Lettura matematica delle ornamentazioni di un prospetto architettonico. The decoration of a façade: a mathematical interpretation.

One of the most interesting examples where art and mathematics have a close relation is certainly that of the ornamentation of flat surfaces. The construction of a "symmetric" ornamentation is linked to the creation of an "elementary" figure, represented in different postures by rotating, reflecting and translating it to then merge the results in a harmonic unity. The mathematical base in this operation relies on the theory of symmetry groups. The old "masons" of the Alhambra had already solved the problem, yet only empirically. They knew, even if they didn't know, on the basis of the fact that laws of mathematics are so natural that they become unavoidable even centuries before its formalization. Here we analyze the structure of some significant wall ornamentations of a direct entrance portal in the "Aljama Mosque" in Cordoba in the light of the symmetry group's theory.