I'm including the script below, using Python as a calculator, showing off the relatively new Decimal type, mainly to solicit feedback as to whether I'm doing anything really dorky (or that could easily be improved dramatically if I just knew what I was doing more). I don't use this type every day. In lobbying to displace calculators in at least some high school math courses, I need to make it evident to teachers that the bigger more colorful displays are well worth it, even though an advanced TI will do extended precision they tell me. It's still not so easy to take screen prints or to compare (as strings perhaps) with published digit sets (e.g. for pi, e, phi, sqrt(2) -- numbers we care about).[1] However, many math teachers are already converts to the bigger screens, i.e. once they have them, would never go back. Even just having the one up front, thanks to the computer projector, is enough in some classrooms (the 1:1 ratio may be what homework is all about, even in OLPC-ville). So if we're this far along the decision tree (in a computerized math lab, say a TuxLab, running free/libre stuff on commodity hardware) then the next challenge is to tout Python, a scripting language, over say Excel or OpenOffice or that IronPython spreadsheet with Python for cell coding. In Windows world, where Python also runs (on Tk in IDLE if you want the GUI, or on ActiveState's or Wing's for scholars...), Excel is a gravity well for many math teachers, or should I say black hole (they never re-emerge)? Does Excel harness IEEE extended precision? I know Mathematica does. For context: The appended script is a fragment of Martian Math where we take a tetrahedral pizza slice out of a spherical pizza (messy analogy) and weigh it (compute its volume). The 120 slices have identical angles, so all have the same volume for a given h (height), the scale factor built in to all the six linear dimensions (the six edges of each pizza slice). I'm changing the value of h from phi/root2 -- where the pizza weighs in at 7.5 -- to a different value (or vice versa), where the pizza weighs in at volume 5. Given this is Martian Math, there's the little matter of needing a conversion factor (syn3) to escape the Earthlings' worshipful fixation on unit-volume cubes (what keeps 'em retarded -- Martian Math is somewhat counter-culture (= counter-intelligence)). Our canonical Martian Math rhombic dodecahedron has a volume of six and has radius 1 i.e. inscribes each ball in a CCP ball packing (same as FCC, the ~0.74 maximum density possible in ordinary space). The volume 5 rhombic triacontahedron (investigated below) is a different animal (different zonohedron) but there's a bridge in that our T, A and B modules all have the same easy volume of 1/24. The latter two (A&B) build the primitive space-filler (i.e. the Mite, pg. 71 Regular Polytopes by Coxeter)) as well as said rhombic dodecahedron (also canonical cube (vol 3), octahedron (vol 4), tetrahedron (vol 1), cuboctahedron (vol 20) etc.). Probably more than you wanted to know, the kind of stuff I've encoded in my rbf.py for those wishing to explore our digital math track in more depth.[2] Kirby Urner Oregon Curriculum Network 4dsolutions.net isepp.org (board) python.org (voting member) wikieducator (wikibuddy) [1] http://mail.geneseo.edu/pipermail/math-thinking-l/2009-November/001329.html (suggesting high precision explorations, ala fractals, as integral to digital math track (DM)) [2] http://www.4dsolutions.net/ocn/cp4e.html --

...

...

from mars import math http://www.wikieducator.org/Martian_Math

=== Python v. 2.6 === from decimal import Decimal, getcontext getcontext().prec = 31 # whole numbers d1,d2,d3,d4,d5,d6 = [Decimal(i) for i in range(1,7)] # fractions dthird = d1/d3 dhalf = d1/d2 # surds droot2 = d2.sqrt() droot5 = d5.sqrt() # constants # http://www.rwgrayprojects.com/synergetics/s09/figs/f86210.html syn3 = d3/pow(droot2, d3) # tetravolume:cubevolume phi = (d1 + droot5)/d2 # golden ratio def tvolume(h): # http://www.rwgrayprojects.com/synergetics/s09/figs/f86411a.html # http://www.rwgrayprojects.com/synergetics/s09/figs/f86411b.html AC, BC, OC = ((h/d2) * (droot5 - d1), (h/d2) * (d3 - droot5), h) base = dhalf * (AC * OC) return dthird * base * BC # T module (1/120th of volume 5 rhombic triacontahedron) h = (phi/droot2) * pow(d2/d3, d1/d3) tvol = tvolume(h) print "T Module" print "T in tetravolumes: ", tvol * syn3 print "Rh Triacontrahedron: ", 120 * tvol * syn3 # E module (1/120th of rhombic triacontahedron with radius 1) h = d1 evol = tvolume(h) print "E Module" print "E in tetravolumes: ", evol * syn3 print "Rh Triacontrahedron: ", 120 * evol * syn3 # K module (1/120th of volume 7.5 rhombic triacontahedron) h = phi/droot2 kvol = tvolume(h) print "K Module" print "K in tetravolumes: ", kvol * syn3 print "Rh Triacontrahedron: ", 120 * kvol * syn3