Geométrie et nombres (pour une description de l'espace): l'héritage de l'antiquité

In the last years the (really never ended) debate about the use of proportionality systems in architecture and figurative arts has been developed. The discussion deals with both the philosophical link about number-geometry-harmony and the cosmological and talismanic meaning of the proportional rations used (sometimes, in an explicit way) in architecture, in analogy with the musical rations. In this paper we are going to examine some cases from different historic periods, focusing on the proportional systems which may be used, on possible common origin, and the motivations which led to different interpretations, going back as an example vedic, Pythagorean, platonic period. We observe that yet in different times, the basic problem deals with developing forms according to the principles of equivalence, invariance and similarity in different scales (“fractality” in modern terms). Moreover are present two appendices: one about vedic geometry and the other on fractal geometry.