How do we fit a three-dimensional world onto a two-dimensional canvas? Answering this question will change the way you look at the world, literally: we'll learn where to stand as we view a painting so it pops off that two-dimensional canvas seemingly out into our three-dimensional space. In this talk, we'll explore the mathematics behind perspective paintings, which starts with simple rules and will lead us into really lovely, really tricky puzzles. One of the surprising results of projective geometry is that it implies that every quadrangle (whether convex or not) is the perspective image of a square. We will describe implications of this result for computer vision, for photogrammetry, for applications of piece-wise planar cones, and of course for perspective art and projective geometry.

Annalisa Crannell is a Professor of Mathematics at Franklin & Marshall College and recipient of both her college's and the MAA's distinguished teaching awards. Her early research was in topological dynamical systems (also known as "Chaos Theory"), but she has become active in working with mathematicians and artists on Projective Geometry applied to Perspective Art. Together with mathematician/artist Marc Frantz, she is the author of Viewpoints: Mathematical Perspective and Fractal Geometry in Art. She especially enjoys talking to non-mathematicians who haven't (yet) learned where the most beautiful aspects of the subject lie.