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arXiv · 2507.17517

Minimal Banach-Tarski decompositions

Cesare Straffelini·Kilian Zambanini
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Abstract

We investigate the problem of finding the minimum number of pieces necessary for dividing a three-dimensional sphere or a ball and reassembling it to form $n$ congruent copies of the original object, generalising a known result by Raphael Robinson.

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Cesare Straffelini, Kilian Zambanini. 2025-07-23. Minimal Banach-Tarski decompositions. https://doi.org/10.4064/fm250713-19-2

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