Pizza with the Q-Club: Shelley Kandola presenting

Join the Department of Mathematics, Computer Science, and Statistics for pizza and snacks at our biweekly Q-Club meeting this Friday.  Shelley Kandola ('13) will be speaking on research she conducted with Dr. V.  

Abstract: In 1924, Banach and Tarski demonstrated that two arbitrary point sets with nonempty interior in Euclidean n-space for n >= 1 are equivalent to each other using a countable decomposition. It is also well known that it is impossible to replicate the Banach-Tarski paradox (i.e. using finitely many subsets) for R using rigid motions. In this poster, we propose a free group similar to the one used in proving the Banach-Tarski paradox whose generators are not rigid motions, but piecewise isometires based on infinite permutation cycles. Using the free group on these generators, we are able to partition the real number line into a disjoint union of subsets that can be transformed via these maps and then reassembled into two identical copies of the original line. The result is a paradoxical finite decomposition of the real number line.