Michele Elia, "Orthant spanning simplexes with minimal volume", International Journal of Mathematics and Mathematical Sciences, vol. 2003, Article ID 585294, 12 pages, 2003. https://doi.org/10.1155/S0161171203210401
Orthant spanning simplexes with minimal volume
A geometry problem is to find an -dimensional simplex in of minimal volume with vertices on the positive coordinate axes, and constrained to pass through a given point in the first orthant. In this paper, it is shown that the optimal simplex is identified by the only positive root of a -degree polynomial . The roots of cannot be expressed using radicals when the coordinates of are transcendental over , for , and supposedly for every . Furthermore, limited to dimension , parametric representations are given to points to which correspond triangles of minimal area with integer vertex coordinates and area.
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