2009/9/27 kirby urner <kirby.urner@gmail.com>: This isn't the kind of critique most people have in mind when they

start questioning the hegemony of the graphing calculator empire.

Definitely not, but what a great perspective, pun intended. - Michel 2009/9/27 Charles Cossé <ccosse@gmail.com>:

...

Hi, this has probably been discussed to death already, but maybe not: The point at which fancy graphing calculators become "necessary" (ie as in one's student career) is the point at which the calculator should be abandoned and Python employed. Just a thought ... delete at will !

-Charles

Hi Charles --

Yeah, that's not controversial as far as I'm concerned, like duh (meaning I agree with you 100%, doesn't everyone?).

For the humanities trained, I have this deep level criticism about how the XYZ coordinate people ala Descartes and so on, failed to think enough about the point of view, i.e. the camera position.

There's this convention of positive x-axis coordinates going off to the right, but of course if your camera is on the other side of the textbook page, so to speak, looking back, then the very same positive axis is off to your left (unless you're standing on your head, relative to the starting position). All this stuff becomes more clear when you run a ray tracing system and actually need to specify the camera position.

Then you come to realize that XYZ has a handedness, that both left and right handed make sense. Current high school textbooks may make lip service reference to that fact, but students rarely appreciate handedness as their spatial geometry abilities are artificially stunted by the graphing calculator curricula which are disappointingly and narrow-mindedly flatlander (landlubbery).

This isn't the kind of critique most people have in mind when they start questioning the hegemony of the graphing calculator empire. It resonates more with art historians, design scientist engineers etc., looking for ways to point out shortcomings in the current "analog math" pipeline (easy as shooting ducks in a barrel (sorry for the violent imagery, diversity panel watching over my shoulder sometimes)).

Here in Oregon, we're working on digital math. We have Intel, other companies, who think every school deserves a real math lab with lots of flatscreens and foss. It's economically self-serving to think this way, but then a lot of our students are interested in being gainfully employed in as silicon foresters, so it's self-serving for them to agree with us (same economy, duh).

Kirby

...

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-- "Computer science is the new mathematics." -- Dr. Christos Papadimitriou

There's this option too, some others: http://matplotlib.sourceforge.net/ Then Sage actually has 3D stuff too e.g.: sage.plot.plot3d.platonic.cube(center=(0, 0, 0), size=1, color=None, frame_thickness=0, frame_color=None, **kwds) to render a 3D cube centered at the origin with default side lengths 1 (how very retro Cartesian eh?). As a vendor of curriculum products (including workshops, other gigs) I'm up front about my suspicion of calculators, not the technology so much as the curricula built around them. Lazy and complacent are the two words that come to mind. Not something you'd wish on your own children. Kirby 2009/9/28 Charles Cossé <ccosse@gmail.com>:

Yup, similar experience here.  And graphing calculators have now been promoted to the point where their importance is probably no longer questioned ... which is too bad ...

There are many ways to graph python-generated computer data.  I have dabbled with many, but for various reasons I continue to use the best one I've ever found: NPLOT.  If you haven't heard of NPLOT it would not surprise me. NPLOT is a Fermilab product, developed about 12 year ago.  It is written in C.  It is a beautiful thing and allows interactive, dynamic exploration of multi-column (aka "ntuple") data in many different representations.

You can download nplot from ftp://ftp.fnal.gov.  It only runs on Linux.  If you are a teacher using Linux and Python then you might very well love what NPLOT can do.  At the heart of it are some very powerful graphing widgets. Your python program just needs to write tab-separated columns of data and NPLOT will read it no problem.  If anyone tries this and needs help, feel free to contact me ... I've used this product extensively for years.  Lots of sample code I could provide.

Anyway, Python + Nplot = GreatAlternativeToGraphingCalculator.

-Charles

2009/9/28 Brian Blais <bblais@bryant.edu>

...

On Sep 27, 2009, at 19:38 , Charles Cossé wrote:

Hi, this has probably been discussed to death already, but maybe not: The point at which fancy graphing calculators become "necessary" (ie as in one's student career) is the point at which the calculator should be abandoned and Python employed.  Just a thought ... delete at will !

Just a month ago, a friend of mine who homeschools her children was asking me about graphing calculators.  Apparently the math curriculum she uses has a number of graphic calculator exercises.  My advice was to buy a nice solar-powered scientific calculator (for $15 at Target), but to ignore the graphing calculator entirely.  Her kids should do the exercises by hand, on graph paper instead.  Anything that is hard enough for you to use a graphic calculator can be done much more easily with a computer. After giving her this advice (which I still stand by), I was thinking about my own experience.  I was going through high school when the first graphic calculators came out, and I had one Junior and Senior year and through college.  I loved to program it, and I loved the big screen where I could see and edit expressions.  However, as I think about it, I can not think of a single problem where I *needed* the graphic calculator, or where it gave me more insight than I could do by hand.  It was a fun toy, but not the best tool.

bb

-- Brian Blais bblais@bryant.edu http://web.bryant.edu/~bblais

-- AsymptopiaSoftware|Software@theLimit          http://www.asymptopia.org

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On Mon, Sep 28, 2009 at 12:18 PM, Jeff Rush <jeff@taupro.com> wrote: << trim >>

My hobby in high school was (simple forms of) relativity and orbital mechanics due to a strong SF interest, so the first program I ever wrote was a time dilation graphing (using punctuation characters) program for trips to nearby stars.  I still have it somewhere on teletype paper and punch tape.  Along the way I lost interest in physics and found the computer far more interesting because it could actually do stuff that changed people's lives without a grant and committee approval. :-)

-Jeff

Speaking of orbital mechanics, this module depending on Visual Python and Python 2.x (x >= 5) uses various complex number techniques to move balls in circles, including a moon around a planet. The sun appears to get bigger and smaller as the default VPython view strives to adjust the frame automatically, which in this case causes some auto-zooming. There's a setting for this, part of the tweakable scaffolding. http://www.4dsolutions.net/ocn/python/orbits.py Of course this teaches about complex numbers, not about gravity wells so much. However, in the animation business, such short cuts are sometimes acceptable as its the special effect you're after, not trying to write a simulator or physics engine per se (don't that we don't have those too in some settings). Kirby """ By Kirby Urner, 4D Solutions, Portland, Oregon (copyleft) 2006 Last revised by the original author: 14 Nov 2006 (added Moon class) Complex numbers provide machinery for rotating in the XY plane, where the Y axis is "imaginary", the X axis "real". When two complex numbers multiply, their magnitudes are multiplied (think of vectors) while their angles get added. By keeping the magnitudes = 1, we focus on the angles. A scale factor applied afterwards can change the radius of the orbit. Or we may use the fact that e**(theta*complex(0,1)) takes us around in a circle. This 2nd technique shows up in a Planet class, easiest for having multiple balls, each with its own radius, color, increment, size of orbit. Since visual is expecting three floating points (x,y,z) for position, we use c.real and c.imag to break c into two floating point numbers for plotting purposes. """ import cmath import math from visual import * def orbit1(): """ multiply clock hand by a one degree incrementer """ m = complex(1,0) # vector pointing to 3 o'clock angle = math.radians(1.0) # normalized to unit radius (clock diameter = 2) onedegree = complex(cos(angle), sin(angle)) theball = sphere(pos = (m.real, m.imag), radius = 0.1, color = color.red ) while True: m = m * onedegree # multiplying causes rotation theball.pos = (m.real, m.imag) rate(100) def orbit2(): """ use e**(theta * i) to get coordinates of rotating ball cmath.exp handles a complex number """ onedegree = math.radians(1.0) i = complex(0,1) angle = 0 theball = sphere(pos = (1,0,0), radius = 0.1, color = color.green ) while True: angle += onedegree coords = cmath.exp(angle * i) theball.pos = (coords.real, coords.imag) rate(50) class Planet (object): # subclassing object gives a 'new style' class """ Orbit around (0,0,0) by increment (degrees) per each move invocation """ def __init__(self, distance=1.0, radius=0.1, increment=1, color = color.red): self.pos = (1.0, 0.0, 0.0) self.distance = distance self.radius = radius self.color = color self.theball = sphere(pos = self.pos, radius = self.radius, color = self.color) self.increment = math.radians(increment) self.angle = 0 def move(self): self.angle = self.angle + self.increment coords = cmath.exp(self.angle * complex(0,1)) self.coords = (coords.real * self.distance, coords.imag * self.distance) self.theball.pos = (self.coords[0], self.coords[1]) class Moon(Planet): """ Orbit around planet (1st argument) by increment (degrees) per each move invocation """ def __init__(self, planet, distance=1.0, radius=0.1, increment=1, color = color.red): super(Moon,self).__init__(distance, radius, increment, color) self.planet = planet def move(self): self.angle = self.angle + self.increment coords = cmath.exp(self.angle * complex(0,1)) self.coords = (coords.real * self.distance + self.planet.coords[0], coords.imag * self.distance + self.planet.coords[1]) self.theball.pos = (self.coords[0], self.coords[1]) def solarsystem(): sun = Planet(distance = 0, radius = 0.8, color = color.yellow) p1 = Planet(distance=6.0, radius=0.3, increment=0.5, color = color.green) p2 = Planet(distance=4.0, radius=0.1, increment=1.0, color = color.red) m1 = Moon(p1, distance = 1.0, radius = 0.1, increment = 3.0, color = color.cyan) while True: p1.move() p2.move() m1.move() rate(50)

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<< trim >>

Well, the curricula have been customized to fit what the calculator can do, with encouragement towards the more upscale models that do some graphing and CAS (fractor equations, solve integrals...).  A lot of what passes for "math" in this day and age is just a glorified calculator, your tax dollars at work to promulgate a niche market of private sector interests -- think defense contracting, same diff.

Meant to say glorified "calculator manual" -- a lot of textbooks actually sell themselves into the private sector by inserting many pages on how to operate this or that name brand model, a form of prostitution given this isn't free software and the school district could just as well supply no-name hand-me-down computers from other government bureaucracies (what Winterhaven PPS did before getting a $10K grant for all that Apple equipment). Winterhaven: http://www.4dsolutions.net/ocn/winterhaven/ (golden age) The Free Geek classes I let ran on Debian. No one was getting rich behind the scenes, hijacking young minds for nefarious purposes. I think students appreciate the integrity of that setup, consider most high schools little more than feeders to Burger King and those places (both for the off-campus meal, and for future employment). Kirby

Brian Blais schrieb:

On Sep 27, 2009, at 19:38 , Charles Cossé wrote:

...

Hi, this has probably been discussed to death already, but maybe not: The point at which fancy graphing calculators become "necessary" (ie as in one's student career) is the point at which the calculator should be abandoned and Python employed. Just a thought ... delete at will !

Just a month ago, a friend of mine who homeschools her children was asking me about graphing calculators. Apparently the math curriculum she uses has a number of graphic calculator exercises. My advice was to buy a nice solar-powered scientific calculator (for $15 at Target), but to ignore the graphing calculator entirely. Her kids should do the exercises by hand, on graph paper instead. Anything that is hard enough for you to use a graphic calculator can be done much more easily with a computer.

After giving her this advice (which I still stand by), I was thinking about my own experience. I was going through high school when the first graphic calculators came out, and I had one Junior and Senior year and through college. I loved to program it, and I loved the big screen where I could see and edit expressions. However, as I think about it, I can not think of a single problem where I *needed* the graphic calculator, or where it gave me more insight than I could do by hand. Hi Brian,

I think I have a counterexample. Run the script, that you can find here: http://svn.python.org/view/*checkout*/python/branches/release26-maint/Demo/turtle/tdemo_chaos.py?revision=73559&content-type=text%2Fplain (or below.) Runs with Python 2.6 or later. It certainly could be mimicked on a (programmable) graphics calculator. What do you think? Regards, Gregor # File: tdemo_chaos.py # Author: Gregor Lingl # Date: 2009-06-24 # A demonstration of chaos from turtle import * N = 80 def f(x): return 3.9*x*(1-x) def g(x): return 3.9*(x-x**2) def h(x): return 3.9*x-3.9*x*x def jumpto(x, y): penup(); goto(x,y) def line(x1, y1, x2, y2): jumpto(x1, y1) pendown() goto(x2, y2) def coosys(): line(-1, 0, N+1, 0) line(0, -0.1, 0, 1.1) def plot(fun, start, colour): pencolor(colour) x = start jumpto(0, x) pendown() dot(5) for i in range(N): x=fun(x) goto(i+1,x) dot(5) def main(): reset() setworldcoordinates(-1.0,-0.1, N+1, 1.1) speed(0) hideturtle() coosys() plot(f, 0.35, "blue") plot(g, 0.35, "green") plot(h, 0.35, "red") # Now zoom in: for s in range(100): setworldcoordinates(0.5*s,-0.1, N+1, 1.1) return "Done!" if __name__ == "__main__": main() mainloop()

It was a fun toy, but not the best tool.

bb

-- Brian Blais bblais@bryant.edu <mailto:bblais@bryant.edu> http://web.bryant.edu/~bblais <http://web.bryant.edu/%7Ebblais>

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On Wed, Sep 30, 2009 at 3:04 AM, Brian Blais <bblais@bryant.edu> wrote:

On Sep 28, 2009, at 16:30 , Gregor Lingl wrote:

Brian Blais schrieb:

 However, as I think about it, I can not think of a single problem where I *needed* the graphic calculator, or where it gave me more insight than I could do by hand.

I think I have a counterexample. Run the script, that you can find here: http://svn.python.org/view/*checkout*/python/branches/release26-maint/Demo/turtle/tdemo_chaos.py?revision=73559&content-type=text%2Fplain What do you think?

The Logistic Map x-->rx(1-x) for varying values of r is easy to examine on a calculator, but excessive by hand. Feigenbaum discovered its periodicities on a calculator without any graphing capability, but having graphs makes insight much easier, in the same way that the Mandelbrot set was discovered mathematically in the 1920s, but became of major interest only after computers permitted it to be visualized. Of course, with a computer, you can visualize the entire bifurcation diagram in a few seconds. http://en.wikipedia.org/wiki/Logistic_map http://en.wikipedia.org/wiki/Bifurcation_diagram The bifurcation diagram of the logistic map is related to the Mandelbrot set, http://www.math.lsa.umich.edu/mmss/coursesONLINE/chaos/chaos6/index.html and has applications in physics, such as a dripping faucet. -- Edward Mokurai (默雷/धर्ममेघशब्दगर्ज/دھرممیگھشبدگر ج) Cherlin Silent Thunder is my name, and Children are my nation. The Cosmos is my dwelling place, the Truth my destination. http://earthtreasury.org/