Form · Study 191

Catenary A hanging chain solves its own equation — a·cosh(x/a), no algebra required. The parabola everyone guesses runs close, and wrong. Invert the sag and you get Gaudí's arch: compression is tension, flipped.

Parameter a—

Sag s— px

Parabola gap Δmax— px

Chain − fit · rms— px

StateTENSION

In 1675 Robert Hooke hid the arch's secret in a Latin anagram — as hangs the flexible line, so, inverted, stands the rigid arch. Gaudí took it literally: he hung his churches upside-down in string and small bags of shot, and read the stone out of the sag. Hooke's solution, unscrambled ut pendet continuum flexile, sic stabit contiguum rigidum inversum

the chain — links & gravity

a·cosh(x/a) — the fit

same-anchor parabola — the guess

their disagreement

Tension

Index How it's made

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