TY - JOUR

T1 - On the Steiner-Routh theorem for simplices

AU - Marko, František

AU - Litvinov, Semyon

PY - 2017/5/1

Y1 - 2017/5/1

N2 - 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.

AB - 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.

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U2 - 10.4169/amer.math.monthly.124.5.422

DO - 10.4169/amer.math.monthly.124.5.422

M3 - Article

AN - SCOPUS:85032624361

SN - 0002-9890

VL - 124

SP - 422

EP - 435

JO - American Mathematical Monthly

JF - American Mathematical Monthly

IS - 5

ER -