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

Abstract

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.Comment: 6 pages, 1 figure. The results and the proofs are elementary. Most of the proofs based on induction. However, it is interesting to see how the formulas line up, and can be generalized to higher levels one by on