paper

Minimal Banach-Tarski decompositions

arXiv:2507.17517 · doi:10.4064/fm250713-19-2

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 congruent copies of the original object, generalising a known result by Raphael Robinson.

22 pages. Online First version accepted for publication in Fundamenta Mathematicae

Minimal Banach-Tarski decompositions · wovepaper