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

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.