This material gives a brief introduction to projecting higher dimensions to two-dimensional paper and shows how to use the technique to draw three-, four- and five-dimensional (hyper)cubes.
Visualization of higher-dimensional objects.
Target Student Population:
Students from high school geometry to graduate level topology.
Prerequisite Knowledge or Skills:
Minimal. Knowledge of points, lines, squares and cubes are enough.
Type of Material:
Classroom demonstration or self-study.
Evaluation and Observation
Nice explanation how higher-dimensional figures are projected to produce a two-dimensional picture.
The explanation is limited to cubes, but then again, that is the learning goal.
Potential Effectiveness as a Teaching Tool
Focused explanation of how to draw hypercubes. Will be successful for this task. It can also inspire the realization that other objects, such as tori (which can also be formally defined as the four-dimensional product of two circles) are drawn similarly.
To widen the scope to other interesting objects like tori, a teacher needs to provide an explanation based on the above remark or something similar. It is not clear whether students could make this type of leap on their own. Then again, these extensions were not part of the original scope.
Ease of Use for Both Students and Faculty
No problems with the use of the applet. Good explanation.
Other Issues and Comments:
Other material that may be of interest to users of this resource:
http://4d.shadowpuppet.net/ (Uses Flash)