Summary

Increasingly, Leonardo "came to realize that mathematics was the key to turning observations into theories" (200). Leonardo's visual thinking gave him a skill with geometry which helped him to understand perspective and proportion. One of his close friends at Milan's court was a mathematician named Luca Pacioli who was both a collaborator in creating court amusements and a teacher of mathematics. Leonardo also drew several geometric drawings for a book Pacioli wrote on the golden ratio, a number series that occurs throughout geometry, art, and nature, and which Pacioli dubbed "divine proportion" (205). Leonardo was particularly fascinated by how the shapes of objects transformed with motion and the ancient challenge of squaring the circle. Many of his notebooks feature pioneering work in the field of topology, "which looks at how shapes and objects can undergo transformations while keeping some of the same properties" (206).

Chapter 14 focuses...