On the Steiner-Routh theorem for simplices

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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 languageEnglish (US)
Pages (from-to)422-435
Number of pages14
JournalAmerican Mathematical Monthly
Issue number5
StatePublished - May 1 2017

All Science Journal Classification (ASJC) codes

  • General Mathematics


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