More Martian Math (multimedia -- guided presentation)
kirby urner
I did some more sketches last night in the faculty lounge,
which is where the time capsule is, the hemi-cylindrical
shelving solution that used to store souvenirs from family
travels, like from when we were a Khadaffy family and so
on (memorabilia), now books.
I bought the markers and tablet at Fred Meyer's and
started fresh. Two of the other faculty, Melody and Lindsey,
were part of the scene, with Melody spending much of
her time in that recliner with the electric blanket (we
do very little space heating in our school). Lindsey is a
musician and student of the little known Paul Treanor,
a Dutch blogger http://web.inter.nl.net/users/Paul.Treanor/ .
In between doing the sketches, taking photographs
(the lighting is somewhat deliberately dark, reflecting the
ambiance) and uploading them to thekirbster at Flickr,
I did my usual Python teaching over the web. This is
an invisible and growing army of logic wielders, a machine
runnable logic so really fast. Some consider it way too
slow, though that's sometimes only by reputation and
not hands on experience.
Here is a picture of the time capsule, close up, as I was
sitting next to it. The media station is adjacent to that.
I've recently added the new DVD biography of Bayard
Rustin, the one shown at the AFSC corporation meeting
a few weeks back in Philadelphia. I'm one of the members
of that nonprofit, representing Quakers of the Pacific
Northwest (some of them).
http://www.flickr.com/photos/17157315@N00/7028378663/in/set-72157624750749042
(shelf is curved -- a challenge for books)
Bayard was a chief leader of the civil rights movement
around Martin Luther King but others in that chapter
were not ready to handle "gayness" as a civil rights issue.
Quakers of my ilk are for the most part past that
and Bayard's memory was being restored, with a
cake and everything.
http://mybizmo.blogspot.com/2012/03/remembering-baryard-rustin.html
His partner was there to cut the cake (Bayard died awhile
ago).
The first sketch of the evening might be posed as
a puzzle, including to young children. Note how you
can make a kind of spiral or spatial zig zag with
three pencils or rods. Two lie on a plane (plain) or
table, making an angle and the third one sticks up,
making a kind of "train" or "Z" of three "cars" or
"vectors". With two such Zs you can make a
tetrahedron, whereas you may wonder if a cube
can be made entirely of rectilinear Zs. That
question is studied in this sketch:
http://www.flickr.com/photos/17157315@N00/7028376067/in/set-72157624750749042
In the next sketch, the opening moves of Martian Math
get more complete treatment. We have a rod that we
understand to be the radius of some sphere. Two such
rods making a 180 degree angle comprise a diameter (D)
of said sphere. 2R = D. We then proceed to build a
cube using only R rods, and a tetrahedron using only
D rods. You might well wonder which has the greater
volume as the Cube is more sphere-like, more voluminous
in its use of space, while a Tetrahedron is a minimalist
construction. On the other hand, the edges are twice
as long.
http://www.flickr.com/photos/17157315@N00/7028376653/in/set-72157624750749042/
The third sketch looks like some kind of necklace or
diagram (on the left). There's some color coding going
on, and some labeling. P, C, T, O, I stands for the five
Platonic solids. They've been arranged symmetrically
around the tetrahedron (T) and as duals to one another
(C & O are duals, P & I are duals, T is dual to itself).
The dual relationship is shown in orange, after which
there is "begetting" shown in pink. When you size a
Platonic and its dual (also Platonic) such that their
edges cross, they beget yet another polyhedron,
which we may call their sum. These are labeled RD
and RT respectively (C is also the sum of the Ts).
T + T = C
O + C = C + O = RD
P + I = I + P = RT
http://www.flickr.com/photos/17157315@N00/6882276066/in/set-72157624750749042/
The last (four of four) redisplays the necklace jewels
as if they were currency. Their relative volumes
determine the dollar amount. The VE or cuboctahedron
($20) is somewhat apart. It's the dual of the RD ($6)
but not sized to intersect with it (not in a begetting mode).
We use its 12 corners to anchor 12 balls around a nuclear
ball, the same ball of which R is the radius and D is the
diameter (so back to sketch 1 and some of the other
nodes in this edge-works / storyboard).
Students with OPDX / AFSC / FNB know that our Biosphere
is flooded with watts, which are also worth paying for in
real dollar terms. That's why the familiar arrow from the
fusion furnace Sun to the Earth, symbolized with a
concentric circles logo (brown inside green inside blue).
You could think of money coming directly from the Sun,
with most of it reflecting back into space (good thing or
we would bake, like in a microwave oven).
http://www.flickr.com/photos/17157315@N00/7028377663/in/set-72157624750749042/
How we size the RT (rhombic triacontahedron) in all this
is a bit of a story. I have worked with other teachers on
riding the NCLB wave (No Child Left Behind) by floating
an NCLB Polynomial and NCLB Polyhedron. Both are
well ensconced in the literature by this point, thanks to
search engines, so its hard to be into NCLB and not
have at least a glimmer awareness of what a rhombic
triacontahedron is, what it looks like. Lots of diamonds.
The next week after AFSC in Philadelphia I was in
Santa Clara at the heart of the Silicon Forest, having a
televised exchange during Q&A with that ESRI guy,
about the Fuller Projection. My voice cuts in at about
29 minutes in the video at the end of this blog post:
http://controlroom.blogspot.com/2012/03/occupy-silicon-valley.html
OK lets try uploading again. Hope the formatting
looks better...
Kirby
Other pictures:
My office on Hawthorne:
http://controlroom.blogspot.com/2012/03/from-bagdad-chat-room.html
Melody (faculty) shows off Flextegrity:
http://controlroom.blogspot.com/2012/03/flextegrity-in-spring.html
Time capsule before books, showing dad (standing) planning Libya:
http://www.flickr.com/photos/17157315@N00/2859780441/
Abbreviations used (some of them):
AFSC = American Friends Service Committee
Esri = Environmental Systems Research Institute in the old day (no
longer considered an abbreviation)
FNB = Food Not Bombs
OPDX = Occupy Portland