Communications of the Korean Mathematical Society (대한수학회논문집)

Korean Mathematical Society (대한수학회)
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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)
  • Received : 2017.02.11
  • Accepted : 2017.05.11
  • Published : 2018.01.31
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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.

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References

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