International Journal of Mathematics and Mathematical Sciences

International Journal of Mathematics and Mathematical Sciences / 2003 / Article

Open Access

Volume 2003 |Article ID 585294 | https://doi.org/10.1155/S0161171203210401

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

Received23 Oct 2002

Abstract

A geometry problem is to find an (n1)-dimensional simplex in n 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 (2n1)-degree polynomial pn(t). The roots of pn(t) cannot be expressed using radicals when the coordinates of A are transcendental over , for 3n15, 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.

Copyright © 2003 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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