Mathematics 104, "Fundamental Problems in Geometry", has a succinct and purposefully vague course catalogue description: Topics are chosen from Euclidean, non-Euclidean, projective, and affine geometry. Highly recommended for students who are considering teaching high school mathematics." The prerequisite is a one-semester course in linear algebra, or permission of the instructor.

During the spring of 1999, the class consisted of sixteen students, at least three from each of the four undergraduate classes and one graduate student in computer science. The text was "The Geometric Viewpoint: A Survey of Geometries" by Thomas Sibley, and the syllabus called for going through the text in order over a period of fourteen weeks. A number of students treated the course in a very conventional way, attending lectures, doing weekly homeworks from the textbook, and taking midterm and final examinations. Others chose to go beyond the standard assignments and to participate in an series of online discussions on geometric topics not included in the text.

The course was to a large extent paperless, with assignments and discussions carried on over a file server in the mathematics department. The communication software had been written by a team of undergraduate research assistants in the summers of 1997 and 1998, and one of those collaborators, John Steinberger, acted as a Teaching Assistant for the course.

The first and one of the most successful discussions is the subject for this article. The original question was posed on January 29, the first weekend of the course. Most of the interchanges occurred during the following week, with additional comments throughout out February, and with a major contribution by the TA on March 14.

There were twenty-six additional discussion topics over the course of the semester, some of which were problems from earlier geometry courses, such as conics in taxicab geometry, numbers of double tangent lines to triples of circles in the plane, the locus of lines halving the area of a triangle and the envelope of planes halving the volume of a tetrahedron, Another new problem was to determine all pentagons such that the five "medians" from a vertex to the midpoint of the opposite side are concurrent.