On Wed, 13 Apr 2005 03:27:06 -0700, Dick Moores <[EMAIL PROTECTED]> wrote:
>Bengt Richter wrote at 03:19 4/13/2005: >>On Wed, 13 Apr 2005 02:06:11 -0700, Dick Moores <[EMAIL PROTECTED]> wrote: >> >> >I need to figure out how to compute pi to base 12, to as many digits as >> >possible. I found this reference, >> ><http://mathworld.wolfram.com/Base.html>, but I really don't understand >> >it well enough. Could someone show me how to do what I need? >> > >> >Thanks, >> > >> >Dick Moores >> >[EMAIL PROTECTED] >> > >>See if this is enough digits for homework? ;-) > >This is not homework, nor am I a student, though I am trying to learn >Python. I'm just trying to help an artist acquaintance who needs (I just >learned) the first 3003 digits of pi to the base 12. > >>Hint: Lambert Meertens. Tweak the algorithm you find ;-) > >Sorry. Your hint is beyond me. > If you google with this line in the slot: lambert meertens pi site:python.org the first hit is http://mail.python.org/pipermail/tutor/2000-August/002143.html In that (scroll down) you will find: -------------------------------------------------- # Based on a algorithm of Lambert Meertens (remember those days of the # B -> ABC-programming language!!!) import sys def main(): k, a, b, a1, b1 = 2L, 4L, 1L, 12L, 4L while 1: p, q, k = k*k, 2L*k+1L, k+1L a, b, a1, b1 = a1, b1, p*a+q*a1, p*b+q*b1 d, d1 = a/b, a1/b1 while d == d1: output(d) a, a1 = 10L*(a%b), 10L*(a1%b1) d, d1 = a/b, a1/b1 def output(d): sys.stdout.write(`int(d)`) sys.stdout.flush() main() # Reading/writing Python source often gives me the impression of # reading/writing a poem! # Layout, indentation, rythm, I like the look and feel! # What does this tiny program do? It is not a sonnet, even not a # pi-sonnet, but it surely produces Pi! -------------------------------------------------- If you replace a, a1 = 10L*(a%b), 10L*(a1%b1) with a, a1 = 12L*(a%b), 12L*(a1%b1) and sys.stdout.write(`int(d)`) with sys.stdout.write('%X'%d`) and run it, I think it will do what you want, even though I haven't worked through exactly what it's doing, though it's pretty. (For confidence I just tried it and decoded the result far enough to match math.pi exactly ;-) (the %X formats hex, but for single digits that's fine for base 12, giving A for 10 and B for 11. If you want bases >16 you'll have to use something like '0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZ'[digitvalue]) BTW, I find that googling restricted to site:python.org is a good bet for python-related info. After that, if no joy, you can of course expand the search. BTW2, I played with using pi digits to various bases as directions for turtle-style plotting, to see if my eye would pick out patterns in the random-seeming sequence. Also played with coloring the vector steps. I.e., set up a base-length (12 in your case) list of (dx,dy) tuples for relative plot vectors and just relatively plot deltalist[pidigitvalue] and update the display so you can see it develop. It was kind of interesting. For bases under 4 you have to decide what to do with the "first" digit ;-) Regards, Bengt Richter -- http://mail.python.org/mailman/listinfo/python-list
