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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
Published by: Mathematical Association of America
Stable URL: http://www.jstor.org/stable/10.4169/amer.math.monthly.121.02.109
Page Count: 11
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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.
Copyright the Mathematical Association of America 2014