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Curves with increasing chords

Published online by Cambridge University Press:  24 October 2008

Günter Rote
Günter Rote
Affiliation:
Institut für Mathematik, Technische Universität Graz, Steirergasse 30, A-8010 Graz, Austria
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Abstract

A curve has increasing chords if AD ≥ BC for any four points A, B, C, D lying on the curve in that order. The length of such a curve that connects two points at distance 1 is at most 2π/Z in two dimensions, which is the optimal bound, and less than 30 in three dimensions.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 115 , Issue 1 , January 1994 , pp. 1 - 12
Copyright
Copyright © Cambridge Philosophical Society 1994

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References

REFERENCES

[1]Croft, H. T., Falconer, J. and Guy, R. K.. Unsolved Problems in Geometry (Springer-Verlag, 1991).CrossRefGoogle Scholar
[2]Larman, D. G. and McMullen, P.. Arcs with increasing chords. Proc. Cambridge Philos. Soc. 72 (1973), 205–207.CrossRefGoogle Scholar
[3]Rote, G. and Tichy, R. F.. The dispersion of point sequences and polygonal approximation of curves. Report 242, Institut für Mathematik, Technische Universität Graz (1992), submitted for publication.Google Scholar