# 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 $\u2102$ to $\u2102$; 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 |