[Edu-sig] python satacad: class 4

[Kirby Urner]

> > Stockpiling WMI.
> 
> Weapons of Mass Instruction.
> 

That reminds me of a piece of Class 4 I forgot to describe.  Remember, this
is billed as a math class, with Python programming as a tool, a means to an
end.  So it's logical that I'd be doing a fair bit of geometry, in addition
to a lot of pure/core Pythonic stuff.

So I have this plastic box containing, among other goodies, a set of stiff
paperboard polyhedra, with black electrical tape along the edges.  Thanks to
help from my friends Trevor and Russ Chu, they're precisely dimensioned for
this demo I do, quite frequently, for audiences of all ages (but mostly
kids).

First, I take out my tetrahedron.  We've already gone over Euler's V + F = E
+ 2.  One face is missing (from all of them) meaning they're containers or
"mixing bowls" of a kind.  Lining the bottom of my plastic box:  some kind
of dried white bean (I forget the technical name for them).  I say:  "OK,
this here tetrahedron will be my unit of measure, my cup."  Then I go into
this riff (how it goes varies from time to time) wherein I fill the other
polys in my box with tetra-units of white bean.  The pleasing result:  cube
= 3 tetvols, octahedron = 4, rhombic dodeca = 6, and cubocta = 20.

Then there's this whole thing about how the cubocta (tetravolume 20) is
really 12 balls around 1 in disguise, then 42, 92, 162 as we pack outward,
layer by layer.  So really, this whole business about the polyhedra embeds
into a sphere packing matrix well known to architects and crystallographers.
We call it the concentric hierarchy.  We don't know why your high schools
don't teach it.  But here at Saturday Academy, we're sure to clue you in
(because we care).

How does all this relate to Python then?  Well, per Class 3, by way of the
figurate numbers, with the polyhedral numbers being a superclass thereof.
We write little Python programs (just a few lines) that spit out these
sequences of triangular, tetrahedral, cuboctahedral numbers (which latter
are also icosahedral numbers, per Jitterbug Transformation).

It's all pretty seamless.  Python, geometry, POV-Ray... From the standpoint
of these students, this is just run-o-the-mill stuff, more ho hum academics,
though admittedly a lot more interesting than what their getting on
weekdays.  But old timers, teachers, onlookers, may appreciate that this
curriculum is 100% subversive of the status quo.  The NCTM doesn't stand a
chance of keeping its standards unchanged, given this kind of content
pumping out and around the Internet in a big way.  We're an engine for
positive change, armed with simply awesome WMI.

Kirby

> 
> Art
>