Representation and Experimentation: A Digital Synthetic Approach

This paper describes the use of the synthetic method through digital generative algorithms in the study of geometry. In particular, this paper describes the construction of a ruled surface that rests on three skew lines in the method of mathematical representation. This study is part of a bigger picture that has as its goal the renewal of the study of geometry according to the synthetic method, in other words through the use of drawing in the virtual laboratory. The drawing in this sense is a logical tool to understand the geometry in space. The possibility of constructing algorithms to generate and control geometric shape allows having a greater control on both the final form and, above all, on the generative process of form itself. This is particularly important for those who have a synthetic approach in the study of geometry. It refers to the ability to view the entire creative process of the shape and the ability to alter some parameters to improve the result. The representation of the algorithms allows having both an overview and a detailed view of the entire creative process.