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David Moore
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Aspiring physicist
Aspiring physicist

197 followers
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A video on mathematical sculpture, group theory, and polyhedra! Enjoy!

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Why do vegans care about polyhedra? Abraham Lincoln.

A video on mathematical sculpture, group theory, and polyhedra! Enjoy!

(Full disclosure: It's my video!)

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Fixed the error in my previous post! +Chris Thomasson. Fixed code:
http://mathb.in/52101
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+Chris Thomasson implementation of the contour line thing I was talking about. Both potentials are sums of random m/r potentials for five masses each. The interesting thing is that the lines appear to terminate, which I wouldn't have thought could happen!

[edit: The lines can't terminate. I made a typo in my code!]

Updated doc fixing some typos and with mathematica source http://mathb.in/52099
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Animated gif!
Polyhedra from orbits of the icosahedral group. Every frame in every polyhedron here has icosahedral rotational symmetry. That's group of size 60, so in general the solids here have 60 vertices. Plotted are some polyhedra with 60/1=60 vertices (truncated icosahedron), 60/2=30 vertices (Icosidodecahedron), 60/3=20 vertices (dodecahedron), 60/5=12 vertices (icosahedron). I take an arbitrary point, hit it with the group action, and plot its convex hull. The numbers 1, 2, 3, 5, are orders of stabilizer groups of special points, and in this case they let you know the number of vertices of each solid without actually counting them
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Here's an idea of how an electron gun works
http://mathandcode.com/2015/09/04/electrongun.html
You might work with an electron gun in a first year college physics lab course*, and find that it has all sorts of knobs/variables. The two most important are the gun voltage, and the grid voltage. Here, the gun voltage is held constant, and you can build your own cylinders and disks at gun or grid voltage however you please! This article shows you how to use the simulation to build a focused electron beam.

*the experiment I'm thinking of is one you can use to find the electron charge:mass ratio. A google search for "electron charge to mass ratio lab electron gun" brings up lots of relevant results/sample labs.

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Here's an idea of how an electron gun works
http://mathandcode.com/2015/09/04/electrongun.html
You might work with an electron gun in a first year college lab course, and find that it has all sorts of knobs/variables. The two most important are the gun voltage, and the grid voltage. Here, the gun voltage is held constant, and you can build your own cylinders and disks at gun or grid voltage however you please! This article shows you how to use the simulation to build a focused electron beam.

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New post on a fun exercise with linearization! http://mathandcode.com/2015/09/02/delaunay.html
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