SEZIONE-AUREA: alcune proprietà geometriche e numeriche con applicazioni al design artistico-architettonico

In this paper a short history of the Golden Section is described, that began from the geometric studies of the Pythagoreans on the property of the pentagon and assumed importance in order to obtain graphical solutions of algebraic equations and construction of some regular polygons and of the five solid platonic ones. The geometric studies of Piero della Francesca on XV century and the publication of Divina Proportione by L. Pacioli marked in the Early Renaissance the beginning of a new interest in the artistic-architectural theories towards the Golden Section. Some numerical properties of the Golden Section were studied with a new interest in XIX century from the mathematicians , and some relationships with Fibonacci numbers were found. In these last two centuries the Golden Section has been applied in several situations in art and architecture to obtain aesthetically pleasant proportions. Some applications in the artistic and architectural fields are shown.