For 10 points, name this curve given by the hyperbolic cosine function, the shape of a hanging chain.
The German mathematician Jungius made necessary the existence of this curve by disproving a common assumption. A road that contains "bumps" in the shape of this curve will allow a square wheel to roll smoothly.  Though it's not a line, the ratio of the area underneath this curve to its length is constant over any horizontal interval. Besides the plane, the surface of revolution of this curve is the only such surface with zero mean curvature.   Robert Hooke was the first to advocate the use of these curves in the construction of arches because of their self-supporting nature. This curve can by drawn by the focus of a parabola rolling along a straight line.  For 10 points, name this curve given by the hyperbolic cosine function, the shape of a hanging chain.
The German mathematician Jungius made necessary the existence of this curve by disproving a common assumption.
catenary [accept hyperbolic cosine before mentioned, I guess]