In this article the authors intend to present a very important topic of the geometry of space: the polyhedra. After having introduced their definition, their presence will be shown in nature, in everyday life and in art, starting from ancient Greece up to the present day. First of all, we will deal with regular polyhedra; subsequently we will introduce the important family, especially in the applications, of the Archimedean polyhedra. Finally, the interesting Goldberg polyhedra will be presented.

In this work we will deal with ellipses and ovals, comparing them both from the geometric point of view and from the one of applications. There is a notable similarity between these curves so often it’s not possible to recognize which of the two figures is, unless we consider other elements to distinguish them. We will show the presence of both curves in architectural works and in treatises, motivating their use, when it’s possible, with geometric and technological considerations.

Recently, several experimental tests devoted to quantitatively establish complementarity relations in quantum systems have been reported. Starting from the results of fully quantum single-particle self-nterference experiments, we critically review the concept of entanglement, arguing that this quantity is a peculiar trait of composite quantum systems, and thus it can be looked as a basic concept of quantum mechanics.