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VARIOUS CENTROIDS AND SOME CHARACTERIZATIONS OF CATENARY CURVES
- Authors
- Bang, Shin-Ok; Kim, Dong-Soo; Yoon, Dae Won
- Issue Date
- 2018
- Publisher
- KOREAN MATHEMATICAL SOC
- Keywords
- centroid; perimeter centroid; area; arc length; catenary
- Citation
- COMMUNICATIONS OF THE KOREAN MATHEMATICAL SOCIETY, v.33, no.1, pp 237 - 245
- Pages
- 9
- Indexed
- SCOPUS
ESCI
KCI
- Journal Title
- COMMUNICATIONS OF THE KOREAN MATHEMATICAL SOCIETY
- Volume
- 33
- Number
- 1
- Start Page
- 237
- End Page
- 245
- ISSN
- 1225-1763
2234-3024
- Abstract
- For every interval [a, b], we denote by ((x) over bar (A), (y) over bar (A)) and ((x) over bar (L), (y) over bar (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 (x) over bar (L) - (x) over bar (A) and (y) over bar (L) = 2 (y) over bar (A). In this paper, we fix an end point, say 0, and we show that one of (x) over bar (L) = (x) over bar (A) and (y) over bar (L) = 2 (y) over bar (A) for every interval with an end point 0 characterizes the family of catenaries among nonconstant C-2 functions.
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