The Mathematics of Painting: the Birth of Projective Geometry in the Italian Renaissance

TL;DR

This paper explores how Renaissance perspective painting influenced the development of projective geometry by analyzing artworks and their underlying mathematical principles, revealing the explicit connection between art and mathematical space extension.

Contribution

It explicitly demonstrates how Renaissance painters' techniques led to the formalization of points at infinity and projective coordinates, bridging art and advanced geometry.

Findings

Renaissance paintings encode projective geometric principles.

Explicit calculations connect artworks to projective space.

The development of projective geometry was influenced by artistic practices.

Abstract

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.