4: How did they do it?
The builders of Gothic vaults left few clues (written or pictorial) about their actual construction methods. John Fitchen employs induction as well as the skills of a detective to figure out how the vaults were designed and built. Nevertheless, he fails the inquisitive reader at one critical point.Fitchen states that the stone ribs supporting the Gothic vaults conform to a curve called, in mathematics, a catenary. The mathematics of catenary curves was first described by Robert Hooke in the late 1600s. This was no less than 150 years *after* the Gothic builders completed their last work. In the absence of a knowledge of the mathematics of catenaries, how did the Gothic builders discover the *only* rib curvature that was self-supporting? (It's not good enough to say the Gothic builders arrived at the correct catenary curve empirically, that is, by trial and error. There was simply no room for error. All would have come tumbling down.) How did they do it?
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