This research analyses the geometric modifications and improvements that the application of the technique of metallurgy meant for architecture. In the early days of engineering and without having the historical burden that architecture bore, the small variations in the classical definition of geometry meant the greatest advances at a structural and conceptual level in the world of metal structures. The use of metal as a structural element capable of containing new uses and responding to the great challenges that progress required was definitive for the development of the new architecture and paradigms of the new century. The new metallic materials and their mathematical and constructive models were the cause and effect of what would be the basis of the great change in modern architecture and engineering and would lay the foundations of today’s world. The interaction of these two new disciplines, architecture and engineering, and their relationship with metal is the basis of this research, which aims to find out where, when, and how these geometric changes took place that started to change the conception of metal structures.