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Two Generalizations of a Property of the Catenary

Vincent Coll and Mike Harrison
The American Mathematical Monthly
Vol. 121, No. 2 (February 2014), pp. 109-119
DOI: 10.4169/amer.math.monthly.121.02.109
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Page Count: 11
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Two Generalizations of a Property of the Catenary
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Abstract A well-known property of the catenary curve is that the ratio of the area under the curve to the arc length of the curve is independent of the interval over which these quantities are concurrently measured. We develop two higher-dimensional generalizations of this invariant ratio, and find that each invariant ratio identifies a class of hypersurfaces connected to classical objects from differential geometry.

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