Italian version

It isn't easy to find arguments on mathematics, art and architecture for didactic use that are well integrated with exhaustive historical and biographical notes and images and reproductions wisely chosen. This is the case with the CD-ROM "Piero Matematico", which is pleasant to navigate and rich in content. The authors are teachers of mathematics (Daniela Gentilin) and art (Ennio Gettanello).

The argument is divided into six parts:

1) mathematics at the threshold of the Renaissance;
2) the life, paintings and writings of Piero della Francesca;
3) a study of the Madonna del Parto;
4) De quinque corporibus regularibus;
5) the Trattato d'abaco and the equations solved by Piero;
6) a study of vaults.

These parts are not separate, but, as good navigation requires, are intimately related to each other.

Initially the reader, or navigator, is reminded of the characteristics of the 'universal man', the artist of the Renaissance in whom knowledge of art, science and technology are brilliantly combined. In this context, with succinct but very meaningful biographic notes, are analyzed Brunelleschi, Alberti, Piero, Durer and Leonardo. Each is brought to life and highlighed with images, their fundamental works, their relationship to other artists and with the mathematicians of the age (for example, with Fra Luca Pacioli for whom the CD contains an interesting table), their knowledge of mathematics and its consequent applications in their artistic activities.

The mathematic notions enucleated are placed into their historic context and expanded upon with references to both past and to future studies. Thus is made clear the influence of Archimedes, Plato, Pythagoras, Euclid, the greatest of medieval mathematicians, Luca Pisano, called Fibonacci, as well as the later studies of Cardano, Tartaglia, Euler and the Bernoulli family.

Specifically in the case of Piero, the Madonna del Parto is analyzed. The entire composition can be inserted into a regular dodecahedron, a fact that is not coincidental in light of Piero's thorough knowledge of the regular polyhedra. In fact, Piero della Francesca was the author of Libellus de quinque corporibus regolaribus, a work that is studied in the CD, bringing to light Piero's recuperation of the Platonic/Pythagorean tradition and the continual references to Euclid and Archimedes (particularly to Archimedes's semi-regular polyhedra). It is highlighted and documented that other examples of the use of the regular dodecahedron in painting and in art in general can be found in the works of Paolo Uccello, Leonardo, Durer and, more recently, Dali, Escher and Saffaro.

The analysis of the Trattato d'abaco, among the writings of Piero, brings our attention to a consideration of the reason for the birth of the abacus schools in the great commercial centers of Italy and Europe and the methods of calculating of Leonardo Pisano (the turn out to be particularly advantageous for the new requirements). An interesting historic table completes the discussion of the history of the abacus.

Finally in the last part of the CD is reconstructed a history of vaults, starting with the pseudo-cupola vaults of prehistoric mediterranean and asian cultures, analyzing the various successive types of vaults (barrel, hemispherical, sail, groin, etc.) up to the most recent ones of Luigi Nervi. The calculation of Piero for the volume of a solid with a pavilion vault is reproduced.

The material contained in the CD is very interesting, never banal, taken from granted or superficial. The work merits an ample diffusion among teachers and students at the high school level and the first years of architecture at the university level, as well as among those who are interested in history, art, architecture and mathematics.

RELATED SITES ON THE WWW
Webmuseum: Piero della Francesca
Piero della Francesca's Tetrahedron Formula
George Hart: Piero della Francesca's Polyhedra
Mark Peterson: The Geometry of Piero della Francesca
The Life of Piero della Francesca
A page from Libellus de Quinque Corporibus Regularibus

ABOUT THE AUTHOR
Orietta Pedemonte, Associate Professor, teaches mathematics in the Faculty of Architecture of the University of Genoa and at the Scuola di Specializzazione in Restauro dei Monumenti (School for Specialization in Restoration of Monuments). Her past research interests were tied to functional analysis, while presently her research is in a) the relationships between mathematics, art and architecture in their historical development; b) mathematical methods in urban design and geographical information systems. She is also in didactic and educational research. She is a member of the Italian Commission of UNESCO.