Along the way, he also proved that any simple polygon in the plane can be decomposed into finitely many pieces and reassembled using translations only to form a square of equal area.
[2][3] It follows from a result of Wilson (2005) that it is possible to choose the pieces in such a way that they can be moved continuously while remaining disjoint to yield the square.
[4] A constructive solution was given by Łukasz Grabowski, András Máthé and Oleg Pikhurko in 2016 which worked everywhere except for a set of measure zero.
[5] More recently, Andrew Marks and Spencer Unger gave a completely constructive solution using about
[6] Lester Dubins, Morris W. Hirsch & Jack Karush proved it is impossible to dissect a circle and make a square using pieces that could be cut with an idealized pair of scissors (that is, having Jordan curve boundary).