# Sierpiński gasket

Let ${S}_{0}$ be a triangular area, and define ${S}_{n+1}$ to be obtained from ${S}_{n}$ by replacing each triangular area in ${S}_{n}$ with three similar and similarly
oriented triangular areas each intersecting with each of the other two at exactly one vertex, each one half the linear scale of the original in size.
The limiting set as
$n\to \mathrm{\infty}$ (alternately the intersection^{} of all these sets) is a *S*ierpiński gasket, also known as a *S*ierpiński triangle^{}.

Title | Sierpiński gasket |
---|---|

Canonical name | SierpinskiGasket |

Date of creation | 2013-05-18 22:53:46 |

Last modified on | 2013-05-18 22:53:46 |

Owner | mathwizard (128) |

Last modified by | unlord (1) |

Numerical id | 41 |

Author | mathwizard (1) |

Entry type | Definition |

Classification | msc 28A80 |

Synonym | Sierpinski triangle |

Synonym | Sierpinski gasket |

Synonym | Sierpiński triangle |

Related topic | MengerSponge |