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ERIC Number: EJ877237
Record Type: Journal
Publication Date: 2010-Mar
Pages: 9
Abstractor: As Provided
Reference Count: 0
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.
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Publication Type: Journal Articles; Reports - Descriptive
Education Level: Higher Education
Audience: N/A
Language: English
Sponsor: N/A
Authoring Institution: N/A