Mailman 3 October 2001 - Edu-sig

Re: [Tutor] help ;-)
by Danny Yoo Oct. 17, 2001

Oct. 17, 2001

On Tue, 16 Oct 2001, dman wrote: > On Tue, Oct 16, 2001 at 09:56:10AM -0700, Sean 'Shaleh' Perry wrote: > | if this list would block any mail whose subject matched r'^\s*help\s*$'? > | > | Please boys and girls tells us what you need. 'I dont understand > | classes', 'why is python dying', 'help me with my homework because I > | am lazy and just go to school to get a degree to go out and make > | money'. Whatever, just give us something to go on. > > Yeah, I usually ignore messages that just say "help" because I don't > have time to read everything. It the subject doesn't appear > interesting and/or something I know about, I tend to ignore it. [Warning: My post is a personal rant, and has little to do with programming in Python.] Yikes. This is starting to sound like something out of ESR's "How to ask Questions the Smart Way" FAQ: http://www.tuxedo.org/~esr/faqs/smart-questions.html It is sometimes a little demoralizing if we get questions that seem to beg for an answer without showing any effort at trying things out. But it is not unexpected: In the culture of education and knowledge, I feel there's an unhealthy tendency to emphasize "The Answer" at the expense of ignoring what motions or Process that people make toward a goal. Math drills do this. Multiple choice questions do this. The SAT does this. And game shows do this all the time. People in Jeopardy are considered geniuses if they can spit out "questions" at the chime of a buzzer, but that's still, in essence, just another Answer that's disconnected from any real understanding. Perhaps those contestants really do know the ideas behind the facts, or perhaps they're just parroting what they remembered from flash cards. How can one tell? Given a large enough database of facts, perhaps a Python dictionary could outperform Alex Trebek. It's my opinion that the educational culture in the United States does real damage to people by not encouraging people encogh to practicing the Process of discovering things. I feel that, instead, schools encourage the impulse to depend on others for an answer, without asking how or why that answer makes sense with what we already know. It's the path of least friction: it's just easier to lure the "teacher" to give an answer, rather than to discover it for oneself. This feeling seems echoed by John Holt's book, "How Children Fail", but perhaps I'm misinterpreting his words. How does this relate back to programming? I believe computer programming can help make Process important again. What makes programming so much different from other "intellectual" things that people can try out is that Process really does matter. One can't get good at programming without building models of what's going on, or without knowing how to ask good questions. When I learned programming, few teachers really knew how to program --- I couldn't depend on my teachers for an Answer, although I could ask them for suggestions on resources that could help me. Nor could I depend solely on reading books, because it was unlikely I could copy an exact answer in the back. But I could combine what I read about books, try interactive experiments with the computer, and try to build some sort of model that would solve what I was looking for. Programming made creativity and invention important again. And even if I couldn't figure out how exactly to solve a problem, I learned how to make things less confusing for myself. I have to admit, though, that I was a little lonely, not to be able to talk to other people about this crazy stuff about circular linked lists or binary arithmetic. I'd better tie this rant somehow with what was discussed earlier... > | Please boys and girls tells us what you need. 'I dont understand > | classes', 'why is python dying', 'help me with my homework because I > | am lazy and just go to school to get a degree to go out and make > | money'. Whatever, just give us something to go on. I agree that it would be nice if people put more effort in, but I think that this was a little rough. Quite a few people who are on Tutor are new at this "programming" sort of thing. Programming is different, alien, and unfamiliar enough that I think some liberties should be given to people who have just started something new. It takes time to break out bad habits, but the fact that people are actually talking to us, complete strangers, about things that aren't part of a standard school curriculum (yet), is a step in the right direction. Let's try to make sure people know that they are welcome here, and that we will do what we can to make it less intimidating.

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PyGeo prensentation
by arthur.siegel＠rsmi.com Oct. 16, 2001

Oct. 16, 2001

Proud to note that I will be giving a presentation of PyGeo to a portion of the math faculty/students at PolyTechnic University in NY tomorrow evening. Their interest is in assessing its usefulness for the dynamic illustration of curriculum material. The professor who arranged the "event" shares my geometric interests, and I think correctly assesses that PyGeo has features relevant to geometric teaching not otherwise available. Hopefully another small step toward Python in the classroom. Art

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re: Real world simulations
by Arthur Siegel Oct. 16, 2001

Oct. 16, 2001

Tim, Have you checked out the VPython demos. http://virtualphoton.pc.cc.cmu.edu/projects/visual/ The visual element is a wonderful motivator, IMO. Art >everyone, >Has anyone used simulation-type problems in an introductory programming >class? I'm trying to avoid overly contrived, typical CS class projects in my >course. Since I'm a science teacher too I think it would be great to sneak a >little science past them while they learn programming. Any ideas? >-Tim

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Real world simulations
by Timothy Wilson Oct. 16, 2001

Oct. 16, 2001

Hi everyone, Has anyone used simulation-type problems in an introductory programming class? I'm trying to avoid overly contrived, typical CS class projects in my course. Since I'm a science teacher too I think it would be great to sneak a little science past them while they learn programming. Any ideas? -Tim -- Tim Wilson | Visit Sibley online: | Check out: Henry Sibley HS | http://www.isd197.org | http://www.zope.com W. St. Paul, MN | | http://slashdot.org wilson(a)visi.com | <dtml-var pithy_quote> | http://linux.com

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Re: [Tutor] Intro to CS (boolean.py)
by Kirby Urner Oct. 16, 2001

Oct. 16, 2001

At 05:39 PM 10/14/2001 -0700, Danny Yoo wrote: >Hi Kirby, > >I've written a small "propositional logic" parser class that you might >find useful: > > http://hkn.eecs.berkeley.edu/~dyoo/python/propositions/ > >I wrote it as an experiment with the Spark parser-generator a month ago. I >haven't been working on it for a while now, and you're welcome to use the >parser if it's useful for you. Impressive stuff Danny, as well as your plans for future features :-D. I don't see 0.3 up yet, but this is a thread I'd like to track. There could be some fun curriculum written around here. Kirby

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PythonCard and turtle geometry
by Kevin Altis Oct. 15, 2001

Oct. 15, 2001

PythonCard http://pythoncard.sourceforge.net/ AFAIK still has the most complete turtle geometry routines for Python, though Guido's turtle.py included with Python is fine if you're using tkinter. I think Guido experimented with the PythonCard turtle, so maybe he can chime in on what he liked and disliked and what improvements he would like to see. There are over twenty scripts included with the turtle sample, the docs directory even includes documentation on Logo commands and the most important issues to be aware of while converting old Logo programs to Python. You can have as many turtles as you want, each is independent, so you should be able to do artificial life experiments similar to what is possible with Starlogo. You can drive the turtle from the shell which has command-completion as well as toolTips for all of the turtle commands. There are screen shots at: http://pythoncard.sourceforge.net/samples2.html I've brought up the the turtle library before on this list, but didn't get much feedback, so I assumed there wasn't any interest. Turtles are fun, so I'm happy to work on this part of PythonCard. I would love to get feedback from people interested in using the turtle library with PythonCard. Note that there is an abstract turtle class, which is suitable for making a tkinter, wxPython, PostScript or serial-port based turtle, say for driving a Legos robot. The abstract turtle api will be improved along with the PythonCard turtle api depending on user demand. In fact, on a related note, in preparation for making SciPy and PythonCard more integrated (SciPy already works with PythonCard and the PyCrust shell) I'm integrating the turtle directly into the PythonCard framework. I posted a message to the list about this last night: http://aspn.activestate.com/ASPN/Mail/Message/PythonCard/802606 The latest release version of PythonCard is always at: http://sourceforge.net/project/showfiles.php?group_id=19015 PythonCard requires Python 2.1 or higher and wxPython 2.3.x, and yes I bug Robin regularly about the Mac port. ka --- Kevin Altis altis(a)semi-retired.com

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boolean expression
by Marc Keller Oct. 14, 2001

Oct. 14, 2001

A variation on your Boolean module, leaving Python evaluates boolean expressions, with local names as arguments: def bin(num,nbits=0): b, q = '', num while q !=0 or nbits > len(b): b, q = `q&1 > 0` + b, q>>1 return b def domainBool(n): return [tuple(map(int,tuple(bin(x,n)))) for x in range(2**n)] def truth(expr,*args): n = len(args) print n*'%s '%args+'|',expr print n*'=='+'|='+len(expr)*'=' locals = {} for v in domainBool(n): for i in range(n): locals[args[i]] = v[i] print n*'%d '%v+'|',center(str(eval(expr,locals)),len(expr)) Examples >>> truth('not a','a') a | not a ==|====== 0 | 1 1 | 0 >>> expr = "(a and not b) or c" >>> truth(expr,'a', 'b', 'c') a b c | (a and not b) or c ======|=================== 0 0 0 | 0 0 0 1 | 1 0 1 0 | 0 0 1 1 | 1 1 0 0 | 1 1 0 1 | 1 1 1 0 | 0 1 1 1 | 1

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Re: quadratic functions
by Kirby Urner Oct. 13, 2001

Oct. 13, 2001

On Fri, 12 Oct 2001 12:08:13 -0700, I wrote: >And is there a more general expression for > > n > f(n,c) = SIGMA k^c = some polynomial of degree c+1 ? > k = 1 > > >The answer to the 2nd question is yes, and the Bernoulli numbers >give us the coefficients of such a c+1 degree polynomial. Just to spell that out at the command line, what we're looking for is a closed form expression for the sum of consecutive integers all to the cth power. What we expect is some polynomial of degree (c+1) with rational coefficients in which the Bernoulli numbers figure (as fractions). So, for example, what is 1^4 + 2^4 + 3^4 + 4^4... n^4? An easy function just does the arithmetic in a loop: >>> from operator import add >>> def sum(n,c): return reduce(add,[i**c for i in range(1,n+1)]) Note that range(1,n) generates the list [1,2...n-1], hence the parameter n+1. [i**c for i in range(1,n+1)] is the sequence of terms in list form, and reduce(add, list) simply sums them up. >>> sum(10,4) 25333 That's the sum of the first 10 natural numbers to the 4th power. Bernoulli got his numbers from Johann Faulhaber, who wrote about this series in 1631.[1] With this series, Bernoulli could brag about how quickly he could get the sum of the 10th powers of the first 1000 natural numbers. Using our sum function: >>> sum(1000,10) 91409924241424243424241924242500L (the L means 'long integer' -- it'll be dropped in later versions of Python, as the integer types become more seamless). But Bernoulli was using a polynomial: >>> summa(10) (1/11)*x**11 + (1/2)*x**10 + (5/6)*x**9 - x**7 + x**5 - (1/2)*x**3 + (5/66)*x The coefficients above aren't naked Bernoulli numbers; they're folded into products which also involve choice(n+1,k), where k is the kth term. kth coefficient = b[k]*choice(n+1,k) (b[k] = kth bernoulli) ------------------ n+1 Given x=1000, the powers are easy to compute. summa(10) returns a polynomial object into which we can substitute a value using p() syntax i.e.: >>> p = summa(10) >>> p(1000) 91409924241424243424241924242500 Let's look at the first 10 bernoullis: >>> bernseries(10) [1, (1/2), (1/6), 0, (-1/30), 0, (1/42), 0, (-1/30), 0, (5/66)] Not so bad. The odd ones become 0 after the 0th, 1st, 2nd. The Bernoulli numbers get pretty crazy (see below) and difficult to compute by hand after the first few. But our computer algorithm, using the Fraction object, is up to the task. Let's ask for the 100th Bernoulli number: >>> bern(100) (-94598037819122125295227433069493721872702841533066936 133385696204311395415197247711/33330) Wow, that took almost 10 seconds. And it agrees with the result posted here (yay): ftp://ftp.cdrom.com/pub/gutenberg/etext01/brnll10.txt We calculate successive bernoullis using Pascal's Triangle. The bernseries algorithm will show how this works if passed a non-zero "show" parameter (2nd argument): >>> bernseries(4,1) b[1] = (1/2) * (1) b[2] = (1/3) * (3*b[1]- 1) b[3] = (1/4) * (6*b[2] - 4*b[1]+ 1) b[4] = (1/5) * (10*b[3] - 10*b[2] + 5*b[1]- 1) [1, (1/2), (1/6), 0, (-1/30)] Those'd be the bernoullis used to compute the sum of consecutive integers to the 4th power. The corresponding 5th degree polynomial: >>> summa(4) (1/5)*x**5 + (1/2)*x**4 + (1/3)*x**3 - (1/30)*x And the result for x = 10? >>> p = summa(4) >>> p(10) 25333 That agrees with our earlier answer. n And note we get the earlier formula for SIGMA k^2 k = 1 >Well, you have metal cluster experiments, written up in >Scientific American (Dec 1998), about agglomerations of atoms ^^^^ 1997 >in icosahedral form transforming into cuboctahedra.[1] How many >atoms in all? These formula will tell you. So how do we do the total number of spheres in a cuboctahedron again? I posted quite a bit about this over on math-teach awhile ago. For each layer, you've got the six squares and 8 triangles, but then you have shared edges and vertices, so adding all the squares and triangles involves double-counting edge spheres and quadruple counting the vertices. The number of edge spheres is 24 * (n-2) and the number of vertices is 12 (see http://www.inetarena.com/~pdx4d/ocn/urner.html for a graphic). So 8*n(n+1)/2 + 4*n^2 - 24*(n-2) - 3*12 should be it. That simplifies to: 10*n^2 - 20*n + 12. This works for n>=2, i.e. a cuboctahedron with 2 spheres along an edge has 12 spheres in that layer, with 3 spheres along an edge has 42, then 92, then 162 and so on (icosahedral shells the same, as per the jitterbug transformation: http://www.inetarena.com/~pdx4d/ocn/numeracy0.html ). What we want is a cumulative number of spheres in all layers. In other words: n 1 + SIGMA (10k^2 - 20k + 12) k=2 the 1 being the nuclear sphere. n 10 SIGMA k^2 = 10 [(1/3)*n^3 + (1/2)*n^2 + (1/6)*n) - 1] k=2 n 20 SIGMA k = 20 [n(n+1)/2 - 1] k=2 n 12 SIGMA 1 = 12[n - 1] k=2 Combining and simplifying gives: Cubocta(n) = (10/3)*n^3 - 5*n^2 + (11/3)*n - 1 (remember to add 1 in front of all the SIGMA terms). Making this a function: >>> def cubocta(n): return int((10/3)*n**3 - 5*n**2 + (11/3)*n - 1) >>> map(cubocta,range(1,11)) [1, 13, 55, 147, 309, 561, 923, 1415, 2057, 2869] That's the first 10 cuboctahedral numbers. Citation: http://www.research.att.com/cgi-bin/access.cgi/as/njas/sequences/eisA.cgi?A… ========= ID Number: A005902 (Formerly M4898) Sequence: 1,13,55,147,309,561,923,1415,2057,2869,3871,5083,6525,8217, 10179,12431,14993,17885,21127,24739,28741,33153,37995,43287, 49049,55301,62063,69355,77197,85609,94611,104223,114465, 125357,136919,149171 Name: Centered icosahedral (or cuboctahedral) numbers, also crystal ball sequence for f.c.c. lattice. Comments: Called "magic numbers" in some chemical contexts. References S. Bjornholm, Clusters..., Contemp. Phys. 31 1990 pp. 309-324. T. P. Martin, Shells of atoms, Phys. Reports, 273 (1996), 199-241, eq. (2). B. K. Teo and N. J. A. Sloane, Magic numbers in polygonal and polyhedral clusters, Inorgan. Chem. 24 (1985), 4545-4558. Links: J. H. Conway and N. J. A. Sloane, Low-Dimensional Lattices VII: Coordination Sequences, Proc. Royal Soc. London, A453 (1997), 2369-2389 (pdf, ps). Formula: (2*n+1)*(5*n^2+5*n+3)/3. Maple: A005902:= n -> (2*n+1)*(5*n^2+5*n+3)/3; ========= Kirby PS: Source code for bernoulli.py is at the Oregon Tips website, along with the mathobjects package upon which it depends: http://www.oregon-tips.org/ [1] See John H. Conway, Richard K. Guy, 'The Book of Numbers' (Springer-Verlag, 1996) p. 106-109 re Faulhaber and Bernoulli numbers.

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Review of Some Math-Through-Programming Themes
by Kirby Urner Oct. 13, 2001

Oct. 13, 2001

Review of Some Math-Through-Programming Themes by K. Urner, Oct 12, 2001 My suggestion to curriculum writers has been to return to the front pioneered using BASIC and Logo: integrate the teaching of paper and pencil algorithms with the coding of same in some computer language, so that students reap the benefits of contemporary engineering. Once programming enters the picture, I prefer a general purpose computer language to a calculator language, as these latter don't supply as broad a foundation in programming, plus the development environment is cramped. I've advocated using this approach starting around 8th grade to learn math concepts by building math objects. This is a sort of hands-on approach, suggestive of shop class or labs, wherein we actually construct gizmos which embody our understanding of the relevant ideas. A first object we might construct is the Fraction object. I emphasize "object" because, unlike with the Logo or BASIC languages of the 1980s, we're now in a position to introduce students to a later programming paradigm, that of objects. This doesn't have to be considered "advanced" -- it's just a paradigm. Newcomers to programming might start with classes and objects just as new users of telephones might start with a wireless unit. The object-oriented approach turns out to be especially handy in mathematics learning, as it often allows us to keep our syntax relatively close to that of the traditional text book notations. For example, with Fraction objects, symbolized by F, we can add, subtract, multiply, divide, and raise them to powers just as we would integers, i.e. with the direct application of the relevant operators: >>> from mathobjects import Fraction as F >>> F(1,2) (1/2) >>> F(1,2) + F(1,3) + F(3,7) (53/42) >>> F(2,3) * F(1,2) (1/3) >>> F(3,5)**2 (9/25) So what? Don't calculators also allow such expressions using numerators and denominators? Sure, many do. The fun and instructive part is that we coded the Fraction object ourselves, and therefore had to develop our understanding of the role of GCD and LCD in these various operations. We actually "built" the object we're now using in the above, simple, expressions.[1] (Note that we'll use the Euclidean Algorithm (EA) to implement GCD -- we really need to bring this ancient method back into pre-algebra, (later we'll introduce and use the extended version or EEA, which plays a critical role in RSA cryptography)).[2] So now that we have a Fraction object, we'd like to explore other algorithms in which Fractions occur, and which would be tedious and error-prone if figured on pencil and paper. In other words, we want to understand the paper and pencil way of doing things, but then code them so we can do the calculations quickly and reliably. Note that I'm not talking about approximating precise answers with floating point operations in this context. On the contrary, now that we have fraction objects, we're in a position to push beyond what floating point numbers are able to tell us. We'll stay in the realm of purely rational numbers p/q, where p and q are both whole (q nonzero). So far, I've explored and written up three useful topics to which our newly developed fraction object might apply: (1) Continued Fractions (recursion, phi) http://www.mathforum.com/epigone/math-teach/smersmarzand (2) Derangements (more links to combinatorics) http://aspn.activestate.com/ASPN/Mail/Message/edu-sig/788963 (3) Bernoulli numbers (links to Pascal's Triangle) http://www.mathforum.com/epigone/nctm.l/flanghoupah All of the above make use of the Fraction object in ways that would be relatively difficult and tedious with paper and pencil. However, by tackling the algorithms and concepts behind the scenes, we nevertheless gain exposure to important techniques and generalizations, as well as history. The Bernoulli numbers thread provides a segue to another math object, the polynomial. They also make an appearance in the context I recently posted about: figurate numbers, as per the approach taken in 'The Book of Numbers' in Conway and Guy, and posted about by myself under the heading of 'Pool Hall Math' (because we're stacking/packing pool balls).[3] After we build the Fraction and Polynomial objects, and use these to anchor a lot of relevant mathematics, we'll move on the the Vector and Matrix objects (which synergize with the previous objects, e.g. the characteristic polynomial of a square matrix -- which might have fractional coefficients).[4] Finally, we might also develop Polyhedron objects, using the matrix and vector objects as a part of their definition. The generic methods for rotating, translating, scaling a poly go in the superclass definition, while the individual polyhedra are defined as subclasses (this follows a classic OO text book model, except usually the text books stick with planar shapes, which are less beautiful and interesting -- why not use the technology to its fuller potential?). Note: rotation of polyhedra provides a segue to quaternion objects if we like -- another way of implementing rotation.[5] All of this connects back to my 'Trends in Early Mathematics Learning' essay, wherein I envision a greater integration of math education and computer science under the more generic umbrella of "numeracy".[6] Kirby [1] Tutorial on developing a Fraction object using the Python language, posted to math-learn: http://www.mathforum.com/epigone/math-learn/starcrumderm [2] Euclidean Algorithm http://www.mathforum.com/epigone/math-learn/vultingsheld http://www.mathforum.com/epigone/nctm.l/sangjalskeld [3] Pool Hall Math http://www.mathforum.com/epigone/nctm.l/ningdimfrimp [4] Characteristic polynomials using mathobjects http://aspn.activestate.com/ASPN/Mail/Message/580745 [5] 'Getting Inventive with Vectors' (CP4E 4-part essay) http://www.inetarena.com/~pdx4d/ocn/numeracy1.html [6] 'Trends in Early Mathematics Learning: Beyond Y2K' http://www.inetarena.com/~pdx4d/ocn/trends2000.html

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Re: [Edu-sig] Logo in Python
by Chris Meyers Oct. 12, 2001

Oct. 12, 2001

>There seems to be a lot of interest in recreating a Logo-like environment >in Python. I keep seeing people re-doing this (I've re-done it myself). > >Is there any interest in joining forces to build something or at least bounce >ideas around? > Sure. Although we probably want to make sure we're talking about the same thing. Starlogo, a spinoff of Logo, is a language described in the book Turtles, Termites and Traffic Jams (Resnick, MIT) for writing massively parrallel programs. A good example is the program where ants find food and bring it back to the nest. I'm not trying to recreate the language, just make a set of base classes that provide all of the common functionality for turtles, patches and an observer. You would subclass these for your particular program. This is only my first idea and I've got just a couple of days work into it. I'm happy to pass the code around (let me make it work first!) and would enjoy hearing other ideas too. Thanks, Chris

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