The Franciscan friar and mathematician Luca Pacioli dedicated his “Summa de arithmetica, geometrica, proportioni et proportionalita” to Federico’s successor Guidobaldo da Montefeltro. The eloquent portrait of him here by Jacopo de’ Barbari, on loan from the Capodimonte Museum in Naples, depicts him demonstrating a Euclidian geometrical figure, a copy of his “Summa” opened at the relevant page on the table in front of him, his left finger marking the appropriate place in the book.
Suspended in midair to the friar’s right is a crystalline polyhedron, with 18 sides composed of 18 equilateral triangles, in three of which can be discerned miniscule reflections of a building resembling Urbino’s Ducal Palace.
This transparent polyhedron at the same time offers a kind of mystical mathematical equivalent of the religiously symbolic white egg that appears suspended in the vault above the Virgin in Piero della Francesca’s “Sacred Conversation,” now at the Brera in Milan, commissioned by Federico and in which he appears kneeling in full armor before the Mary.

www.nytimes.com/…/09iht-conway09.…