The first project is a remake of some scenes from
The Flat Torus in the Three-Sphere,
a film originally created in 1968. The same programs that produce the
small animations, also produce the frames for a single-frame animation
in full color, with 24 bit planes.
The second project is a story board for a remake of a "classic" film
is described in "Complex Function
Graphs". The most recent version has been completed on May 16,
1995. This document appears as one of the samples for a proposed
totally electronic journal.
A research project in progress is the
self-linking of curves on the
3-sphere. This includes some small animations in Fnord and
illustrations and a small film using another program, fourd. Only an
mpeg player is necessary to show these animations.
On a Macintosh equipped with Geometer's Sketchpad, it is possible to
view the movies connected with "Monge
and Desargues, Identified".
A new project is a "sketchpad"
for spherical geometry, with interactive demonstrations in Fnord.
Another project comes from linear algebra. This short treatment of the geometry of least squares uses computer generated standard illustrations in traditional textbook mode, although the images are in a format that can be transmitted electronically. There is also a prototype interactive demonstration using Fnord.
There is also a "traditional" electronic publication on the
volume of an n-dimensional ball,
written after a morning session for high-school students visiting the
Geometry Center. The text is written in TeX, converted, along with
the illustration to postscript, so that it can be read using a
postscript viewer or printed out.
A recent project, in collaboration with
Davide Cervone at the Geometry Center,
involves a study of the Klein
bottle rotating in four-dimensional space. The film clips in
this section are generated by the program FrontStage designed by
Davide Cervone for use in conjunction with Geomview.
Another project connected with a long-standing effort to understand
tight
embeddings of surfaces is a module for constructing examples of
arbitrarily high topological complexity. The accompanying figures
were designed using the Fnord program for a survey article in
collaboration with Wolfgang Kühnel.
In addition to the properly mathematical projects, there is a long-standing and extensive effort to study the life and works of Edwin Abbott Abbott. The text of his famous book, Flatland is available here as well.
In progress is a partially updated 1990 article concerning Flatland and Hypergraphics.
Here, for use in talks about interactive computer laboratories in calculus of several variables, is a simulation of a session using the program Fnord. For a version using only black and white images, choose this.