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CENTROIDS AND SOME CHARACTERIZATIONS OF CATENARIES
- Authors
- Kim, Dong-Soo; Moon, Hyung Tae; Yoon, Dae Won
- Issue Date
- 2017
- Publisher
- KOREAN MATHEMATICAL SOC
- Keywords
- centroid; perimeter centroid; area; arc length; catenary
- Citation
- COMMUNICATIONS OF THE KOREAN MATHEMATICAL SOCIETY, v.32, no.3, pp 709 - 714
- Pages
- 6
- Indexed
- SCOPUS
ESCI
KCI
- Journal Title
- COMMUNICATIONS OF THE KOREAN MATHEMATICAL SOCIETY
- Volume
- 32
- Number
- 3
- Start Page
- 709
- End Page
- 714
- 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 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 show that one of ($) over bar (L) = (x) over bar (A) and (y) over bar (L) = 2 (y) over bar (A) characterizes the family of catenaries among nonconstant C-2 functions. Furthermore, we show that among nonconstant and nonlinear C-2 functions, (y) over bar (L)/(x) over bar (L) = 2 (y) over bar (A)/(x) over bar (A) is also a characteristic property of catenaries.
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