chapter  6
27 Pages

## Circling the Square: The Meaningful Use of Φ and Π in the Paintings of Piero della Francesca

ByPERRY BROOKS

The physical, metaphysical, and esthetic associations of the irrational number known successively in mathematical history as “mean and extreme ratio,” “the golden section,” and φ ([1+√5]/2, or 1.618. . .)—based on the division of a line into two parts, such that the ratio of the whole to the greater part equals the ratio of the greater to the lesser part-fascinated certain commentators of the fi rst half of the twentieth century, notably Matila Ghyka in writings such as his 1931 book Le nombre d’or . 2 The four diagrams of Figure 6.1 show ways of generating the proportion and some of its properties.