Animated Illustrations

Here are a few animated illustrations that are discussed in one or 
more notes on this site.

Kinematics of a Hypocycloidal Engine
This applet illustrates the workings of an unconventional internal
combustion engine.

24 Electrons on a Sphere
This shows the minimum energy configuration of 24 charged particles 
on the surface of a sphere.  The colors of the edges denote their 
lengths.  Notice that the surface of this solid consists of 24/4 
perfect squares, 24/3 perfect triangles, 24/2 additional "bi-gons", 
and of course 24/1 vertices, all arranged so that each vertex is 
identical.  In addition, the vertices have a "handedness", so there 
are really two distinct versions of this solid.

Bell-Ringing Solid
This shape is what's called a "truncated octahedron", one of the 13 
Archimedian solids.  It has six square faces and eight hexagonal 
faces, making a total of 14 faces.  The number of edges is 36, as 
required by Euler's formula  F + V - E = 2.  There is an interesting 
connection between this solid and the patterns of bell ringing.

Kepler's Rhombic Dodecahedron
This is one of the most fascinating of the simple solids, with an 
interesting correspondence to "the shape of coincidences".

The Stars In The Sky
This applet shows the positions of all 297 stars with magnitudes 
less than 3.5, projected onto a sphere like a planetarium.

The above illustrations are discussed in the notes
The Stars In The Sky
Hypocycloidal Engine
Min-Energy Configurations of Electrons on a Sphere
Ringing of the Changes (The Shape of 4!)
Meeting Probabilities and The Shape of Coincidence