This project is developing an illustrated undergraduate text in projective geometry applied to perspective art, which is suitable for use in sophomore- or junior-level mathematics courses for mathematics majors, students pursuing computer graphics, or mathematically talented art majors. The project builds on the prior NSF-funded work of one of the PIs, which resulted in the publication of the undergraduate text, "Viewpoints: Mathematical Perspective and Fractal Geometry in Art" and a series of Viewpoints Mathematics and Art workshops for undergraduate instructors. The project is 1) developing a series of materials (papers, classroom modules, homework exercises), 2) testing the materials in the classes at Franklin and Marshall College and Southwestern University and evaluating these materials formally, 3) presenting these materials (via talks, journal publications, web distribution, and mini-courses) to other instructors for their feedback, and 4) publishing, marketing, and disseminating the text. This course enhances knowledge of geometry and gives readily-accessible applications that can be used in teaching, in studies where this type of projective geometry course is relevant, and in fulfilling mathematics course requirements with content that is relevant to non-math majors.
When people say something like "geometry allows you to see the world in a different way", we mean that literally. Projective Geometry and perspective art allow us to transform a three-dimensional world onto a two dimensional canvas (and sometimes, back again). An NSF-supported three-person team of mathematicians and artists are developing a set of inquiry-based lessons that allow students to learn projective geometry by drawing pictures and taking photographs. Students find the mathematics compelling; they also discover that their artistic skills improve dramatically. Many students begin the course drawing only stick figures and cartoons; by the end of the course students are constructing architectural masterpieces, using only ruler, pencil, eraser---and their brains. The materials developed in this project not only help students learn higher levels of mathematics, but they also help mathematicians learn about the visual arts. The researchers in this project have presented their materials to hundreds of mathematicians and their students; they have trained four dozen faculty on using the materials in their own classes. Why is this project important? Traditionally, mathematics instructors have focused on applications of our field to quantitative disciplines (the sciences, engineering, economics, and finance). But with the advent of computer-generated visuals for movies and videogames, the visual arts have become a rich field for mathematical exploration, inquiry, and research.
