This is the summary of a presentation given at the Joint Mathematics Meetings, January 10-13, 1996, Orlando, Florida.

The project of deciding if a collection of points in space do or do not lie on a circle has been very successful in my recent linear algebra classes. Students understand the problem and, given the background of the problem, the motivation for solving it. The project forces them to integrate their knowledge of several parts of the course and some earlier work in other courses. Moreover, since it sounds easier than it usually turns out to be, students get hooked on the problem. I believe they come to understand to some extent how the mathematics they know could be useful in a "real world" setting. (The project was inspired by work done at Ford Motor Company.)

In this project, each student is given a data set of 10 points in space. Either working individually or in groups, the students determine whether the points of each data set lie on a circle or not. I have used this project in a second course in linear algebra for math majors, in a first course for sophomore engineering students, and in a first course for graduate engineering students. Some numerical software (we use Matlab) and ideas about subspaces, least squares approximations, and Gram-Schmidt orthogonalization are needed for the project.

This talk will describe the project, its background, and some of its pedagogical aspects. Matlab routines to generate the data points are available on the Web at

http://www.math.purdue.edu/~cowen/CircleProj.html

Carl C. Cowen, Purdue University, West Lafayette