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A. 755

Part of KoMaL A Problems 2019/2020

Problems(1)

Symmetric Polygon into a Square

Source: KöMaL A. 755

10/12/2019
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.)
combinatoricsgeometry