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
Nth root Any expression containing a radical, whether it is a square root, a cube root, or a higher root, is called a "radical expression", and if it contains no transcendental functions or transcendental numbers it is called an algebraic expression. In calculus, roots are treated as special cases of exponentiation, where the exponent is a fraction: Roots are particularly important in the theory of infinite series; the root test determines the radius of convergence of a power series. Roots can also be defined for complex numbers, and the complex roots of 1 (the roots of unity) play an important role in