A Property Characterizing the Catenary

@article{Parker2010APC,
  title={A Property Characterizing the Catenary},
  author={Edward Parker},
  journal={Mathematics Magazine},
  year={2010},
  volume={83},
  pages={63 - 64}
}
Summary We show that the area under a catenary curve is proportional to its length in the following sense: given a catenary curve, we can take any horizontal interval and examine the ratio of the area under the curve to the length of the curve on that interval, and we find that the resulting ratio is independent of the chosen interval. This property extends to the three-dimensional case as well: the volume contained by a horizontal interval of a catenoid surface is proportional to its surface… Expand
6 Citations
VARIOUS CENTROIDS AND SOME CHARACTERIZATIONS OF CATENARIES
Two Generalizations of a Property of the Catenary
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A Characteristic Averaging Property of the Catenary
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Hanging Around in Non-Uniform Fields
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Various centroids and some characterizations of catenary rotation hypersurfaces
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