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Symmetric Polygon into a Square

Source: KöMaL A. 755

October 12, 2019
combinatoricsgeometry

Problem Statement

Prove that every polygon that has a center of symmetry can be dissected into a square such that it is divided into finitely many polygonal pieces, and all the pieces can only be translated. (In other words, the original polygon can be divided into polygons A1,A2,…,AnA_1,A_2,\dotsc ,A_n, a square can be divided into polygons a B1,B2,…,BnB_1,B_2,\dotsc ,B_n such that for 1⩽i⩽n1\leqslant i\leqslant n polygon BiB_i is a translated copy of polygon AiA_i.)
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