Equidecomposability and discrepancy; a solution of Tarski's circle-squaring problem

  title={Equidecomposability and discrepancy; a solution of Tarski's circle-squaring problem},
  author={Mikl{\'o}s Laczkovich},
  journal={Journal f{\"u}r die reine und angewandte Mathematik (Crelles Journal)},
  pages={117 - 77}
  • M. Laczkovich
  • Published 1990
  • Mathematics
  • Journal für die reine und angewandte Mathematik (Crelles Journal)
Tarski's circle-squaring problem asks whether a disc is equidecomposable to a square; that is, whether a disc can be decomposed into finitely many parts which can be rearranged to obtain a partition of a square [16]. The problem was motivated by the well-known Banach-Tarski theorem stating that in /S* any two sets are equidecomposable provided that they are bounded and have non-empty interior. In particular, any ball is equidecomposable to any cube. On the other band, the existence of a Banach… 

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