Mailman 3 April 2010 - Edu-sig

Radical Math: debugging help?
by kirby urner April 13, 2010

April 13, 2010

Below is current source for ch.py, a module for exploring volume relationships starting with a "ground state" (a default) known as the concentric hierarchy of polyhedra. The user begets various polyhedra from their class definitions, then resizes them at will, perhaps using the * operator in place of the scale method: >>> import ch >>> rt = ch.R_Triac() >>> rt.volume 7.5 >>> rt = rt * pow(2/3., 1/3.) DEBUG: a star is born: a new R_Triac >>> rt.volume 5.0000000000000009 >>> rt.edge 0.61771467052713269 >>> rt = ch.R_Triac() >>> rt.edge 0.70710678118654757 >>> rt.edge_name 'long face diagonal' The concentric hierarchy is formed from the five Platonics, a primitive set that is closed under the operation of "make my dual". When the duals combine, e.g. the tetrahedron with itself, you have the option to intersect the edges so as to form yet another polyhedron (not necessarily Platonic). Here's what you can do with the five Platonics in that regard (i.e. o + o.dual == something). tetrahedron + tetrahedron == cube octahedron + cube == rhombic dodecahedron icosahedron + pentagonal dodecahedron == rhombic triacontahedron There's some question as to how to scale these relative to one another, when defining a ground state. The tetrahedron, cube, octahedron and rhombic dodecahedron all have obvious volume relationships if you start in this way. Anyway, here's my puzzle: I'm using Python 2.6, but my call to Poly.__init__ within its subclasses would surely be more stylish where super() used instead. However, all my trials with super(), have so far resulted in errors. If you fix this and even provide a clear explanation as to how this fix works, you might become part of a famous inner circle. The concentric hierarchy is poised to take the world by storm, at least in NCTM circles. Here's a lesson plan I've been touting. http://www.bfi.org/our_programs/bfi_community/synergetics (follow link to NCTM web site) Kirby PS: all the dual combos are rhombohedra i.e. have rhombic faces. You may criss-cross these diamond faces to get tri-rectangular tetrahedral wedge shapes that include the center point. In the case of the cube and rhombic dodecahedron, one gets the same shape, called a Mite in this namespace (for "minimum tetrahedron" -- it's a space-filler). In the case of the rhombic triacontahedron, one gets the T-module (T for triacontahedron). Provided our scaling is done right, 3 * T = Mite (volumetrically speaking). I will be adding these in a next edition. My thanks to David Koski for technical assistance on this project. *====== ch.py ====== from math import sqrt as radical phi = (1 + radical(5))/2 class Poly: def __init__(self, edge = 1, edge_name = "edge", volume = 1, greekname = "Tetrahedron"): self.edge = edge self.edge_name = edge_name self.volume = volume self.greekname = greekname def scale(self, scalefactor): edge = self.edge * scalefactor # edge unbound to self volume = self.volume * pow(scalefactor, 3) # likewise volume print("DEBUG: a star is born: a new %s" % self.__class__.__name__) return self.__class__(edge = edge, edge_name = self.edge_name, volume = volume, greekname = self.greekname) __mul__ = __rmul__ = scale # e.g. tetra = tetra * 3 def __repr__(self): return "Polyhedron of type %s (vol: %s)" % (self.greekname, self.volume) class Tetra( Poly ): pass class Cube( Poly ): def __init__(self, edge = 1, edge_name = "face diagonal", volume = 3, greekname = "Hexahedron"): Poly.__init__(self, *(edge, edge_name, volume, greekname)) class Octa( Poly ): def __init__(self, edge = 1, edge_name = "edge", volume = 4, greekname = "Octahedron"): Poly.__init__(self, *(edge, edge_name, volume, greekname)) class R_Dodeca( Poly ): def __init__(self, edge = 1, edge_name = "long face diagonal", volume = 6, greekname = "Rhombic dodecahedron"): Poly.__init__(self, *(edge, edge_name, volume, greekname)) class R_Triac( Poly ): def __init__(self, edge = radical(2)/2, edge_name = "long face diagonal", volume = 7.5, greekname = "Rhombic Triacontahedron"): Poly.__init__(self, *(edge, edge_name, volume, greekname)) class Icosa ( Poly ): def __init__(self, edge = 1, edge_name = "edge", volume = 5 * phi**2 * radical(2), greekname = "Icosahedron"): Poly.__init__(self, *(edge, edge_name, volume, greekname)) class Cubocta ( Poly ): def __init__(self, edge = 1, edge_name = "edge", volume = 20, greekname = "Cuboctahedron"): Poly.__init__(self, *(edge, edge_name, volume, greekname))

1 2

[ANNC] pynguin-0.7 (python turtle graphics application)
by Lee Harr April 13, 2010

April 13, 2010

Pynguin is a python-based turtle graphics application. It combines an editor, interactive interpreter, and graphics display area. It is meant to be an easy environment for introducing some programming concepts to beginning programmers. http://pynguin.googlecode.com/ This release changes the method of starting and stopping the separate code-running threads. It should be much less susceptible to lock-ups and crashes, though I am still experiencing occasional problems. Pynguin is tested with Python 2.6.4 and uses PyQt (4.6) for its GUI elements. Pynguin is released under GPLv3. Changes in pynguin-0.7: - fixed deadlock when running with many pynguins at instant speed - new threading model greatly reduces problems with lock-ups - added more multi-pynguin examples - added commands turnto('random') and lineto('random') - added more random color possibilities ('rlight', 'rmedium', 'rdark') - allow named colors and html-style colors - added command clear() - added equation plotting examples - cartesian and polar - re-center on (0, 0) when moving view splitter - added svg/pdf worksheets Changes in pynguin-0.6: - fixed crash when using new_pynguin() - fixed possible crash during startup (due to race condition) - added goto('random') and xy() to easily get coordinates - added keyword args for fill -- fill(color=..., rule=...) - added easier access for fillcolor 'random' - added examples using multiple pynguins - remove any added pynguins when using reset() - set window title when using Save As... - better error messages when loading file with errors - whitespace cleanup when saving files - render About image and title at runtime - more examples Changes in pynguin-0.5: - catch errors when processing graphic move queue - capture and hold stdout and stderr - call str() on argument to write - guard against sending non-int to color _________________________________________________________________ Hotmail: Trusted email with Microsoft’s powerful SPAM protection. https://signup.live.com/signup.aspx?id=60969

3 5

Re: [Edu-sig] Why Python?
by chris＠seberino.org April 12, 2010

April 12, 2010

On Sun, Apr 11, 2010 at 09:51:48PM -0400, calcpage(a)aol.com wrote: > As a Computer Science teacher, I am used to teaching my students a > number of introductory languages before they get to AP CS. I am never > satisfied with just one approach. I am going to dump all that in favor > of python next year. So, if Computer Science teachers end up using > python, I will be in the odd position of teaching only python for 2 > years of High School. You know, that wouldn't be all bad, my students > would then have a lot more experience with python before the AP exam. > As a Math teacher, this scenario is also appealing as I would have more > time fo math topics too (Discrete Math or Pythonic Math)! Jorge I've enjoyed your comments on AP Calc list and now here. Ever heard of Teach Scheme/Reach Java (http://http://www.teach-scheme.org)? I like the idea of starting the AP CS year with a clean language and then "reaching" or finishing with Java. I wonder if AP CS with Python and Java would be ideal. Ideally we would have the same kids for a few years so that we could really sail in math classes with kids that know Python fairly well. cs

2 1

Re: [Edu-sig] Why Python?
by Daniel Ajoy April 12, 2010

April 12, 2010

On Sun, 11 Apr 2010 21:51:16 -0500, <edu-sig-request(a)python.org> wrote: >>> Likewise, an introductory computer language should be >>> close to self-explanatory. ?It will be difficult to get math and science >>> teachers to accept it, if they have to make extra efforts explaining the >>> notation. ?Getting math and science teachers to accept computation as a >>> vital part of their curricula is my current focus, so I wouldn't try to push >>> something like your example above. > > There are a number of math, science, and Computer Science textbooks in > which APL or J is the math notation throughout, being taught only as > needed without interrupting the main sequence of ideas. I can give you > citations. There is very little done in this manner in any other > programming language. (If you have seen some, please send me the > information.) I much prefer this approach to the usual one of teaching > programming language syntax and semantics in a vacuum, with no > systematic application to anything. I attest to this. Those books use the language as "executable notation". I've been trying to do the same with LogoFE for some time, here for example: http://neoparaiso.com/logo/olimpiada-matematica-nivel-1.html You might notice there is very few procedure definitions. Solutions to problems are simply transformations of inputs into outputs. The process of finding a solution to a problem is simply: showing (printing) the steps that convert the inputs into the solution. Daniel

1 0

~~Hi~~
by Sven De Mol April 11, 2010

April 11, 2010

http://www.srednovekoven-ohrid.com.mk/SX7yJVqiJB.htm

1 0

Confused how teach geometry and importance of teaching geometry in 21st century.
by chris＠seberino.org April 10, 2010

April 10, 2010

I'm teaching high school math to homeschoolers and I'm looking for how to make geometry year meaningful. I'm having a "crisis of confidence" because from my viewpoint, algebra was 10x more useful for future math and science work. The only thing I can remember that was useful from geometry was a few volume and area formulas. That can justify maybe a month but not a whole YEAR of geometry!?!? cs P.S. Yes yes I know that geometry is meant to teach logical reasoning. Maybe one can get that from chess, debate club and other activities as well if not better? People also say geometry is where you learn proofs. Couldn't proofs be just as easily emphasized in all the other math classes? -- _______________________________________ Christian Seberino, Ph.D. Email: chris(a)seberino.org _______________________________________

7 8

Re: [Edu-sig] using Python as a calculator
by Daniel Ajoy April 10, 2010

April 10, 2010

On Sat, 10 Apr 2010 11:23:23 -0500, <edu-sig-request(a)python.org> wrote: > I humbly disagree that this is the right place to start. I teach > students with diverse backgrounds -- some extremely bright and others > really behind in school and using Python as a calculator is one thing > they would all agree is terrifically boring and not so compelling. > How many students have ever said "man, I really wish I had a trig > table right now?" What kind of things do you think kids would find exciting about programming? I've identified these things: Turtle Graphics Sprite Animations Virtual Robot programming Number crunching Make the computer do your homework In "number crunching" I try to collect all the things that excite students about making the computer show its awesome powers of calculation. I think there is an element of excitement in making a program that makes the computer work a lot to produce results. Maybe, that table falls into this category. I have the impression that using a programming language as a calculator is boring, too. But if we use it to help us solve homework I think it becomes interesting. Thinks like, solve: (x + 2) / 10 = 100 to solve do.while [ make "x random 1000 ] [not (:x + 2) / 10 = 100] print :x end solve 998 Daniel

1 0