Bolyai Gerwien Theorem
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High Quality Content by WIKIPEDIA articles! In geometry, the Bolyai Gerwien theorem states that any two simple polygons of equal area are equidecomposable; i.e. one can cut the first into finitely many polygonal pieces and rearrange the pieces to obtain the second polygon. "Rearrangement" means that one may apply a translation and a rotation to every polygonal piece. Unlike the generalized solution to Tarski's circle-squaring problem, the axiom of choice is not required for the proof, and the decomposition and reassembly can actually be carried out "physically"; the pieces can, in theory, be cut with scissors from paper and reassembled by hand.…mehr

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High Quality Content by WIKIPEDIA articles! In geometry, the Bolyai Gerwien theorem states that any two simple polygons of equal area are equidecomposable; i.e. one can cut the first into finitely many polygonal pieces and rearrange the pieces to obtain the second polygon. "Rearrangement" means that one may apply a translation and a rotation to every polygonal piece. Unlike the generalized solution to Tarski's circle-squaring problem, the axiom of choice is not required for the proof, and the decomposition and reassembly can actually be carried out "physically"; the pieces can, in theory, be cut with scissors from paper and reassembled by hand.