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