# ham sandwich theorem

Let ${A}_{1},\mathrm{\dots},{A}_{m}$ be measurable bounded^{} subsets of ${\mathbb{R}}^{m}$. Then there exists an $(m-1)$-dimensional hyperplane^{} which each ${A}_{i}$ into two subsets of equal measure.

This theorem has such a colorful because in the case $m=3$ it can be viewed as cutting a ham sandwich in half. For example, ${A}_{1}$ and ${A}_{3}$ could be two pieces of bread and ${A}_{2}$ a piece of ham. According to this theorem it is possible to make one to simultaneously all three objects exactly in half.

Title | ham sandwich theorem^{} |
---|---|

Canonical name | HamSandwichTheorem |

Date of creation | 2013-03-22 13:59:43 |

Last modified on | 2013-03-22 13:59:43 |

Owner | mathcam (2727) |

Last modified by | mathcam (2727) |

Numerical id | 6 |

Author | mathcam (2727) |

Entry type | Theorem |

Classification | msc 54C99 |

Related topic | BorsukUlamTheorem |