It is shown in  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)|
|Number of pages||14|
|Journal||American Mathematical Monthly|
|State||Published - May 1 2017|
All Science Journal Classification (ASJC) codes