Question

What is the difference between a catenary arch and a parabolic arch?

Answer

The catenary is a curve formed by a perfectly flexible free-hanging cable suspended from its endpoints. When inverted and constructed of solid materials, this form becomes an arch that is very efficient at supporting its weight. This form was used by Gaudi in the crypt of the Church of Colonia Guell. The weight-per-horizontal-unit varies along the cable or arch.

A parabolic arch is in the form of a parabola. This is the form taken by a flexible cable supporting uniformly spaced loads as would be the case in a suspension bridge.