English

Minimal Banach-Tarski Decompositions

Logic 2025-07-24 v1 Group Theory

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

Cite

@article{arxiv.2507.17517,
  title  = {Minimal Banach-Tarski Decompositions},
  author = {Cesare Straffelini and Kilian Zambanini},
  journal= {arXiv preprint arXiv:2507.17517},
  year   = {2025}
}

Comments

18 pages

R2 v1 2026-07-01T04:15:17.506Z