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 $ℝ$ to $ℝ$ is injective, but not as a mapping from $ℂ$ to $ℂ$; 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