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Bolyai-Gerwien Theorem

Definition

Two polygons are congruent by dissection iff they have the same area. In particular, any polygon is congruent by dissection to a square of the same area. Laczkovich also proved that a circle is congruent by dissection to a square (furthermore, the dissection can be accomplished using translations only).

Related term

dissection

Associated person

János Bolyai

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