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http://dx.doi.org/10.4134/CKMS.c170041

VARIOUS CENTROIDS AND SOME CHARACTERIZATIONS OF CATENARY CURVES  

Bang, Shin-Ok (Department of Mathematics Chonnam National University)
Kim, Dong-Soo (Department of Mathematics Chonnam National University)
Yoon, Dae Won (Department of Mathematics Education and RINS Gyeongsang National University)
Publication Information
Communications of the Korean Mathematical Society / v.33, no.1, 2018 , pp. 237-245 More about this Journal
Abstract
For every interval [a, b], we denote by $({\bar{x}}_A,{\bar{y}}_A)$ and $({\bar{x}}_L,{\bar{y}}_L)$ the geometric centroid of the area under a catenary curve y = k cosh((x-c)/k) defined on this interval and the centroid of the curve itself, respectively. Then, it is well-known that ${\bar{x}}_L={\bar{x}}_A$ and ${\bar{y}}_L=2{\bar{y}}_A$. In this paper, we fix an end point, say 0, and we show that one of ${\bar{x}}_L={\bar{x}}_A$ and ${\bar{y}}_L=2{\bar{y}}_A$ for every interval with an end point 0 characterizes the family of catenaries among nonconstant $C^2$ functions.
Keywords
centroid; perimeter centroid; area; arc length; catenary;
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Times Cited By KSCI : 6  (Citation Analysis)
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