- Some of you may be interested in making more detailed 2D creatures and
their environments than we did during the first weeks of class. You could
work out carefully their internal body structures, and their machines, and
other such items, and then explain them carefully in a written report.
Someone with a more literary bent might want to write a story about people
in such a world and how they interact with each other and their
surroundings.
- Some group might want to write a play or dance along the lines of
Flatland that expresses life in a two-dimensional world and how a flat
creature can understand three dimensions. A more daring choreographer
could try to show us four-dimensional objects through dance or
pantemime.
- Others may want to use the computer to make a series of movies like
the ones that I've been showing you. There are lots of sequences that
could be used to illustrate the 2D-3D and 3D-4D analogs. A careful
study of several of this together with movies and clear explanitory
text (perhaps as a web site) would make a very nice project.
- Those with more mathematical background might want to look at the
way that coordinates and functions work in four dimensions. For
example, for a surface in four-space, can we compute tangent
directions and normal directions like we do in calculus? Some
computer graphics would make a nice addition to this project as well.
- In class, we calculated the diameters of cubes in various dimensions
(we say the long diagonal of the n-cube was of length sqrt(n)). There
are other measurements we could compute as well. What is the volume
of the n-sphere, for example?
- For those interested in model building, it would be nice to have a
good set of views of the hypercube with various of the cubes
highlighted. We have seen several views of the hypercube and will see
several more next week. A carefully made set of models would make a
great project. There are also objects other than the hypercube that
could be made (such as the analogs to the triangle and other shapes).
- We used slicing to understand the hypercube, but so far we have only
sliced it in one direction. Later this week or next week we will be
slicing the hypercube in other directions, and will find some very
interesting shapes. A set of models showing the slicing sequences in
various directions would be a truely lovely project. Electronic
models and movies are also a possibility for this, though physical
models are the nicest.

Comments to: dpvc@union.edu

Created: May 12 1999 --- Last modified: May 24, 1999 10:19:06 AM