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Descriptive Dynamics and Combinatorics听Seminar

听

Title:听circle squaring

Abstract:听We show that a closed disk and square with the same area are equidecomposible with听听pieces. A simple argument implies that the pieces are also听. Indeed the argument takes advantage of closure properties of the class of sets that are both听听and听. More generally, we show that if听听and听听have the same positive Lebesgue measure and small boundary, then they are equidecomposible with pieces that are countable unions of finite Boolean combinations of translates of听,听听and open sets. This is joint work with Narmada Varadarajan and Felix Weilacher.

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