Resumen de A Property Characterizing the Catenary

Edward Parker

• 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 area in the same sense. We also show from this property that the centroid of the area under an interval of a catenary is the midpoint of the segment connecting the centroid of the catenary and the x-axis.