Duplication of the cube-one of the fundamental problems of Greek geometry, together with squaring the circle and trisecting the angle. It asks whether, given a cube of a certain size, it is possible to construct a cube of double the original size, using only a compass and a straightedge. Although the Greeks came up with several ingenious methods for doubling the cube, they were never able to do so without resorting to additional instruments. It is, in fact, impossible to double the cube with only a compass and a straightedge, but a proof of this fact did not come until more than two thousand years after the problem was first posed.

There are several different stories about the origin of the cube-doubling problem. One story, mythological in origin, says that King Minos of Crete ordered a tomb built for his son Glaucus...