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 Pełczynski 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.
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Research supported by a grant from a cooperation between the Deutsche Forschungsgemeinschaft in Germany and the National Research Foundation in South Africa. Parts of this paper were written during a visit to the Department of Mathematics, Applied Mathematics and Astronomy of the University of South Africa.
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Martini, H., Swanepoel, K. Equiframed Curves – A Generalization of Radon Curves. Monatsh. Math. 141, 301–314 (2004). https://doi.org/10.1007/s00605-003-0052-3
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DOI: https://doi.org/10.1007/s00605-003-0052-3