UW Math 497 Autumn 1997; Th 5:30-7:50

GEOMETRY IN THREE DIMENSIONS -- INTERACTIVE APPROACHES

Instructor: Caspar R. Curjel

Department of Mathematics, University of Washington, Seattle, WA

We live in 3-dimensional space, and our everyday material world is full of geometric objects such as lines, planes, curves, surfaces, and solids. Yet geometric reasoning in 3-space is hard to learn and awkward to teach. Why does 3D-geometry seem to be so much less accessible than geometry in the plane? One reason is that geometric reasoning requires some ability to visualize geometric objects in 3-space, that is, some ability to work with the objects in one's mind as if one saw them in front of one's eyes. Visualization, in this special sense of the word, does not come naturally to everybody. But it can be learned.

The purpose of the course is to have students develop 3D-visualization skills and use them for basic geometric reasoning.

Students will work in different hands-on modes, so to speak, as follows:

Physical Models

Students manipulate physical models of lines and planes. The models were developed for a series of National Science Foundation workshops for mathematics instructors and have been presented in Minicourses at national mathematical meetings.

Drawing

Students learn the basics of several drawing techniques. The techniques enable students to make recognizable drawings of geometric objects, and to read off from these drawings quantitative and qualitative information on events in 3-space.

The presentation of the topics discussed is adjustable to levels ranging from junior/senior High School to the sophomore year at college. Thus, the course will be of interest to High School teachers and college instructors, to undergraduate and graduate students planning to teach mathematics or any subject which requires geometric reasoning, and in general to individuals interested in different approaches to learning and teaching geometry.

• There are no formal prerequisites other than having had at one point at least one quarter of calculus.
• Students need to have a computer account to exchange e-mail with the instructor. Students without access to a computer will be provided with a temporary computer account.
• There is no required text.
• The course carries three credits.
• To receive credit students have to attend class meetings, turn in homework, complete projects, write reports, and pass a non-threatening final examination.
• Students will work in groups as well as on their own.