A geometry problem is to find an (n−1)-dimensional simplex in
ℝn of minimal volume with vertices on the positive
coordinate axes, and constrained to pass through a given point
A in the first orthant. In this paper, it is shown that the
optimal simplex is identified by the only positive root of a
(2n−1)-degree polynomial pn(t). The roots of pn(t) cannot be expressed using radicals when the coordinates of A are
transcendental over ℚ, for 3≤n≤15, and
supposedly for every n. Furthermore, limited to dimension 3,
parametric representations are given to points A to which
correspond triangles of minimal area with integer vertex
coordinates and area.