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On Shortest Polygonal Approximations to a Curve

  • Karl Menger
Chapter
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Abstract

Let F be a set consisting of n points of a metric space. If \({{F}^{P}} = [{{p}_{1}},{{p}_{2}}, \ldots ,{{p}_{n}}]\) is a polygon (i.e., a finite ordered set) consisting of the points of F, we set \(1({{F}^{P}}) = \sum {{p}_{i}}{{p}_{{i + 1}}}\), where pipi+1 denotes the distance from pi to pi+1. The smallest of the n! numbers 1(FQ) formed for the n! permutations Q of the numbers 1, 2,…, n will be denoted by λ(F). Thus λ(F) is the length of the shortest polygon that can be inscribed into F.

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Copyright information

© Springer-Verlag Wien 2003

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  • Karl Menger

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