On Shortest Polygonal Approximations to a Curve

Karl Menger

A chapter in Selecta Mathematica, 2003, pp 81-86 from Springer

Abstract: 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.

Date: 2003
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DOI: 10.1007/978-3-7091-6045-9_12

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