Volumes of n-simplices with vertices on a polynomial space curve

Details Volumes of n-simplices with vertices on a polynomial space curve Volumes of n-simplices with vertices on a polynomial space curve

2009-11-20

arxiv.org/abs/0911.4117v1

Mathematics

Combinatorics

6 pages, 1 figure. The results and the proofs are elementary. Most of the proofs based on induction. However, it is interestin

Scientific paper

In this paper, we give a formula for the area of the triangle formed by the
vertices that live on a given polynomial, and we generalize this formula to the
volumes of $n$-simplices with vertices on a polynomial space curve. To prove
these results, we use induction arguments and a well known identity for
complete symmetric polynomials.

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