Notices of the International Consortium of Chinese Mathematicians

Volume 10 (2022)

Number 2

The mathematics of painting: the birth of projective geometry in the Italian Renaissance

Pages: 11 – 29



Graziano Gentili (Dipartimento di Matematica e Informatica, Università di Firenze, Italy)

Luisa Simonutti (Istituto per la Storia del Pensiero Filosofico e Scientifico Moderno, Milano, Italy)

Daniele C. Struppa (Chapman University, Orange, California, U.S.A.)


We show how the birth of perspective painting in the Italian Renaissance led to a new way of interpreting space that resulted in the creation of projective geometry. Unlike other works on this subject, we explicitly show how the craft of the painters implied the introduction of new points and lines (points and lines at infinity) and their projective coordinates to complete the Euclidean space to what is now called projective space. We demonstrate this idea by looking at original paintings from the Renaissance, and by carrying out the explicit analytic calculations that underpin those masterpieces.


Renaissance, Piero della Francesca, painting, perspective, analytic projective geometry, points and lines at infinity

The first author was partially supported by INdAM and by Chapman University.

The second author was partially supported by ISPF-CNR and by Chapman University.

Published 6 February 2023