In
physics and
geometry, a
catenary[p] is the
curve that an idealized hanging
chain or
cable assumes under its own
weight when supported only at its ends. The curve has a U-like shape, superficially similar in appearance to a
parabola, but it is not a parabola: it is a (scaled, rotated)
graph of the
hyperbolic cosine. The curve appears in the design of certain types of
arches and as a cross section of the
catenoid—the shape assumed by a soap film bounded by two parallel circular rings.