Geometry and construction. Theory of principal curvature lines in stone stereotomy

Abstract

The paper illustrates the theoretical and practical study of the theory of curvature lines elaborated by Gaspard Monge at the end of the eighteenth century, and its application to the construction of cut stone architecture, with particular reference to the specific case study of an ellipsoidal vault (proposed by Monge and revisited by Hachette and Leroy). The intent is to optimize the construction of these lines in the method of the mathematical representation, at least for the case study. The link that exists between the theories of descriptive geometry and the stereotomic design principles is significant. Theoretical geometric constructions, seemingly abstract, are applied in the practice of construction and become, at times, a prerequisite to solving complex cases such as that presented.

Keywords

• principal curvature lines
• confocal quadrics
• focal curves
• Dupin’s theorem
• ellipsoidal vault
• stereotomy