International Conference on Mathematical Sciences, Bolu, Turkey, 23 - 27 November 2010, vol.1309, pp.213-218
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 homogeneous symmetric polynomials.