Mathematical Aspects of Leonardo’s Production in Milan

Leonardo da Vinci is traditionally considered as one of the most notable guests in Milan, of all times. The opportunity to consider this important protagonist of the Renaissance, artist and scientist at the same time, leads us to analyze more closely the period he spent in Milan at the Sforza Court. Particularly we refer to the works carried out by him in this context: he worked as painter and engineer of the Duke Ludovico il Moro. He realized in Milan some of his important paintings: the most famous work is certainly the Last Supper, the large fresco in the Refectory of Santa Maria delle Grazie. He planned also new fortifications for the Sforza Castles and, as hydraulic engineer, he increased and improved the net of canals, called Navigli, crucial for the transport of commodities and goods through Lombardy and neighbouring regions. In the first Milanese period Leonardo met Luca Pacioli, one of the most important mathematicians of that time. Their friendship increased his interest in mathematics and led him to produce many papers, rich of geometrical figures like lunulae and polyhedra. The Codex Atlanticus, preserved in the Veneranda Biblioteca Ambrosiana in Milan, is also a large collection of examples of the mathematical and physical studies of Leonardo. The sheets of the Codex, separated in the last restoration, appear periodically in exhibitions. In this chapter we will present some peculiar results related to lunulae, drawn by Leonardo for a treatise never completed, called De Ludo Geometrico.