This text is a reflection that, with the benefit of practical examples, proposes to reason on the relationship between an idea and its representation, between a sketch, analogical and digital models, and on the “mental” tools which manage this relationship. It is furthermore a reflection on the theoretical and practical implica- tions of the concept of fold, or better, on the act of folding, as a concrete and tangible capture of the infinitesimal that directs a tectonic possibility. To do this, to try and control the infinitesimal as a measure that gives structure to contemporary design, both at the architectural and the urban scale, a delving into mathematics as the algorithm that manages the machine, was necessary. This publication is based on the doctoral dissertation in Urban and Architectural Design presented at the Politecnico of Milan and on the research and teaching activities developed by the author in that school and, subsequently, at the University of Cape Town.

Matteo Fraschini is a senior lecturer at the School of Architecture Planning and Geomatics of the University of Cape Town where he teaches in the Masters of Urban Design and of Architecture. His teaching and research activity is centred on architectural and urban design methods in relationship with the different scales of the contemporary city.