Visualizing the Fourth Dimension
HONR 245
Spring 2005
Mon, Fri 2:50-4:20
Copley 200
Instructor: Richard Hammack Office hours:
Office: 238 Copley Monday, 9:45--10:45
Work: 752-7210 (and voice mail) Wednesday, 9:45--10:45; 1:30 -- 2:30
Home: 353-8572 (before 9:30 p.m., please) Friday, 9:45--10:45
Fax: 752-4724 and by appointment

This is a course on the geometry of four-dimensional space. We begin with an informal analysis of two- and three-dimensional Euclidean space, and with the Platonic and Archimedean solids in these spaces. Then we explore the analogous structures that exist in four (and even higher) dimensions. Our exploration is primarily visual. We use computer graphics and animation -- as well as ruler-and-compass constructions -- to create images of higher-dimensional objects. We discuss the historical development of the idea of the fourth dimension, as well as its influence on science, technology and twentieth century art. The only prerequisites are a basic understanding of high school geometry and algebra, and a good imagination.

The course meets in the Mathematics Department's Mac Lab, although we will not use the computers every day. You will often use a mathematical software package called Mathematica to create, project and draw three- and four-dimensional objects. No prior computer experience is necessary.

Your grade is determined by homework, participation, a portfolio and a final project. Details follow.

Homework: There will be frequent graded homework. These assignments will take various forms, including -- but not limited to -- written work, mathematical work, drawings, three-dimensional models, and computer programs.

Participation: Participation means that you in some way demonstrate intellectual involvement in the course. It does not necessarily mean that you ask questions and volunteer answers. Active participation may include putting extra effort into homework, taking advantage of office hours, and displaying preparedness, dedication and intellectual curiosity. Spotty attendance can lower your participation score.

Portfolio: Over the semester, you will develop a portfolio of images (computer generated and/or hand made) and three-dimensional models.

Project: Instead of taking a final exam, you will do a final project. This project can be a paper, computer program or visual work on a topic of your choice, subject to my approval.

Your final grade will be determined by the following weights:
Homework 25%
Portfolio 25%
Participation 25%
Final project 25%

You will probably need the following supplies:
Pad of drawing paper
Plastic 45-45-90 triangle
T-square (optional)
Plastic 30-60-90 triangle
Masking tape (optional)
Colored pencils or pens
Calculator (optional)
X-acto knife or scissors
Protractor (optional)

Information about this course is posted on the Internet. To find it, go to my home page ( and click on "HONR 245." There you will find the syllabus, homework assignments, a calendar, and other announcements.

Office: Please feel free to stop by my office whenever you have a question, or if you just want to chat. You are welcome to come by any time that I am there, even outside of posted office hours. I will also be happy to schedule an appointment.