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.

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, and identifies all those of the first magnitude.

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 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

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