[ slightly improved over Math Forum draft ] Probably a fault line or cultural divide between acutely differing schools of thought, is in this area of tiling or mosaic making. Some schools consider this a stupid waste of time, others a core topic, whereas a 3rd group stays more neutral on the issue, and a tiny 4th group has no idea what I'm talking about.
I'm in the second group (core topic) as tiling is to spacefilling as figurate are to polyhedral numbers. We may start in a plane, in deference to some millenia of pre-NASA reflex conditioning, but we're still on a runway, accelerating, and before long (way sooner than in traditional curricula), we'll be airborne, moving up into higher D. Tetrahedra are most definitely a feature of K-5. If NCTM doesn't grasp that, it's missing the boat. Back to tiling: we have the classifications, the Escher lithographs (which follow into Part Two), and the tie ins to Mesopotamian religions, the three biggies especially, and their respective sacred geometries. I know "sacred geometry" is taboo in traditional mathematics, but this is ~M!, Katrina Network type stuff, closer to George Bush Sr.'s "voodoo economics" (except managed more by geeks (Bush was more of a jock, not that we can't share power)). Rolling forward, we get to the Kepler-Penrose aperiodic tiling studies, various heuristics, again finding echoes in Part Two (in what some Russians call stereometry), where we likely look at Hargittai & Hargittai (Hungarian), plus Chakovian coordinates (quadrays, simplicials, whatever nomenclature). I've already made the case for Polyhedra numerous times. Thanks to breakthroughs in architecture in the 20th century, we're obligated to teach about the hexapent in some way shape or form. Katrina Network is strong on this, but you'll find other sources. Top of my list would be J. Baldwin's 'Bucky Works' (packed with ~M!). For a more prefrequency approach, I recommend Cromwell's 'Polyhedra', and its cartoon proof of Euler's V + F = E + 2 based on the interdigitating trees of Von Staudt's. And of course we're not about to bleep over Fuller's volumes tables, nor MITEs, nor the Jitterbug Trans- formation -- all pure gold as far as we're concerned. So to recap... Given I'm of a school which regards tiling as core, I'm putting my shoulder behind two big initiatives in computer science these days: CP4E and HP4E. CP4E was hatched by Guido, BDFL of Python Nation, and DARPA, and carried forward billiantly (at least one doctoral dissertation already on file, about our early beginnings as a think tank slash on-line community [1]). HP4E was hatched by yours trully, though mostly as a marketing gimmick in homage to CP4E and Wanderer Glenn Stockton's global matrix campaign. I certainly take advantage of Python a lot, using its generators (a recent feature) to spit out successive terms in figurate and polyhedral number sequences, e.g. 1, 3, 6, 10... and 1, 12, 42, 92... (see my Focal Points for more details, plus my CP4E website, one of many curriculum "hot springs" in our cyberspace-based Python Nation [2][3]). Kirby [1] John Miller's PhD dissertation, Promoting Computer Literacy Through Programming Python (1.37 MB), looks at the issues around teaching with Python, and explores some of the threads taken up on edu-sig. http://www.python.org/community/sigs/current/edu-sig/ [2] Focal Points: http://mybizmo.blogspot.com/2006/09/focal-points.html [3] CP4E website: http://www.4dsolutions.net/ocn/cp4e.html === For more on ~M!: http://worldgame.blogspot.com/2007/01/m.html -- http://mail.python.org/mailman/listinfo/python-list
