I did a quick coin of HP4E but haven't used it for much since: http://mathforum.org/kb/thread.jspa?threadID=1437142&tstart=0 Basically, I'm refining the "gnu math" concept, addressing concerns about the New Math resonance, which one teacher worried had "Titanic" connotations (as in "went down").[1] But I'm pointing to what we've saved from that shipwreck: an emphasis on bases (as in subtraction in base eight), and on Venn Diagrams (boolean algebra), and on Sets (unions and intersections). All that stuff is still in the mainstream, from Saxon to Singapore (those're textbook allusions, much talked about on the math-teach list I frequent). Gnu math uses a non-proprietary substrate on top of proprietary hardware (e.g. Intel's, AMD's...) to keep computer programming a "for everybody" sport, i.e. we won't wall them out on the basis of price alone (never a good way to promote a meritocracy). Yes, gnu software also runs on proprietary operating systems, and yes, we might someday have an open source chip, i.e. the designs are free and clear to anyone with a fab (still a huge barrier to entry at this point -- clean rooms ain't cheap). But until that blessed day, when it's all open source as far as the eye can see (the Debian ideal), I'm not averse to using whatever public venues they leave open to us laypeople (even as we keep fighting to make inroads). In the gnu math I envision, sets are just another data structure (added somewhat late to Python, as dictionaries with null values, only keys, did pretty much the same work). We're not as beholden to early 20th century philosophies of mathematics, which made the set front and center in some theory of types, with Russell's paradox about what might be "empty" or not. Per Wittgenstein, all that Cathedral talk does *not* underwrite what we do in the Bazaar (set theoretic logic provides a painted foundation under a painted castle, to paraphrase the guy). The genesis of mathematics is ordinary ethno-arithematic, and as such is "all in the open" i.e. doesn't depend on special Harry Potter powers to see in "higher dimensions" (another position of mine: contra the HyperCross Dogmatists (but I'm fine with Coxeter's polytopes and recognize their utility in higher mathematics (but a hypercube is *not* the same thing as a time machine remember, per 'Regular Polytopes' on page 119))).[2] So yeah, we've got sets (lists, dictionaries...), and math.pi, and pi generators, and let's not forget phi. Phi is actually at least as important as pi as a curriculum asset, once we're into the greek letters and spooky greek metaphysics ("infinitely extended infinitely thin planes" and all that ghostly stuff). People tend to dismiss phi, out of bias against anything to do with the pentacle. Holdover superstitions. But we can't deny the pentagon its due, phi being the reciprocal of its edge-to-diagonal ratio, although some call that tau. Five-fold symmetry *is* important in Nature. Who are we, the naked apes, to argue with her wisdom? In fact, we've done a lot of homework on pentagon math right here on edu-sig, including in the form of continued fractions (a perennial favorite, as phi is "just ones" all the way to the bottom, like turtles). Plus you've got this convergence to phi along the Fibonacci sequence, already paradigm generator in the Pythonic literature, right up there with Guido's cute little gcd function. I'm still liking the fact of fib.next()/fib.next() getting closer and closer to the most irrational irrational, every time we hit the Enter key (again, the bigger number will be in the denominator, given left-to-right evaluation, so the convergence is to 0.618..., not to 1.618...).

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from __future__ import division

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def fibs(a=0,b=1): while True: yield a a,b = b,a+b

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genfib = fibs() genfib.next()/genfib.next() 0.0 genfib.next()/genfib.next() 0.5 genfib.next()/genfib.next() 0.59999999999999998 genfib.next()/genfib.next() 0.61538461538461542 genfib.next()/genfib.next() 0.61764705882352944 genfib.next()/genfib.next() 0.6179775280898876 genfib.next()/genfib.next() 0.61802575107296143 genfib.next()/genfib.next() 0.61803278688524588 genfib.next()/genfib.next() 0.6180338134001252 genfib.next()/genfib.next() 0.61803396316670656 genfib.next()/genfib.next() 0.61803398501735796 genfib.next()/genfib.next() 0.61803398820532507 genfib.next()/genfib.next() 0.61803398867044324

A general thrust of gnu math is to use OO concepts to build awareness of "maths as extended type systems" (class hierarchies if you will). That's a bridge to our Fuller School geometry, as we regard the Tetrahedron as a kind of superclass object or parent, for the whole idea of Polyhedron in general. You have edges, vertices, faces (V + F = E + 2), and an inside and outside. Every subsequent Polyhedron inherits those elements, and the machinery to go with 'em. And we don't have anything simpler. The sphere is actually much more complicated to think about, given its reliance on a continuum hypothesis. The tetrahedron is friendlier to discrete math engines like Python. We don't need some infinitely perfect pi to think about our what's in our tree.[3] If you've followed my rbf.py thread's evolution, you know that it builds on a primitive vector class (of the kind any first year student could write), and face-tuples, to define a vocabulary of primitive prefrequency polyhedra. If I go:

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from rbf import Tetrahedron, Octahedron, Cube mycube = Cube() mytetra = Tetrahedron() myocta = Octahedron()

and then ask for volumes I get:

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mycube.volume 3.0 mytetra.volume 1.0 myocta.volume 4.0

Whereas if you *haven't* been following my rbf.py's thread's evolution, you'll probably just be asking yourself "Why?" at this point. Because that's how we've designed our little zen rock garden in Synergetics.[4] The tetrahedron is unit volume, given it anchors the Polys class hierarchy (introduces the whole idea of an inside versus outside for example). Two tetrahedra, per Kepler's stella octangula, define a Cube of thrice the volume. And that Cube's dual, with edge intersections at 90 degrees, is the Octahedron of volume 4, and anchors our 6-rayed XYZ coordinate system (which, notice, comes somewhere on down the hierarchy tree i.e. the primitive tetra is topological such that no coordinate system machinery need apply). OK, that's a lot of verbiage. You're likely happy I don't flood edu-sig with all these threads. When I'm blabbing about Bucky a lot, I tend to firehose in the direction of some Bucky-friendly e-list, like Synergeo on Yahoo. Or maybe I'm on wittgenstein-dialognet (pretty quiet lately), or just discussing stuff privately among Wanderers (wwwanderers.org). Finally, in addition to Glenn's global matrix, I've been caught up in Sam's and LaJean's scenario. They've been trying to cobble together a website, using a content management system. I've brought this up on edu-sig because I thought it relevant to our community, given Python has one or more of the flagship CMSs out there. We shouldn't over sell them (CMSs) to people who just need static web content and could get by with XHTML/CSS. Client side WYSIWYG tools make it easy to avoid server-side dependence. Unless you're hosting the server yourself, beware of getting captured by your own ISP. However, in the case of flextegrity.com, I think it's turning out OK. They're likely to need those fancy CMS features down the road (implemented in PHP in their case), i.e. it was never all that "static" a design (even though it may have started out that way). Kirby 4D Solutions Portland, Oregon Notes: [1] re 'Titanic' http://mathforum.org/kb/message.jspa?messageID=5055407&tstart=0 [2] Coxeter & 4d: http://controlroom.blogspot.com/2006/08/more-dimension-talk.html [3] More About Pi: http://groups.yahoo.com/group/synergeo/message/28550 [4] rock garden: http://www.grunch.net/synergetics/volumes.html