Doubling the cube given length times . In music theory, a natural analogue of doubling is the octave (a musical interval caused by doubling the frequency of a tone), and a natural analogue of a cube is three repetitions of the same interval. In this sense, the problem of doubling the cube is solved by the major third in equal temperament. This is a musical interval that is exactly one third of an octave. It multiplies the frequency of a tone by , the side length of the Delian cube. Doubling the cube Doubling the cube, also known as the Delian problem, is
Cube root or the other of the two complex cube roots of 1. For complex numbers, the principal cube root is usually defined as the cube root that has the greatest real part, or, equivalently, the cube root whose argument has the least absolute value. It is related to the principal value of the natural logarithm by the formula If we write "x" as where "r" is a non-negative real number and "θ" lies in the range then the principal complex cube root is This means that in polar coordinates, we are taking the cube root of the radius and dividing the