Hanging chain (catenary)
Realizes: hyperbolic cosine / thrust line
A chain suspended from two fixed points and left to hang under gravity settles into a curve that exactly realizes the hyperbolic cosine. Gaudí used physical catenaries (inverted) to design the arches of the Sagrada Família. Speed: instantaneous (static equilibrium). Capacity: single function evaluation (hyperbolic cosine).
Examples
Gaudi: Flipping Catenaries
How Gaudí used inverted hanging chains to find the optimal thrust line for arches, then mirrored the result to design the Colònia Güell chapel
MINIMIZE
instantaneous
single-op
J
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Gaudí's Hanging Chain Models — dataphys.org
Historical overview of Gaudí's polyfunicular models using weighted strings for the Colònia Güell church
MINIMIZE
instantaneous
single-op
J