More Mathematics . . .
This section contains a hodgepodge collection of mathematical
entertainments. Some of the links connect to activities that I put
together for various courses I've taught, others connect to interesting
things that I simply wanted to share. In particular, you can find
here streaming feeds (through YouTube) of various short animated
films that I've put together which illustrate different mathematical
objects.
I think that every college student should read the following wonderful
essay by Prof. T.W. Körner (Cambridge University), which should
perhaps be titled:
How
to listen to a mathematics lecture
A brief description accompanies each link below. Enjoy!

Geodesics
between conjugate points in the 3sphere

Stereographic
Projection
 This film (approx. 5 mins long) illustrates
streographic projection for the circle and the 2sphere keeping
in mind the goal of training your mind to visualize objects in
the 3sphere using stereographic projection. Hopefully, the animations
will help you to understand this conformal map.

Cyclic Subgroups of
the Loop Group of SU(2)
 I don't really know what to say about
these, other than that I think they are really neat.

Hopf Fibration Experience
 Alan Hatcher's book on algebraic topology
has a very nice description of how to view the Hopf fibration
of the 3sphere by circles. I took up the task of creating an
animation which illustrated this geometrically. I literally computed
an infinitesimal generator of the circle action in stereographic
coordinates and used a RungeKutta scheme to evolve the orbits.
Low and behold Hatcher's picture emerged! The way I see it, if
you're going to make a mathematics movie, why not do it with some
style!

Limits with von Koch's
Curve, Sierpinski's Gasket and the Chaos Game
 This was a class activity I put together
for my Brief Calculus students. It uses limits to compute the
"perimeter" of von Koch's snowflake curve, and the area
of Sierpinski's gasket. It finishes with a link to a nice java
applet hosted on a German site which plays the chaos game rapidly.

Fun with Möbius strips
 I put together this activity a number of years ago. It has
some accompanying worksheets and is a handson exploration of
some properties of Möbius strips. Great for junior mathematicians!

Fascinating Property of Circles
 This is another very amusing handson activity which illustrates
an interesting fact from classical algebraic geometry. The worksheet
shows how to use paper folding to construct an interesting family
of lines associated to a given circle. The family lines has an
envelope which one can see directly in the folds in the paper.
That's all that I am going to say. I don't want to give away what
happens.
