POEMS in Newton's Aerodynamic Frustum

Autor/inn/en	Sampedro, Jaime Cruz; Tetlalmatzi-Montiel, Margarita
Titel	POEMS in Newton's Aerodynamic Frustum
Quelle	In: College Mathematics Journal, 41 (2010) 2, S.145-153 (9 Seiten)Infoseite zur Zeitschrift PDF als Volltext Verfügbarkeit
Sprache	englisch
Dokumenttyp	gedruckt; online; Zeitschriftenaufsatz
ISSN	0746-8342
Schlagwörter	Geometric Concepts; Geometry; College Mathematics; Mathematics Instruction + Suchen Sie Ihr Suchwort? Elementare Geometrie; Geometrie; Mathematics lessons; Mathematikunterricht
Abstract	The golden mean is often naively seen as a sign of optimal beauty but rarely does it arise as the solution of a true optimization problem. In this article we present such a problem, demonstrating a close relationship between the golden mean and a special case of Newton's aerodynamical problem for the frustum of a cone. Then, we exhibit a parallel relationship between the general case of this problem and a general family of means called POEM's (for "p"th Order Extreme Means). The POEM's share with the golden mean certain algebraic and geometric properties (established by Falbo), and also a remarkable minimizing physical property. Sadly, here is yet another situation in which an interesting property of the golden mean is "not" unique but is matched by the other means. (As Provided).
Anmerkungen	Mathematical Association of America. 1529 Eighteenth Street NW, Washington, DC 20036. Tel: 800-741-9415; Tel: 202-387-5200; Fax: 202-387-1208; e-mail: maahq@maa.org; Web site: http://www.maa.org/pubs/cmj.html
Erfasst von	ERIC (Education Resources Information Center), Washington, DC
Update	2017/4/10