Le superfici rigate e le superfici sviluppabili: una rilettura attraverso il laboratorio virtuale

The objective of this study is to reveal the properties of ruled surfaces and developable surfaces through Virtual laboratory and, overall, to be a contribution to the renewal of descriptive geometry. The basis of the research lies within the scientic foundations of drawing and of mathematical representation method. The study’s structure can be divided into two essential moments: - the historical recognition on ruled surfaces from the point of view of solid geometry and descriptive and projective geometry, going from the treaty of J.N. P. Hachette (1828) to the texts of G. Fiedler (1878), F. Aschieri (1888) and G. Fano (1925); - the rereading of theoretical propositions concerning this two type of surfaces, through a series of experiments carried out within the virtual laboratory of new descriptive geometry. A virtual laboratory can be de_ ned as a digital workshop, where it is possible to control directly in a three-dimensional space the problems of shapes’ generation that may be found in geometry and architecture. As a matter of fact, computer, besides its limits in modeling, has proved to be an essential tool for the display of some properties of ruled surfaces. Several theoretical concepts I have analyzed are only enunciated in literature, but were never represented. The reason is the complexity of these drawings that could only be realized with the rule and compasses at that time. I am referring to some properties explained by J. N. P. Hachette and G. Fano, but not only these. Hachette was a mathematician, as was Monge before him. Most of his thoughts on ruled surfaces are the result of analytical studies or geometrical intuitions; as a consequence, when the representation becomes too complex it is left to the readers’ imagination. In conclusion, the objective of this research is also to reveal through representation what was only enunciated with words on theoretical basis. In this respect, I believe that the greatest contribution of informatics revolution to the study of descriptive geometry is the consolidation of drawing as an instrument of the logic, in other words as a tool for discovery and verication of geometrical thoughts.