# cube of a number

The cube of a number $x$ is the third power (http://planetmath.org/GeneralAssociativity) $x^{3}$ of $x$.  Similarly one may speak of the cube of an element $x$ in any semigroup with the operation denoted multiplicatively (cf. general associativity).

The volume of a cube (i.e. regular (http://planetmath.org/RegularPolyhedron) hexahedron (http://planetmath.org/Hexahedron)) with $a$ is $a^{3}$; hence the name.

The cube function$x\mapsto x^{3}$  from $\mathbb{R}$ to $\mathbb{R}$ is injective, but not as a mapping from $\mathbb{C}$ to $\mathbb{C}$; one has  $x^{3}=y^{3}$  always when  $\frac{x}{y}=\frac{-1\pm i\sqrt{3}}{2}$,  the third root of unity.

 Title cube of a number Canonical name CubeOfANumber Date of creation 2013-03-22 15:07:13 Last modified on 2013-03-22 15:07:13 Owner pahio (2872) Last modified by pahio (2872) Numerical id 15 Author pahio (2872) Entry type Definition Classification msc 20-00 Synonym cube Synonym third power Related topic SquareOfANumber Related topic PowerFunction Related topic CubeRoot Related topic CubanPrime Related topic SemicubicalParabola Defines cube function