An idealized chain or heavy rope, suspended from both ends in a uniform gravitational field, takes the shape of a curve known as the catenary. The English scientist, engineer, architect, and Renaissance man Robert Hooke (1635–1703) observed that an inverted catenary is the ideal shape for an arch made of rigid material: "Ut pendet continuum flexile, sic stabit contiguum rigidum inversum." The catenary has been used in architecture for arches, vaults, and domes that can hold their own weight without additional supports. But does Hooke's recipe really work? In this talk, we will put it to the test by demonstrating 3D-printed models of catenary arches and arches shaped according to other curves. Which one will prove to be the most stable? Along the way, we will look at examples of buildings that make use of the catenary, including works of the Catalan architect Antoni Gaudí (1852–1926) in Barcelona. Designing and 3D-printing the models raised many questions. How many parts should an arch consist of? Where should the pieces be cut? How can we make the (in)stability of the different arches easy to see? We looked for answers using mathematical and physical idealizations, together with a dose of common-sense reasoning. We believe that the catenary provides an excellent setting for hands-on teaching of mathematics. The topic can be adapted to students of different ages and levels of mathematical knowledge, while naturally connecting mathematics with physics, architecture, and the visual arts.