Its equation is given by a hyperbolic cosine function and when inverted, this curve is the ideal shape of an arch, as there is almost no shear stress between the individual stones of the arch.
This is a roulette traced out by the focus of a parabola rolled along a straight line. The surface formed by rotating this curve around the x-axis is a minimal surface, and can be formed by dipping two circles into a bubble solution and drawing them apart slowly. Its equation is given by a hyperbolic cosine function and when inverted, this curve is the ideal shape of an arch, as there is almost no shear stress between the individual stones of the arch. The Gateway Arch is built in the shape of an inverted one of these with both ends hung at the same height. For 10 points, name this curve formed when a piece of rope is hung freely from two points, pulled down by nothing but its own weight.
This is a roulette traced out by the focus of a parabola rolled along a straight line.
{catenary} curve (prompt on “{catenoid}”)