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Self-approaching curves

Published online by Cambridge University Press:  01 January 1999

CHRISTIAN ICKING ,
ROLF KLEIN  and
ELMAR LANGETEPE
CHRISTIAN ICKING
Affiliation:
FernUniversität Hagen, Praktische Informatik VI, D-58084 Hagen, Germany
ROLF KLEIN
Affiliation:
FernUniversität Hagen, Praktische Informatik VI, D-58084 Hagen, Germany
ELMAR LANGETEPE
Affiliation:
FernUniversität Hagen, Praktische Informatik VI, D-58084 Hagen, Germany
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Abstract

We present a new class of curves which are self-approaching in the following sense. For any three consecutive points a, b, c on the curve the point b is closer to c than a to c. This is a generalisation of curves with increasing chords which are self- approaching in both directions. We show a tight upper bound of 5·3331… for the length of a self-approaching curve over the distance between its endpoints.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 125 , Issue 3 , January 1999 , pp. 441 - 453
Copyright
Cambridge Philosophical Society 1999

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Footnotes

This work was partially supported by the Deutsche Forschungsgemeinschaft, grant Kl 655/8-2.