On the Steiner–Routh Theorem for Simplices

DOI10.4169/amer.math.monthly.124.5.422zbMath1391.51024OpenAlexW2605964770MaRDI QIDQ4575262

František Marko, Semyon Litvinov

Publication date: 13 July 2018

Published in: The American Mathematical Monthly (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.4169/amer.math.monthly.124.5.422

Mathematics Subject Classification ID

(n)-dimensional polytopes (52B11) Length, area and volume in real or complex geometry (51M25)

Related Items (2)

Ceva's and Menelaus' theorems for higher-dimensional simplexes ⋮ Unnamed Item

Cites Work

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• Some new transversality properties
• Ceva, Menelaus, and selftransversality
• Routh's theorem for tetrahedra
• A Menelaus-Type Theorem for the Pentagram
• A generalization of the theorems of Menelaos and Ceva on $n$-dimensional figures
• Several properties of vertex hyperplanes of normal polyhedron
• On the orthocenter of normal polyhedron
• A Generalization of Ceva's Theorem
• Euler's Ratio-Sum Theorem and Generalizations
• A Generalization of Ceva's Theorem to Higher Dimensions
• Simultaneous Generalizations of the Theorems of Ceva and Menelaus
• A New Proof of Routh's Theorem
• Ceva, Menelaus, and the Area Principle
• Ceva's and Menelaus' Theorems and Their Converses via Centroids
• A Generalization of Routh’s Triangle Theorem
• The Volume Principle
• Theorems of Menelaos and Ceva for polygons in the spherical $n$-dimensional space
• A certain generalization of the theorems of Menelaos and Ceva

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