«The curved line belongs to God»: the use of ruled surfaces in the architecture of Antoni Gaudí

We introduce the concept of ruled surface and we describe some examples (namely the one-sheeted hyperboloid, the hyperbolic paraboloid, the helicoid and the conoid), illustrating their main technical features. Then, we explain how, where and why (both from the technical and the symbolic point of view) Antoni Gaudí uses such surfaces to get his peculiar architecture, pervaded by curved shapes, which on one hand is the heir of the gothic and traditional Catalan architecture and, on the other hand, anticipates the flavour of the modern topological one. A quick glimpse at the latter concludes the paper.