Why Computer Graphics?
The emerging field of computer graphics offers a rich variety of problems for investigation to a high-school geometry class. Many of the mathematical ideas and algorithms required to generate complex, three-dimensional visualizations—of the sort now routinely seen in movies, in advertisements, and on TV—derive from simple plane geometry and arithmetic. Students often find examples drawn from computer graphics compelling, both because these problems are applied—i.e., motivated by tangible, practical questions rather than solely by theoretical or pedagogic requirements—and because their objects of study are usually pictorial in nature. The unifying goal of computer graphics is to design "good pictures," where "good" might separately be defined as pretty, accurate, informative, realistic, or inexpensive. From the students' perspective, problems drawn from computer graphics are often fun to work, because their domain is the broad world of all possible pictures and images, as opposed to the restricted, traditional geometric domain of points, lines, and circles.
This paper surveys a number of problems and topics drawn from computer graphics, and explores them through the lens of dynamic geometry software. In particular, I comment on a number of Sketchpad sketches [Jackiw95] that I've collected from my work and that of friends, colleagues, teachers, and students. Readers with access to the Web are encouraged to read this paper from the St. Olaf Proceedings Web site, where copies of these sketches can be accessed electronically. (Obviously, it's more satisfying to explore these sketches interactively than to read static text about how they could be manipulated through software!) Rather than develop or endorse a single curricular strategy for bringing such topics into a classroom, I hope that the problems outlined below are sufficiently interesting and diverse that readers who teach geometry will experiment with integrating them into classes and curricula that already exist.