Here is the so-called Brera Altarpiece, painted by Piero della Francesca, showing the condottiere Federico da Montefeltro in adoration of the Virgin and Child, surrounded by saints. Piero della Francesca is famous for his writings on perspective and solid geometry, but this composition was actually governed by a simple two-dimensional geometrical scheme whose logic would have been familiar to any compass-wielding Gothic architect or early medieval craftsman. To see this, start by considering a few details of the painting. First, its sides have been slightly trimmed, and the elbows of John the Baptist at left, and of Andrew at right, thus appear slightly truncated. Second, these two saints hold their attributes in ways that serve as geometrical markers, which is particularly conspicuous in the case of the Baptist’s staff. Both the staff and Andrew’s book are aligned at 22.5 degrees from the vertical.