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

c1 = mandelbrot(1) next(c1) 1 next(c1) 2 next(c1) 5 next(c1) 26 next(c1) 677 ci = mandelbrot(1j) next(ci) 1j next(ci) (-1+1j) next(ci) -1j next(ci) (-1+1j) next(ci) -1j next(ci) (-1+1j)

Taking inventory of what I have so far in my Python toolkit: Figurate Numbers Pascal's Triangle (triangular and tetrahedral numbers) Fibonacci Numbers (converge to phi, pentagon math) Vectors (VPython -- xyz, spherical coordinates etc.) Prime Numbers (sieves) Prime Numbers (trials by division) Polyhedra (as Python objects: scale, rotate, translate) Polyhedral Numbers (icosahedral, geodesic spheres) Modulo Numbers (override __mul__, __add__) Finite Groups (Python module) Euclid's Algorithm (Guido's gcd) Euclid's Extended Algorithm (needed for inverses) Totient and Totative (gcd based) Fermat's Little Theorem (assert...) Euler's Theorem for Totients (assert...) Mandelbrot Set (chaotic sequences) Miller-Rabin (or Jython probablePrime) RSA.encrypt(m, N) RSA.decrypt(c, N, d=secretkey) ... I've ordered these roughly in sequence of first encounter, assuming numerous loop-backs and repetitions (Saxon a good model -- called spiraling with scaffolding), thinking roughly grades 9-12, though some adults will do this sequence as a refresher or first time exposure to basic numeracy. This is in no way a complete list, just a smattering of dots, curriculum "nodes" as it were. For some of it, I'd expect to switch more into a "music appreciation" mode i.e. we spend too little time explaining why on earth we do so much around polynomials, make them an in-depth vocational exercise without promising anything specific about their job relevance. When was the last time any of you needed to factor a polynomial for work, and couldn't use Mathematica? Time was, if you lived in Pisa and could factor a 3rd or 4th degree polynomial of a specific form, you could attract a patron for a kind of cerebral cockfighting that went on. """ In 1530, NiccolĂ˛ Tartaglia (1500-1557) received two problems in cubic equations from Zuanne da Coi and announced that he could solve them. He was soon challenged by Fiore, which led to a famous contest between the two. Each contestant had to put up a certain amount of money and to propose a number of problems for his rival to solve. Whoever solved more problems within 30 days would get all the money. Tartaglia received questions in the form x3 + mx = n, for which he had worked out a general method. Fiore received questions in the form x3 + mx2 = n, which proved to be too difficult for him to solve, and Tartaglia won the contest. """ [ http://en.wikipedia.org/wiki/Cubic_equation ] The lack of an historical dimension in modern math teaching is just another symptom of out-of-control overspecialization, what we're seeking to counter with these more integrative approaches. Moving to executable notations is a clear sign of the times, ample evidence that "time marches on", so it makes sense that we're more time-aware, no longer supposing that the grade school math of our grandparents is the math of our children. Since when did time stand still? I've got more ideas for offering refresher numeracy courses to adults at the Math Forum. A lot of the focus will be instructional game playing on LCDs, sometimes with real money involved, definitely working towards credentialing i.e. adding scores to transcripts, which implies access to testing centers. The coffee shop may still be the best place to study, bone up for that job interview. http://www.youtube.com/watch?v=bfgO-LXGpTM Kirby