Animated (Java) Illustrations
Here are a few animated illustrations that are discussed in one or
more notes on this site. These are best viewed with Internet Explorer.
This applet shows the positions of all 297 stars with magnitudes
less than 3.5, projected onto a sphere like a planetarium.
This applet illustrates the workings of an unconventional internal
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.
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.
This is one of the most fascinating of the simple solids, with an
interesting correspondence to "the shape of coincidences".
The above illustrations are discussed in the notes
The Stars In The Sky
Min-Energy Configurations of Electrons on a Sphere
Ringing of the Changes (The Shape of 4!)
Meeting Probabilities and The Shape of Coincidence
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