The ruled surfaces in stone architecture

The stereotomic architecture is composed of ashlars made off-site and laid dry. The choice of the masonry depends on the geometrical, structural, aesthetic aspects and the mechanical properties of the material used. The fragility of the stone prevents the production of thin and sharp angles, which might break. Therefore, the angles formed by planes tangent to adjacent surfaces should tend, if possible, to a right angle. The search for the perpendicularity between the surfaces of the ashlars has brought, in stereotomy, to the widespread use of ruled surfaces (better if developable), used as a facing surfaces, but even more as junction surfaces. The choice of such surfaces is due to the fact that they could be reproduced accurately in the workshop of the stone-cutter through the movement of an auction. Although the story of the stereotomy evidences a recurring use of ruled surfaces, it is with the school of Monge that studies on these surfaces start taking shape. Among the applications of the students of Mezière some cases, brilliantly solved thanks to the properties of these surfaces, stand out. Re-examining now part of this repertoire and transposing it into a digital environment has a dual purpose: to study and represent through the methods of mathematical representation some properties inquired to date only from the point of view of mathematical analysis; to propose, with the digital tools of design and material processing, building systems that are still highly topical.