In 1837 Pierre Wantzel published a proof of the impossibility of trisecting an arbitrary angle or of doubling the volume of a cube, based on the impossibility of constructing cube roots of lengths [REF].
Then in 1882 Lindemann showed that \pi is a transcendental number, and thus that it is impossible by straightedge and compass to construct a square with the same area as a given circle [REF].