Doubling the Cube/Historical Note

Historical Note on Doubling the Cube
The exercise to construct a cube double the volume of a given cube, using a compass and straightedge construction, was an exercise that the ancient Greeks failed to succeed in.

This was one of three such problems: the other two being Squaring the Circle and Trisecting the Angle.

There are several techniques available that use other tools, but these were considered unacceptably vulgar to the followers of.

According to legend, Athens was being ravaged by a plague. The Oracle at Delphi instructed the people that a new altar to Apollo had to be built which was twice the size of the existing one, which was cubic in shape.

The word size was misunderstood, and the new altar had each of the linear dimensions doubled, whereas apparently they should have doubled its volume instead. Hence, unfortunately, the gods were not appeased, and the desired abatement of the plague did not happen.