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Transforming polygons - Colegiul Național din Iași (Iași - Roumanie)

Titre du sujet: 
Transforming polygons
Let A and B be two polygons of the same area. Can A be cut into polygons which by rearrangement form the polygon B? In particular cases (eg A an equilateral triangle, B a square), what is the minimum number of polygons with the required property?
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Sujet | by Dr. Radut