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- W2000478469 abstract "The paradox of Banach, Tarski, and Hausdorff shows that any two bounded sets M,N subseteq E 3 with non-empty interior are equidecomposable. The result remains true if M and N are replaced by collections of sets. We present quantified versions of the paradox by giving estimates for the minimal number of pieces in such decompositions. The emphasis is on replications of sets M , i.e., on the equidecomposability of M with k copies of M , k ≥ 2 . In particular, we discuss the problem of replicating the cube." @default.
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- W2000478469 date "2001-01-01" @default.
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- W2000478469 title "Simple Paradoxical Replications of Sets" @default.
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- W2000478469 doi "https://doi.org/10.1007/s004540010077" @default.
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