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Equichordal curves

Published online by Cambridge University Press:  14 November 2011

F.J.Craveiro de Carvalho  and
S.A. Robertson
F.J.Craveiro de Carvalho
Affiliation:
Departamento de Matemática, Universidade de Coimbra, 3000 Coimbra, Portugal
S.A. Robertson
Affiliation:
Faculty of Mathematical Studies, Southampton University, Southampton SO9 5NH, U.K.
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Synopsis

In this paper we extend the notion of equichordal curve to closed simple curves in ℝn. Although it is not known if an equichordal curve can have more than one fulcrum, we show that, for plane curves, any fulcrum is inside the curve. We establish connections with the theories of transnormal and self-parallel curves and lower bounds for the length and chordal area are obtained. Such bounds are the best possible.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 110 , Issue 1-2 , 1988 , pp. 85 - 91
Copyright
Copyright © Royal Society of Edinburgh 1988

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