The many frescoes showing the Last Supper of Jesus and the Apostles painted in Florence in the Renaissance have already been studied at length by art historians. However they have never been analyzed and investigated from the point of view of the relationship between art and perspective science, and the relationship between the shape of the room that they decorate and the shape of the space that they depict. Perspective science was being mathematically codified and put into written words by Piero della Francesca in the very days in which Domenico Ghirlandaio painted two frescoes in the convents of San Marco and Ognissanti. We can thus consider Ghirlandaio's paintings as being pioneering art works that mark a turning point in this artistic genre, and we will try to understand how and to what extent he mastered the trompe l'oeil effects that he produced.

The pentagon as a tool for fortresses’ drawingStarting from the fifteenth century, the diagram of many fortresses has a pentagonal shape. Among the best known fortresses, in Italy we find the Fortezza da Basso of Florence, the Cittadella of Parma, the Cittadella  of Turin,  Castel Sant’Angelo in Rome. The aim of this article is to analyze the reasons that link form and geometry to the planning of the design and the layout of pentagonal fortresses. The pentagon is a polygon tied to the golden section and to the Fibonacci sequence and it is possible to construct it starting from the golden triangle and its gnomon. This construction of the pentagon is already found in the book De Divina Proportione by Luca Pacioli and is particularly convenient for planning pentagonal fortresses. If one wants to draw the first approximated golden triangle, one can just consider the numbers of the Fibonacci sequence, for example 5 and 8, which establish the relationship between the sides: 5 units is the length of the base and 8 units the length of the equal sides. In the second isosceles triangle, which is the gnomon of the first, the base is 8 units long and equal sides are 5 units long; half of this isosceles triangle is the Pythagorean triangle (3, 4, 5). This characteristic of the golden triangles, that was already known by the Pythagoreans and, in a certain sense, contained in the symbol of their School, allows to build a pentagon with only the use of the ruler and the set square. The distinctive trait of the construction just described makes preferable to use the pentagon in the layout of the military architectures in the fieldworks. We have verified the relationship between numbers, shape and size in the layout of Castel Sant’Angelo (1555-1559) in which the approximate pentagon was the instrument for the generation of its form.

In 1938/39, the Accademia delle Belle Arti di Brera published the competition Camillo Boito entitled Project for a theatre to be used for performances of lyrical art. A group of students, G. Belloni, A. Fiocchi, A. Magnaghi-Delfino, M. Terzaghi, from the Regio Politecnico di Milano attended to the contest and won the first prize. The design of the theatre, which was meant to arise on a free area in a public garden, with a seating capacity of 3000, plus 200 on the stages, had as its motto Tremila 3000. All seats, as often happens in Italian theatres, had to be in conditions of visibility as uniform as possible. Bibliographic sources are limited to a single article published on Costruzioni Casabella signed by Giuseppe Pagano. The documentary and iconographic sources were found in the Historical Archive of the Accademia delle Belle Arti di Brera and at the CASVA (Centre for Advanced Studies on Visual Arts) in Milan. This work analyses the drawings for the identification of the basic module and the rational schemes used by the creators for the definition of the project presented in the competition. The research shows a rational use of the square module, learned during the years of apprenticeship at Terragni's Como studio, which will be the common denominator in most of the projects that will be carried out by the Magnaghi-Terzaghi studio, in particular in the Casa dei Nidi (House of the Nests) (1939) and in the BICA building (1955).

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