### Abstract

It is shown in [28] that, using only tools of elementary geometry, the classical Steiner-Routh theorem for triangles can be fully extended to tetrahedra. In this article, we first give another proof of the Steiner-Routh theorem for tetrahedra, where methods of elementary geometry are combined with the inclusion-exclusion principle. Then we generalize this approach to (n - 1)-dimensional simplices. A comparison with the formula obtained using vector analysis yields an interesting algebraic identity.

Original language | English (US) |
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Pages (from-to) | 422-435 |

Number of pages | 14 |

Journal | American Mathematical Monthly |

Volume | 124 |

Issue number | 5 |

DOIs | |

Publication status | Published - May 1 2017 |

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### All Science Journal Classification (ASJC) codes

- Mathematics(all)