Orthant spanning simplexes with minimal volume
| Autor: | Michele Elia |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2003 |
| Předmět: | |
| Zdroj: | International Journal of Mathematics and Mathematical Sciences, Vol 2003, Iss 63, Pp 3995-4006 (2003) |
| Druh dokumentu: | article |
| ISSN: | 0161-1712 1687-0425 01611712 |
| DOI: | 10.1155/S0161171203210401 |
| Popis: | 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. |
| Databáze: | Directory of Open Access Journals |
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