Since Antiquity, and initially in ancient Greece, solutions have been sought for the following three problems, using only compass and straightedge: (1) the squaring of the circle: construct a square equal in area to a circle; (2) the duplication of the cube: given a cube, construct the edge of a second cube whose volume is double that of the first; (3) the trisection of an angle: divide an arbitrary angle into three equal angles.