Routh's theorem for simplices (original) (raw)
2014, arXiv (Cornell University)
It is shown in [28] that, using only tools of elementary geometry, the classical Routh's theorem for triangles can be fully extended to tetrahedra. In this article we first give another proof of Routh's theorem for tetrahedra where methods of elementary geometry are combined with the inclusionexclusion 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. 2010 Mathematics Subject Classification. 97G30. Key words and phrases. Routh's theorem, inclusion-exclusion principle, tetrahedra, (n − 1)−dimensional simplices. 1 The authors would like to thank Mark B. Villarino of the University of Costa Rica for bringing this reference to their attention.
Loading Preview
Sorry, preview is currently unavailable. You can download the paper by clicking the button above.