Problem 1124

Can a square and a circle of the same area be decomposed into a finite number of congruent parts?

Status

SolvedProved

An accepted solution exists. The statement is true.

Proved: the site credits Laczkovich's 1990 theorem, which gives the decomposition with translations alone; see the claim page (Laczkovich, 1990).

Er81b: Erdős, P., My Scottish Book 'Problems'. The Scottish Book (1981), 27-35 (page numbers are given for the 2nd edition of The Scottish Book).
La90b: Laczkovich, M., Equidecomposability and discrepancy; a solution of Tarski's circle-squaring problem. J. Reine Angew. Math. (1990), 77-117.
MaUn17: Marks, A. and Unger, S., Borel circle squaring. Ann. of Math. (2) 186 (2017), no. 2, 581-605; arXiv:1612.05833.
GMP17: Grabowski, Ł., Máthé, A. and Pikhurko, O., Measurable circle squaring. Ann. of Math. (2) 185 (2017), no. 2, 671-710; arXiv:1501.06122.