## Thursday, December 24, 2009

### Real and Rational Numbers

:: vZome: octa + 1/4 tets by D. Koski ::

Today's triangle, one of them, was the Wittgenstein list and Math Forum. True, the reforms aren't that radical in the sense of sudden. This was a slow phase-in and got going long before I started tracking. Like when Arthur Loeb was writing Remarks on Some Elementary Volume Relationships... in 1965, I was still in Portland, just starting on New Math in 1st or 2nd grade.

We've got plenty of stuff on-line by now. Google Books has a lot of the Peter Pearce book, which I'm borrowing from Flextegrity Inc. What a gold mine.

The pace has been glacial, which is maybe reassuring. Geological time is cosmic time, so maybe it's more likely to stick?

My suggestion to Bill Marsh, who was following cues from Dr. Wu, was to handle real irrationals and rationals as a part of the same Uru-like vista and (this part is new) to use our wholesome whole number volumes tables to motivate the rational part, the discussion of fractions.

:: vZome: 1/24th of 1 ::

Historically, we've not had much option to toss around non-rectilinear blocks with volumes like 1/8, 1/24, 1, 4, 6. Our "wrong angle" family has been more out of sync, out of sight out of mind, with relatively intimidating irrational volumes. I'm among the first generation of math teacher able to avail of this new pedagogical tool, complete with world-readable literature, toys, kits, computer animations, even a world map.

The real numbers discussion, including incommensurability, would be with reference to the edges or vectors, with lots of surds, phi, sqrt(2). Associating number and length is primal, many authors agree.

Discovering the diagonal of a square is not a ratio of two integers was a big Greek achievement. In our own age: the discovery of chaos, even in the Newtonian realm, might be of parallel magnitude. So using a cube's edges to anchor this history of the irrationals is already the way it's done. We're not rocking any boats by staying with sqrt(2) and phi distances. Jay Kappraff's Connections: The Geometric Bridge Between Art and Science , as does Glenn Stockton's stuff.

The suggestion from Dr. Wu, with which Bill Marsh agreed, was to get the number line going earlier, even before fractions, as "measuring numbers". There's an interval based approach, pinning a number down by zig-zagging in, using binary biting.

The other scene graph
was about local institutions. I tossed my hat in the ring (again) as this curriculum writer with a website named Oregon Curriculum Network. Lots of Python stuff, also some J. Free and open source software, with a math teacher's bias (I used to be one, St. Dominic Academy in NJ). There's also some precedent for the Martian Math stuff.

I also mentioned ISEPP in my Math Forum column, as a source of opportunities. Example: my academic discount on that first international conference on buckminsterfullerene, thanks to some official letterhead. That wasn't such an easy trip, driving to Santa Barbara and back, however it was a great adventure. I still remember that German chemist I hung out with.

Another opportunity: the recent field trip to ONAMI, thinking back to the field trip and the Zome kit I saw there, for making a Buckyball -- like going full circle. Pearce had his own most excellent connector kit, which I seem to recall using or at least seeing a few times.

This got me talking about Scott Vorthmann's vZome and Dave Koski's latest art. The quarter tets on the octa faces, giving the rhombic dodecahedron, is one of my favorites (up top).

Dave is quite attuned to the fact that a left A-module might get different edge colors in vZome when turned inside out. From a Synergetics perspective, this is less than ideal, given the left A and the right A both have the same edge lengths. Something to do with the hubs? The software allows

Brian posted an impassioned contribution to our Wanderers archive. He's an ecologist with a conscience, sometimes disappointed by the politics buffeting our commons. I've been in there with my math teacher hat, seemingly preoccupied with remote esoterica. Polyhedra? WTF.

In the physical therapy waiting room, I read most of that New Yorker article about Georgia, the one in the former Soviet Union. Pretty amazing stories. I also met Peter Ford that day, me thinking like a Pacific Rimmer, yakking about politics.

PPRC just called, 1 AM. Punishment Park, by Peter Watkins, is cued up, an ultra-dark product of the tumultuous Vietnam years. I might review it later. Watched the director's intro. Few venues show this film.