONE solid ball into five pieces, apply certain rigid motions to them (basically rotate them), and put them together to get TWO solid balls of exactly the same size as the original! Submitted by
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