Doubling the Cube

a celebrated mathematical problem. According to a Grecian legend, the problem originated in the following manner: The people of Delos were afflicted by a pestilence due to the darts of Apollo. On consulting the oracle of the god, they were directed to double the size of his altar, which happened to be a perfect cube. This they did, but the pestilence continued. Upon consulting the oracle again they were told that they must double the size of this altar without changing its shape. Hence the problem of finding a cube which shall have just twice the volume of a given cube is called the Delian problem. The difficulty of the problem lies in the fact that no number obtained by doubling a cube is itself a perfect cube. The perfect cubes are: 1, 8, 27, 64, 125, 216, 343, 512, 729, 1000, 1331, 1728 etc. Their doubles are 2, 16, 54, 128, 250, 432, 686, 1024, 1458, 2000, 2662, 3456, etc. We see readily that none of the doubles are perfect cubes. In order to produce a cube by multiplying a cube the multiplier must also be a cube. The multiplier 2 is not a cube; hence the impossibility of the problem.