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Equiframed curves - a generalization of Radon curves

Martini, Horst and Swanepoel, Konrad (2004) Equiframed curves - a generalization of Radon curves. Monatshefte fur Mathematik, 141 (4). pp. 301-314. ISSN 0026-9255

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Abstract

Equiframed curves are centrally symmetric convex closed planar curves that are touched at each of their points by some circumscribed parallelogram of smallest area. These curves and their higher-dimensional analogues were introduced by Peczynski and Szarek (1991, Math Proc Cambridge Philos Soc 109: 125–148). Radon curves form a proper subclass of this class of curves. Our main result is a construction of an arbitrary equiframed curve by appropriately modifying a Radon curve. We give characterizations of each type of curve to highlight the subtle difference between equiframed and Radon curves and show that, in some sense, equiframed curves behave dually to Radon curves.

Item Type: Article
Official URL: http://www.springerlink.com/content/103082/
Additional Information: © 2004 Springer
Library of Congress subject classification: Q Science > QA Mathematics
Sets: Departments > Mathematics
Rights: http://www.lse.ac.uk/library/usingTheLibrary/academicSupport/OA/depositYourResearch.aspx
Funders: Deutsche Forschungsgemeinschaft, National Research Foundation in South Africa
Date Deposited: 16 Oct 2009 09:40
URL: http://eprints.lse.ac.uk/25458/

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