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A geometry problem is to find an (nÃ¢ÂˆÂ’1)-dimensional simplex in Ã¢Â„Ân 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 (2nÃ¢ÂˆÂ’1)-degree polynomial pn(t). The roots of pn(t) cannot be expressed using radicals when the coordinates of A are transcendental over Ã¢Â„Âš, for 3Ã¢Â‰Â¤nÃ¢Â‰Â¤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

Orthant spanning simplexes with minimal volume