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 -