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ERIC Number: EJ877237
Record Type: Journal
Publication Date: 2010-Mar
Pages: 9
Abstractor: As Provided
Reference Count: 0
ISBN: N/A
ISSN: ISSN-0746-8342
POEMS in Newton's Aerodynamic Frustum
Sampedro, Jaime Cruz; Tetlalmatzi-Montiel, Margarita
College Mathematics Journal, v41 n2 p145-153 Mar 2010
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.
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
Publication Type: Journal Articles; Reports - Descriptive
Education Level: Higher Education
Audience: N/A
Language: English
Sponsor: N/A
Authoring Institution: N/A