Yep, no doubt about it, we have some worthy generators, have only scratched the surface with Ramanujan's so far (fun to have extended precision decimal type for more context, cross-checking pi to a couple hundred digits maybe -- we've got that here too). You can't create vacancies for positions you've not thought of, and this "gnu math teacher" idea, of someone equipped to do both algebra and computer languages at the same time, pre-college, is a vast empty field the way I see it, precious few practitioners. You might say that's because there's no demand, but I see plenty of kids very hungry for this material, going out of their way to find it on-line. I'm just thankful we have the Internet, as those getting hooked up, including the lucky XO set, don't have to slave through a lot of pre-computerite nonsense before getting to the good stuff. Or rather, they maybe get to slave away by day (with traditional black or white boards) and learn by night (when free to use Youtube). I'm not sure how loyal this generation will be though, to those factory-style schools, given their own growing up experience. Maybe it's time to put those behind us? Do they serve a real purpose, other than day care? Some came to that position long ago, but I'm less radical, think we could pipe services like Safari into Winterhaven, our local Hogwarts, and keep those math labs humming. I know many geeks who "do the right thing" and support public schooling, work to update the curriculum, get involved in the democratic process. The temptation is to circle the wagons and do "company schools" like before Oregon became a state. Parents in high tech just don't see the point of making junior a "prisoner of malpractice" for so many years. Town-gown relations break down over such issue, employers flee elsewhere, like to Bangalore. In Portland, we keep working on bridging the gap, via OS Bridge for example (planned for June) i.e. we'd like to keep attracting high tech sector employers and their families, on the basis of our having strong schools (one of our competitive edges, besides skiing and snow boarding, great wine and cheese, beer, coffee...). Kirby On Mon, Jan 26, 2009 at 6:12 PM, Gregor Lingl <gregor.lingl@aon.at> wrote:
kirby urner schrieb:
This is just to get junior experimenting with convergence / divergence on the complex plane. c is our variable.
Per this Wikipedia article (fine to project in class, why not, though "teacher reading from encyclopedia" shouldn't come off as mechanical):
See: http://en.wikipedia.org/wiki/Mandelbrot_set Also: http://www.4dsolutions.net/ocn/fractals.html
IDLE 3.0a2
def mandelbrot(c):
z = 0 + c while True: yield z z = z ** 2 + c
May I again add an interesting thing, this time another indispensable generator, more exactly: three of them:
def feigenbaum1(c,x): while True: yield x x = c*x*(1-x)
def feigenbaum2(c,x): while True: yield x x = c*x-c*x*x
def feigenbaum3(c,x): while True: yield x x = c*(x-x**2)
along with this testing/experimenting function:
def feigenbaumtest(feigenbaum, iterations=80): f = feigenbaum(3.93, 0.5) for i in range(iterations): res = next(f) return res
feigenbaumtest(feigenbaum1, 4) 0.24761176565334103 feigenbaumtest(feigenbaum2, 4) 0.24761176565334098 feigenbaumtest(feigenbaum3, 4) 0.24761176565334167 feigenbaumtest(feigenbaum1, 40) 0.43518828176766455 feigenbaumtest(feigenbaum2, 40) 0.43518808407096854 feigenbaumtest(feigenbaum3, 40) 0.43518950764209768 feigenbaumtest(feigenbaum1) 0.70329204370098442 feigenbaumtest(feigenbaum2) 0.8147039925205275 feigenbaumtest(feigenbaum3) 0.66573747868397481
Certainly something which demonstrates a (by many) unexpected relation between maths and computer science.
Regards, Gregor