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Three Impossible Problems of Antiquity

Solve these three problems, within the constraints of Greek construction rules: use only an unmarked straightedge and a compass (preferably collapsible)...no measurement markings permitted on the straightedge.

Problem 1: Given an arbitrary angle, construct an angle one third as large.

Problem 2: Construct a square equal in area to the area of any given circle.

Problem 3: Given a cube, construct a cube that has twice the volume.


Source: Greece, circa 300 B.C.