Funicular curve

This duality was noticed by Robert Hooke in 1675 ("as hangs the flexible line, so, but inverted, will stand the rigid arch").

[2] If the hanging rope carries just its own weight (in this case it is usually called a "chain" and is equivalent to a free-standing arch with no external load), the resulting curve is a catenary.

[4] Both polygons were introduced by Pierre Varignon (Nouvelle Mecanique ou Statique, 1725) and became the basis of the graphic statics in the second half of the 19th century.

[5] Multiple ropes with weights can be connected together forming a hanging chain model of a complete structure.

The method can also be applied to arbitrary three-dimensional structures, as first shown by Gaudi while designing the church of Colònia Güell.