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Wallace–Bolyai–Gerwien theorem
Theorem on polygon dissections / From Wikipedia, the free encyclopedia
In geometry, the Wallace–Bolyai–Gerwien theorem,[1] named after William Wallace, Farkas Bolyai and P. Gerwien, is a theorem related to dissections of polygons. It answers the question when one polygon can be formed from another by cutting it into a finite number of pieces and recomposing these by translations and rotations. The Wallace–Bolyai–Gerwien theorem states that this can be done if and only if two polygons have the same area.
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Wallace had proven the same result already in 1807.
According to other sources, Bolyai and Gerwien had independently proved the theorem in 1833 and 1835, respectively.