Re: Compute pi to base 12 using Python?
[EMAIL PROTECTED] [EMAIL PROTECTED] wrote: Nick Craig-Wood wrote: [EMAIL PROTECTED] [EMAIL PROTECTED] wrote: I'm using GMPY (see code). [snip] If you are using gmpy you might as well do it like this. gmpy.pi() uses the Brent-Salamin Arithmetic-Geometric Mean formula for pi IIRC. This converges quadratically, and it will calculate you a million places without breaking a sweat. It would be nice if that were documented. What do I have to do, go get the documentation for the original GMP to find out what else is in GMPY that they didn't include in the doc file? pydoc gmpy works for me. Not sure how you use pydoc on windows, but you can do this... import gmpy help(gmpy) Help on module gmpy: NAME gmpy FILE /usr/lib/python2.3/site-packages/gmpy.so [snip] Help on built-in function pi: pi(...) pi(n): returns pi with n bits of precision in an mpf object [snip] The original gmp documentation is sensible also, since gmpy is really just a thin wrapper to it. There is also the gmp source code too. -- Nick Craig-Wood [EMAIL PROTECTED] -- http://www.craig-wood.com/nick -- http://mail.python.org/mailman/listinfo/python-list
Re: Compute pi to base 12 using Python?
Nick Craig-Wood wrote: [EMAIL PROTECTED] [EMAIL PROTECTED] wrote: Nick Craig-Wood wrote: [EMAIL PROTECTED] [EMAIL PROTECTED] wrote: I'm using GMPY (see code). [snip] If you are using gmpy you might as well do it like this. gmpy.pi() uses the Brent-Salamin Arithmetic-Geometric Mean formula for pi IIRC. This converges quadratically, and it will calculate you a million places without breaking a sweat. It would be nice if that were documented. What do I have to do, go get the documentation for the original GMP to find out what else is in GMPY that they didn't include in the doc file? pydoc gmpy works for me. Not sure how you use pydoc on windows, but you can do this... import gmpy help(gmpy) Help on module gmpy: NAME gmpy FILE /usr/lib/python2.3/site-packages/gmpy.so [snip] Help on built-in function pi: pi(...) pi(n): returns pi with n bits of precision in an mpf object [snip] Thanks, didn't know you could do that. And I'm glad you didn't reply until today, because I learned how to do it the hard way: import gmpy f = dir(gmpy) def print_docs(f): for q in f: if q[:2]=='__': pass else: d = 'gmpy.' + q + '.__doc__' e = eval(compile(d,'string','eval') print e print print_docs(f) That's 3 new functions I learned, dir(), compile() and eval(). And now that I know help(), I'll probably never need them, but hopefully will remember them. Even better, I realize the inadequecy of the doc strings of a program I wrote. Now that I know how to use them interactively, I can make them more useful. The original gmp documentation is sensible also, since gmpy is really just a thin wrapper to it. I already looked. Utterly useless. There is also the gmp source code too. That helped, as there's a list of the function names in the source code, but help() makes it unnecessary. You still have to wonder, though, with as easy as this is, how the gmpy documention ended up incomplete. I'm always reminded of something I read in the National Lampoon: You know what a fuck-up you are at work, how would anything get done if everyone was like you? Well, the sad fact is everyone _is_ just like you...including the air traffic controller who's supposed to be tracking your flight but has just looked away because he dropped a cigarette ash and burned a hole in his trousers... So I suppose I shouldn't complain, after all, I got something positive out of it. -- Nick Craig-Wood [EMAIL PROTECTED] -- http://www.craig-wood.com/nick -- http://mail.python.org/mailman/listinfo/python-list
Re: Compute pi to base 12 using Python?
Tim Roberts wrote at 22:05 4/16/2005: Dick Moores [EMAIL PROTECTED] wrote: # 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! It sure does. When I ran it my jaw dropped. I had 7,947 CORRECT digits in 2 minutes 0 seconds (by my stopwatch)! How do you know? I think the 7,912th digit is wrong. ;) I suppose you're joshing, Tim, but I really did check by using my trusty def compareSequences(seq1, seq2): find first index at which two sequences differ if s1 == s2: print Sequences are identical return None if len(seq1) = len(seq2): shorterOrEqualSequence = seq2 else: shorterOrEqualSequence = seq1 for index in range(len(shorterOrEqualSequence)): if seq1[index] != seq2[index]: print sequences first differ at index, index print s1 at that index is, s1[index] print s2 at that index is, s2[index] break if index == len(shorterOrEqualSequence)-1: print sequences are identical thru end of shorter sequence at index, index == I got the correct pi from http://www.ballandclaw.com/upi/pi.5.html. By inspection of the text file I copied this to (removing the 3. of 3.1), the 7,912th digit is 2 (I'm using Textpad). If you begin with 31, which what the speedy script does, the 7,912th digit is 6. Now, I've shown you mine. Show me yours. ;-) Dick -- http://mail.python.org/mailman/listinfo/python-list
Re: Compute pi to base 12 using Python?
M.E.Farmer wrote at 23:18 4/14/2005: Using the GNU bc utility: $ bc -l bc 1.06 Copyright 1991-1994, 1997, 1998, 2000 Free Software Foundation, Inc. This is free software with ABSOLUTELY NO WARRANTY. For details type `warranty'. scale = 3000# number of output places wanted obase = 12 # output base print 4 * a(1) # pi = 4*arctan(1) Wow! this got me the 3003 (changed from 3000) digits of pi to base 12 in 60.8 secs. No, I didn't count them yet, nor am I sure they're correct. But I'd bet on them.. Could someone remind me how to get the output of bc -l into a text file on Windows? (I've tried employing pi3003.txt in various ways) OR, how to copy and paste from the command line window, or whatever that window is called? (Sorry for the OT question.) BTW I found a nice set of SCO UNIX man pages at http://www.rt.com/man/. Dick -- http://mail.python.org/mailman/listinfo/python-list
Re: Compute pi to base 12 using Python?
Dick Moores wrote: M.E.Farmer wrote at 23:18 4/14/2005: Using the GNU bc utility: $ bc -l bc 1.06 Copyright 1991-1994, 1997, 1998, 2000 Free Software Foundation, Inc. This is free software with ABSOLUTELY NO WARRANTY. For details type `warranty'. scale = 3000# number of output places wanted obase = 12 # output base print 4 * a(1) # pi = 4*arctan(1) Wow! this got me the 3003 (changed from 3000) digits of pi to base 12 in 60.8 secs. No, I didn't count them yet, nor am I sure they're correct. But I'd bet on them.. Could someone remind me how to get the output of bc -l into a text file on Windows? (I've tried employing pi3003.txt in various ways) OR, how to copy and paste from the command line window, or whatever that window is called? (Sorry for the OT question.) Works for me (using the Cygwin version though) when I do C:\cygwin\bin\bc -l pi12.txt Otherwise, to copy from the command prompt window: open the system menu (icon in the top left corner of the window) and choose Edit-Mark. Then select what you want to copy and press Enter or choose Edit-Copy in the system menu. -- If I have been able to see further, it was only because I stood on the shoulders of giants. -- Isaac Newton Roel Schroeven -- http://mail.python.org/mailman/listinfo/python-list
Re: Compute pi to base 12 using Python?
On Sun, 17 Apr 2005 01:00:46 -0700, Dick Moores [EMAIL PROTECTED] wrote: M.E.Farmer wrote at 23:18 4/14/2005: Using the GNU bc utility: $ bc -l bc 1.06 Copyright 1991-1994, 1997, 1998, 2000 Free Software Foundation, Inc. This is free software with ABSOLUTELY NO WARRANTY. For details type `warranty'. scale = 3000# number of output places wanted obase = 12 # output base print 4 * a(1) # pi = 4*arctan(1) Wow! this got me the 3003 (changed from 3000) digits of pi to base 12 in 60.8 secs. No, I didn't count them yet, nor am I sure they're correct. But I'd bet on them.. Could someone remind me how to get the output of bc -l into a text file on Windows? (I've tried employing pi3003.txt in various ways) OR, how to copy and paste from the command line window, or whatever that window is called? (Sorry for the OT question.) To copy from the command window to the clipboard: 1. Scroll top of desired stuff to make it visible near top 2. Hold down Alt 3. Tap Space Bar 4. Release Alt 5. Tap e 6. Tap k 7. Use mouse or arrow keys to place cursor on top left corner of desired box 8. Hold down Shift 9. Use arrow keys or mouse-with-left-button-pressed to go to bottom right character of desired box 9a. If the bottom is out of sight, keep holding shift down and pretend you can cursor down below bottom. the attempt should make the screen scroll up and select more desired material. If you overshoot, don't panic, just keep holding down shift and use arrows (the are slower) or mouse-with-left-button-still-down to move to desired bottom right corner. 10. Release mouse button if using that 11. Release Shift 12. Press Enter That should copy to the clipboard and make the selection box revert to normal display. Pasting from clipboard is up to you. Pasting into the command window from clipboard is 2-5 above, and Tap p HTH PS. Redirecting with from a script whose interpreter was started by windows extension association doesn't work on some version of windows. To be safe, invoke the interpreter explicitly, e.g., python myscript.py [whatever args here] pi3003.txt If myscript.py is not in the current directory, use a sufficient path to it. If your windows is having that problem, the same will happen with a perl script or other script when you run it as just myscript.ext ... and depend on windows to start the right interpreter. Regards, Bengt Richter -- http://mail.python.org/mailman/listinfo/python-list
Re: Compute pi to base 12 using Python?
Roel Schroeven wrote at 01:45 4/17/2005: Dick Moores wrote: M.E.Farmer wrote at 23:18 4/14/2005: Using the GNU bc utility: $ bc -l bc 1.06 Copyright 1991-1994, 1997, 1998, 2000 Free Software Foundation, Inc. This is free software with ABSOLUTELY NO WARRANTY. For details type `warranty'. scale = 3000# number of output places wanted obase = 12 # output base print 4 * a(1) # pi = 4*arctan(1) Wow! this got me the 3003 (changed from 3000) digits of pi to base 12 in 60.8 secs. No, I didn't count them yet, nor am I sure they're correct. But I'd bet on them.. Could someone remind me how to get the output of bc -l into a text file on Windows? (I've tried employing pi3003.txt in various ways) OR, how to copy and paste from the command line window, or whatever that window is called? (Sorry for the OT question.) Works for me (using the Cygwin version though) when I do C:\cygwin\bin\bc -l pi12.txt But how or when do you enter the lines scale = 3000 obase = 12 print 4 * a(1) Otherwise, to copy from the command prompt window: open the system menu (icon in the top left corner of the window) and choose Edit-Mark. Then select what you want to copy and press Enter or choose Edit-Copy in the system menu. Thanks! You've just relieved years of frustration. Dick -- http://mail.python.org/mailman/listinfo/python-list
Re: Compute pi to base 12 using Python?
Dick Moores [EMAIL PROTECTED] writes: C:\cygwin\bin\bc -l pi12.txt But how or when do you enter the lines scale = 3000 obase = 12 print 4 * a(1) You could put them into a file, say pi.bc. Then run bc -l pi.bc -- http://mail.python.org/mailman/listinfo/python-list
Re: Compute pi to base 12 using Python?
Bengt Richter wrote at 02:26 4/17/2005: Could someone remind me how to get the output of bc -l into a text file on Windows? (I've tried employing pi3003.txt in various ways) OR, how to copy and paste from the command line window, or whatever that window is called? (Sorry for the OT question.) To copy from the command window to the clipboard: 1. Scroll top of desired stuff to make it visible near top 2. Hold down Alt 3. Tap Space Bar 4. Release Alt 5. Tap e 6. Tap k 7. Use mouse or arrow keys to place cursor on top left corner of desired box 8. Hold down Shift 9. Use arrow keys or mouse-with-left-button-pressed to go to bottom right character of desired box 9a. If the bottom is out of sight, keep holding shift down and pretend you can cursor down below bottom. the attempt should make the screen scroll up and select more desired material. If you overshoot, don't panic, just keep holding down shift and use arrows (the are slower) or mouse-with-left-button-still-down to move to desired bottom right corner. 10. Release mouse button if using that 11. Release Shift 12. Press Enter That should copy to the clipboard and make the selection box revert to normal display. Pasting from clipboard is up to you. Pasting into the command window from clipboard is 2-5 above, and Tap p Thanks for showing me another way. But Roel Schroeven's to copy from the command prompt window: open the system menu (icon in the top left corner of the window) and choose Edit-Mark. Then select what you want to copy and press Enter or choose Edit-Copy in the system menu. seems to be easier. PS. Redirecting with from a script whose interpreter was started by windows extension association doesn't work on some version of windows. To be safe, invoke the interpreter explicitly, e.g., python myscript.py [whatever args here] pi3003.txt Thanks very much for this. What kind of args could I use here? Dick -- http://mail.python.org/mailman/listinfo/python-list
Re: Compute pi to base 12 using Python?
Paul Rubin wrote at 02:35 4/17/2005: Dick Moores [EMAIL PROTECTED] writes: C:\cygwin\bin\bc -l pi12.txt But how or when do you enter the lines scale = 3000 obase = 12 print 4 * a(1) You could put them into a file, say pi.bc. Then run bc -l pi.bc OK, now that I've got Textpad trained to open .bc files, I'm thinking of things to store in them. I'm sure I'll want to put in some remarks as well. What should I use to mark the remarks. #, //, or what? The bc man page at http://www.rt.com/man/bc.1.html is tough. Any suggestion for more easily understandable help? And finally (maybe), is it possible to employ bc within a Python script? Thanks, Dick -- http://mail.python.org/mailman/listinfo/python-list
Re: Compute pi to base 12 using Python?
PS. Redirecting with from a script whose interpreter was started by windows extension association doesn't work on some version of windows. To be safe, invoke the interpreter explicitly, e.g., python myscript.py [whatever args here] pi3003.txt Thanks very much for this. What kind of args could I use here? Any that your script allows or understands. an example: python c:/Python22/Lib/PySourceColor.py -i- -s -l c:/MyFile.py c:/tmp/myfile.html A few things that might help you write a well behaved script: if sys.stdin.isatty(): direct else: redirected This snippet can determine if you have redirected IO. I just found this and it looks informative. http://www.jpsdomain.org/windows/redirection.html hth, M.E.Farmer -- http://mail.python.org/mailman/listinfo/python-list
Re: Compute pi to base 12 using Python?
Dick Moores [EMAIL PROTECTED] wrote: # 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! It sure does. When I ran it my jaw dropped. I had 7,947 CORRECT digits in 2 minutes 0 seconds (by my stopwatch)! How do you know? I think the 7,912th digit is wrong. ;) -- - Tim Roberts, [EMAIL PROTECTED] Providenza Boekelheide, Inc. -- http://mail.python.org/mailman/listinfo/python-list
Re: Compute pi to base 12 using Python?
Dick Moores [EMAIL PROTECTED] wrote: M.E.Farmer wrote at 23:18 4/14/2005: Nice collection of unix tools, Cygwin not needed. http://unxutils.sourceforge.net/ Thank you! But a question. I've download both UnxUtils.zip and UnxUpdates.zip. I'm planning to put the contents of UnxUtils.zip in a directory and then move the contents of UnxUpdates.zip, which has many of the same filenames, to the same directory. Should I just let Windows replace the old files with the updated ones? Yes. -- - Tim Roberts, [EMAIL PROTECTED] Providenza Boekelheide, Inc. -- http://mail.python.org/mailman/listinfo/python-list
Re: Compute pi to base 12 using Python?
Dick Moores wrote: Paul Rubin wrote at 18:20 4/13/2005: Dick Moores [EMAIL PROTECTED] writes: 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? Using the GNU bc utility: $ bc -l bc 1.06 Copyright 1991-1994, 1997, 1998, 2000 Free Software Foundation, Inc. This is free software with ABSOLUTELY NO WARRANTY. For details type `warranty'. scale = 3000# number of output places wanted obase = 12 # output base print 4 * a(1) # pi = 4*arctan(1) I don't believe GNU bc is available for Windows, is it? Thanks, Dick Moores [EMAIL PROTECTED] Nice collection of unix tools, Cygwin not needed. http://unxutils.sourceforge.net/ hth, M.E.Farmer -- http://mail.python.org/mailman/listinfo/python-list
Re: Compute pi to base 12 using Python?
M.E.Farmer wrote at 23:18 4/14/2005: Nice collection of unix tools, Cygwin not needed. http://unxutils.sourceforge.net/ Thank you! But a question. I've download both UnxUtils.zip and UnxUpdates.zip. I'm planning to put the contents of UnxUtils.zip in a directory and then move the contents of UnxUpdates.zip, which has many of the same filenames, to the same directory. Should I just let Windows replace the old files with the updated ones? This seems obvious, but I wanted to make sure. I'm using Win XP Pro. Thanks, Dick Moores -- http://mail.python.org/mailman/listinfo/python-list
Re: Compute pi to base 12 using Python?
Sounds good should work fine ;) M.E.Farmer -- http://mail.python.org/mailman/listinfo/python-list
Re: Compute pi to base 12 using Python?
[Dan] Now you've got me curious. Why would an artist want the first 3003 digits of pi to the base 12? [Dick] He says, Do you know how I can get base12 pi? Because the chromatic scale is base12. c c# d d# e f f# g g# a a# b He should read Douglas Adams' fictional essay Music and Fractal Landscapes, from Dirk Gently's Holistic Detective Agency: I believe that there must be a form of music inherent in nature, in natural objects, in the patterns of natural processes. A music that would be as deeply satisfying as any naturally occurring beauty [...] You can see the text here: http://66.102.9.104/search?q=cache:3Ni6gRXCcJgJ:tash.dns2go.com/FTP/P800/Books%2520txt/Douglas%2520Adams%2520-%2520Dirk%2520Gently%27s%2520Holistic%2520Detective%2520Agency.txt+%22douglas+adams%22+%22Music+and+Fractal+Landscapes%22hl=en or via this tinyurl: http://tinyurl.com/6ugnk (Search within that page for the phrase Music and Fractal Landscapes. Or Google for it, which is how I found the link.) -- Richie Hindle [EMAIL PROTECTED] -- http://mail.python.org/mailman/listinfo/python-list
Re: Compute pi to base 12 using Python?
He says, Do you know how I can get base12 pi? Because the chromatic scale is base12. c c# d d# e f f# g g# a a# b Dick It might feel more natural to do this with 'e' (2.718...) --greg -- http://mail.python.org/mailman/listinfo/python-list
Re: Compute pi to base 12 using Python?
[Doug Schwarz] The chromatic scale is based on one twelfth powers of two, i.e., if the frequency of a note in the scale is f(n), then the frequency of the next note is given by f(n+1) = f(n) * 2^(1/12) This easy view of things has been known for a long time, but has only been popular (relatively) recently. Traditionally, scale designers were definitely running after rational proportions between scale notes, not fearing some problems they necessarily create, because such scales are often nicer and interesting to the musical ear. I should relate this discussion to Python somehow! :-) Easy, as I have a few Python programs doing various scale computations -- I should try to bundle these together somewhere in my personal Web site, some day... -- François Pinard http://pinard.progiciels-bpi.ca -- http://mail.python.org/mailman/listinfo/python-list
Re: Compute pi to base 12 using Python?
[Bengt Richter] It might also be interesting to keep a running sum of the base 12 values and use sum % 88 to select piano keys, to let it walk intervals outside of a single octave ;-) The generated would then run from the low octaves to high octaves monotically, then start over again and again. Maybe a more interesting approach might be to pick the note in the same octave, the octave below or above, where the new note is closest to the preceding one. a random walk picture was interesting. Using the closest note would have similarity with a random walk, given digits are seemingly random. On a random walk, one gets away from the departure point on average, the distance being proportional to sqrt(N) where N is the number of steps. So, when using the closest note, one would need a corrective device nevertheless so notes are kept near the middle of the range of comfortable audible frequencies. Anyone have an easy python midi interface for windows to play on the sound card? I could generate a .wav file to play tones, but midi would be much more compact ;-) There are surely many. I use my own (Python) interfaces on Linux, and even there, by combining a few tools, it is rather easy to get .WAV files out of MIDI. In any case, googling around might help. -- Franois Pinard http://pinard.progiciels-bpi.ca -- http://mail.python.org/mailman/listinfo/python-list
Re: Compute pi to base 12 using Python?
On 13 Apr 2005 19:05:01 -0700, Paul Rubin http://phr.cx@nospam.invalid wrote: Dick Moores [EMAIL PROTECTED] writes: I don't believe GNU bc is available for Windows, is it? I don't know. It probably works ok under Cygwin at least. bc definitely works on cygwin, and is available at http://gnuwin32.sourceforge.net/packages/bc.htm for windows. Make sure you download both the dependencies and the binary package for it to work. I put the dll from the dependancy archive in c:/winnt/system32 and it worked. It should be noted that running the win32 bc from cygwin messed up my terminal, so I recommend running it from a cmd window (which worked fine). Peace Bill Mill bill.mill at gmail.com -- http://mail.python.org/mailman/listinfo/python-list
Re: Compute pi to base 12 using Python?
[EMAIL PROTECTED] [EMAIL PROTECTED] wrote: I'm using GMPY (see code). [snip] If you are using gmpy you might as well do it like this. gmpy.pi() uses the Brent-Salamin Arithmetic-Geometric Mean formula for pi IIRC. This converges quadratically, and it will calculate you a million places without breaking a sweat. import gmpy from math import log bits = int(3003*log(12)/log(2)) pi=gmpy.pi(bits+100) gmpy.fdigits(pi, 12, 3003) '3.184809493b918664573a6211bb151551a05729290a7809a492742140a60a55256a0661a03753a3aa54805646880181a3683083272bbba0a370b12265529a828903b4b256b8403759a71626b8a54687621849b849a8225616b442796a31737b229b2391489853943b8763725616447236b027a421aa17a38b52a18a838b01514a51144a23315a3009a8906b61b8b48a62253a88a50a43ba0944572315933664476b3aabb77583975120683526b75b462060bb03b432551913772729a2147553531793848a0402b999b5058535374465a68806716644039539a8431935198527b9399b112990abb0383b107645424577a51601b3624a88b7a676a3992912121a213887b92873946a61332242217aa7354115357744939112602ba4b18a3269222b528487747839994ab223b65b8762695422822669ba00a586097842a51750362073b5a768363b21bb1a97a4a194447749399804922175a068a46739461990a2065bb0a30bbab7024a585b1a84428195489784a07a331a7b0a1574565b373b05b03a5a80a13ab87857734679985558a5373178a7b28271992a3894a5776085083b9b238b2220542462888641a2bab8b3083ab49659172a312b78518654494a068662586a181835a64440b2970a122813975898815367208905801032881449223841428763329617531239b9! a657405584014534390b587625606bb80923795944b43757a431b039556282978a6a49590553490ba1844947175637a908247b50127722464441380a852b0847b5813019bb70a67663b426565434069884476132193344ba55a2128a03838974606b851b2979321a408067225a5aa4b3464a1a17473595333909ab9127079655b3164b68b9b28a9b818a220a025ab0934203995b7a62a7aa739355340539ba3182905b193905603a43b660b9426a92294697144a896a5b2339358bb2b7294bb89635b071a6351211360b820b1882ab8433b54757b87a373284b1ba182a10326476b369a4a6365b58b8018994bb152556765475a704bb94b6b2a39458971a8b90512786b5029404818644323552916170b3abb7363496427b088b68725a68570040617949289077b278069a09b559324b8a66828b40549b0296065b2300330592569a7b76b92ba1293585b6a9b604567a0901362856373b4b56897946256b4172b1b50474351364749a33996a81ba8847347a8411b850b79a03018291672aa0945656a159aa6aa0a845531a592005b8a34366b882257107b190969a846474836a9800750778920ba797297a2791101b0685a86bb704b9baa17b055293679843b35215b0a8b1182b611953b080aa5431b219907a8448a81b1a9493245676b88013b470335240859594158621014216! 619553246570601967448b470174b9244892444817453865a4003b5aa7176451aab906 [EMAIL PROTECTED]' -- Nick Craig-Wood [EMAIL PROTECTED] -- http://www.craig-wood.com/nick -- http://mail.python.org/mailman/listinfo/python-list
Re: Compute pi to base 12 using Python?
Steve Holden wrote at 22:29 4/13/2005: Dick Moores wrote: Steve Holden wrote at 19:12 4/13/2005: Dick Moores wrote: Dan wrote at 18:02 4/13/2005: On Wed, 13 Apr 2005 03:27:06 -0700, Dick Moores [EMAIL PROTECTED] wrote: I'm just trying to help an artist acquaintance who needs (I just learned) the first 3003 digits of pi to the base 12. Now you've got me curious. Why would an artist want the first 3003 digits of pi to the base 12? He says, Do you know how I can get base12 pi? Because the chromatic scale is base12. c c# d d# e f f# g g# a a# b Dick So it's, like, the guy is going to play pi? So why does the melody have 3003 notes? Sorry, he's just a friend of a friend. If I find out I'll post. Here's his site if you want to poke around for yourself. Maybe his email address is there. Dick Where? Sorry about that. http://www.kenjikojima.com/ Dick -- http://mail.python.org/mailman/listinfo/python-list
Re: Compute pi to base 12 using Python?
Dick Moores wrote at 18:40 4/14/2005: Sorry about that. http://www.kenjikojima.com/ I just listened to Kojima's NEW Chorus Pi (Japanese) / 2:28 Chorus: MacinTalk Voices. The music was created from the constant PI. on that page. The vocal is singing the digits of base-10 pi. ten is . or decimal point zero is 0 inchi is 1 ni is 2 san is 3 ta? is 4 (don't understand that ta or tan, but it must be 4) go is 5 roku is 6 -- in the music 6 sounds like raku nana is 7 hachi is 8 ku is 9 Take a look/listen to String Quartet Pi / 5:06 and the process of data The music was created from the constant PI (3.141592...) to 3,000 decimal places by programming. Lots of details there on the music. Dick -- http://mail.python.org/mailman/listinfo/python-list
Compute pi to base 12 using Python?
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] -- http://mail.python.org/mailman/listinfo/python-list
Re: Compute pi to base 12 using Python?
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? ;-) (Digits A and B are 10 and 11 in decimal respectively) 3184809493B918664573A6211BB151551A05729290A7809A492742140A60A55256A0661A03753A3AA54805646880181A 3683083272BBBA0A370B12265529A828903B4B256B8403759A71626B8A54687621849B849A8225616B442796A31737B2 29B2391489853943B8763725616447236B027A421AA17A38B52A18A838B01514A51144A23315A3009A8906B61B8B48A6 2253A88A50A43BA0944572315933664476B3AABB77583975120683526B75B462060BB03B432551913772729A21475535 31793848A0402B999B5058535374465A68806716644039539A8431935198527B9399B112990ABB0383B107645424577A 51601B3624A88B7A676A3992912121A213887B92873946A61332242217AA7354115357744939112602BA4B18A326 9222B528487747839994AB223B65B8762695422822669BA00A586097842A51750362073B5A768363B21BB1A97A4A1944 47749399804922175A068A46739461990A2065BB0A30BBAB7024A585B1A84428195489784A07A331A7B0A1574565B373 B05B03A5A80A13AB87857734679985558A5373178A7B28271992A3894A5776085083B9B238B2220542462888641A2BAB 8B3083AB49659172A312B78518654494A068662586A181835A64440B2970A12281397589881536720890580103288144 9223841428763329617531239B9A657405584014534390B587625606BB80923795944B43757A431B039556282978A6A4 9590553490BA1844947175637A908247B50127722464441380A852B0847B5813019BB70A67663B426565434069884476 132193344BA55A2128A03838974606B851B2979321A408067225A5AA4B3464A1A17473595333909AB9127079655B3164 B68B9B28A9B818A220A025AB0934203995B7A62A7AA739355340539BA3182905B193905603A43B660B9426A922946971 44A896A5B2339358BB2B7294BB89635B071A6351211360B820B1882AB8433B54757B87A373284B1BA182A10326476B36 9A4A6365B58B8018994BB152556765475A704BB94B6B2A39458971A8B90512786B5029404818644323552916170B3ABB 7363496427B088B68725A68570040617949289077B278069A09B559324B8A66828B40549B0296065B2300330592569A7 B76B92BA1293585B6A9B604567A0901362856373B4B56897946256B4172B1B50474351364749A33996A81BA8847347A8 411B850B79A03018291672AA0945656A159AA6AA0A845531A592005B8A34366B882257107B190969A846474836A98007 50778920BA797297A2791101B0685A86BB704B9BAA17B055293679843B35215B0A8B1182B611953B080AA5431B219907 A8448A81B1A9493245676B88013B470335240859594158621014216619553246570601967448B470174B924489244481 7453865A4003B5AA7176451AAB90681A949786154AA040477382BA69371041710B8728458A23979252B254236753A44A 1900AA283536A227648812525743868B410A567794663359A6726A5286783328135114789B7645505B047848020A730A 9557B206776AA56A19682744107901306B29008808619866B4911A05264B872A46B5376383932699531B449195640B62 A63622830886247A47B3957169861239358041AA281333622AA15912B0A636047A489BB0726282A78B96671B27305A96 52496B9B999011A7BA36898891665B1A6009058978850A21B01A158A1473B84A192B8672542A2A7056581995207A436A 5B3BA2824637A3112ABB57176468206A071200A327B3216425148100786502AA21236ABB35499277670A126973058340 3B1922A483856007301983989159BB688A58B602339806B63002A339A50B0BA533B84827793913081070A32595A10180 3A9A20234691B1A0B623274B69B0B44688195169461059543A252BB05208720BA13118266A872B26B9B584959B451795 19534B221A335A2BB6971B3276B3A63A5B791723109B176529BB90651584279B7825712521B8269800738B07A62B1454 7884414451224092937165625696557A78799A82126613535A36B410309B759976119777B895801074B9779B9B513753 8B2799951012273399BB818B721967957713B90947B2A11A6A665848B22B531726616515939323229080B8AB574AA749 4773AB411A57150203067A112944833235A86153803A98689A0762B79835413A46B347888A4AAB259665694B93129B62 1391751430A98B002620718437A7B85B891179479651AA3410663715415B55BA47AA59465AB81567B7655780A8038135 85230122578485B071A529692B19A6537B28616A63556816945380634A90470354AAB303884B7B09B2037B95405BA145 704B19B14AA8028810881AB6072441194A875477836B37704B5199062319A336375437403562A663B835B891957883AB Hint: Lambert Meertens. Tweak the algorithm you find ;-) Regards, Bengt Richter -- http://mail.python.org/mailman/listinfo/python-list
Re: Compute pi to base 12 using Python?
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. Dick Moores [EMAIL PROTECTED] -- http://mail.python.org/mailman/listinfo/python-list
Re: Compute pi to base 12 using Python?
# [EMAIL PROTECTED] / 2005-04-13 03:27:06 -0700: Bengt Richter wrote at 03:19 4/13/2005: 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. it says use google. -- How many Vietnam vets does it take to screw in a light bulb? You don't know, man. You don't KNOW. Cause you weren't THERE. http://bash.org/?255991 -- http://mail.python.org/mailman/listinfo/python-list
Re: Compute pi to base 12 using Python?
Dick Moores 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. How many stars are in *? You probably answered 25. This means that, for convenience, you've broken down the row of stars into ** + ** + *, that is, 2 tens with 5 left over, which the base-10 numeral system denotes as 25. But there's no reason other than tradition why you should arrange them into groups of 10. For example, you could write it as + + + *, or 3 eights plus 1. In octal (base-8) notation, this is written as 31; the tens place in octal represents eights. In general, in the base-r numeral system, the nth digit to the left of the ones digit represents r^n. For example, in the binary number 11001, the place values for each digit are, right to left, 1, 2, 4, 8, and 16, so the number as a whole represents 1×16+1×8+0×4+0×2+1×1=16+8+1=25. This analogous to 25=2×10+5 in base-10. It's also possible to write it as 3×8+0×4+0×2+1×1 = 3001 base 2, but by convention, base-r only uses the digits in range(r). This ensures a unique represenation for each number. This makes 11001 the unique binary representation for decimal 25. Note that for bases larger than 10, the digits will be numbers that are not single digits in base 10. By convention, letters are used for larger digits: A=10, B=11, C=12, ... Z=35. For example, the number (dec) 2005 = 1×12³+1×12²+11×12+1×1 is represented in base-12 by 11B1. Fractions are handled in a similar manner. The nth place to the right of the radix point (i.e., the decimal point, but that term is inaccurate for bases other than ten) represents the value radix**(-n). For example, in binary, 0.1 = 1/2 = dec. 0.5 0.01 = 1/4 = dec. 0.25 0.11 = 1/2 + 1/4 = 3/4 = dec. 0.75 0.001 = 1/8 = dec. 0.125 0.01010101... = 1/4 + 1/16 + 1/64 + ... = 1/3 0.0001100110011... = 1/10 = dec. 0.1 The last row explains why Python gives: 0.1 0.10001 Most computers store floating-point numbers in binary, which doesn't have a finite representation for one-tenth. The above result is rounded to 53 signficant bits (1.100110011001100110011001100110011001100110011010×2^-4), which is exactly equivalent to decimal 0.155511151231257827021181583404541015625, but gets rounded to 17 significant digits for display. Similarly, in base-12: 0.1 = 1/12 0.14 = 1/12 + 4/144 = 1/9 0.16 = 1/12 + 6/144 = 1/8 0.2 = 2/12 = 1/6 0.3 = 3/12 = 1/4 0.4 = 4/12 = 1/3 0.6 = 6/12 = 1/2 0.8 = 8/12 = 2/3 0.9 = 9/12 = 3/4 0.A = 10/12 = 5/6 Notice that several common fractions have simpler representations in base-12 than in base-10. For this reason, there are people who believe that base-12 is superior to base-10. (http://www.dozenalsociety.org.uk) Could someone show me how to do what I need? You'll need 3 things: (1) An algorithm for computing approximations of pi. The simplest one is 4*(1-1/3+1/5-1/7+1/9-1/11+...), which is based on the Taylor series expansion of 4*arctan(1). There are other, faster ways. Search Google for them. (2) An unlimited-precision numeric representation. The standard float isn't good enough: It has only 53 bits of precision, which is only enough for 14 base-12 digits. The decimal module will probably work, although of course its base-10 internal representation will introduce slight inaccuracies. (3) A function for converting numbers to their base-12 representation. For integers, this can be done with: DIGITS = 0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZ def itoa(num, radix=10): is_negative = False if num 0: is_negative = True num = -num digits = [] while num = radix: num, last_digit = divmod(num, radix) digits.append(DIGITS[last_digit]) digits.append(DIGITS[num]) if is_negative: digits.append(-) digits.reverse() return ''.join(digits) For a floating-point number x, the representation with d decimal places count be found by taking the representation of int(round(x * radix ** d)) and inserting a . d places from the right. -- http://mail.python.org/mailman/listinfo/python-list
Re: Compute pi to base 12 using Python?
Dan Bishop wrote at 04:07 4/13/2005: (3) A function for converting numbers to their base-12 representation. For integers, this can be done with: DIGITS = 0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZ def itoa(num, radix=10): is_negative = False if num 0: is_negative = True num = -num digits = [] while num = radix: num, last_digit = divmod(num, radix) digits.append(DIGITS[last_digit]) digits.append(DIGITS[num]) if is_negative: digits.append(-) digits.reverse() return ''.join(digits) I see this works perfectly for integers. Thanks! For a floating-point number x, the representation with d decimal places count be found by taking the representation of int(round(x * radix ** d)) and inserting a . d places from the right. But I'm sorry, but I can't follow you. I do have the first 1 or so places of pi base 10 (http://mathwithmrherte.com/pi_digits.htm), but could you show me what to do with, say, just 3.14159? I apologize for being so dense. Dick Moores [EMAIL PROTECTED] -- http://mail.python.org/mailman/listinfo/python-list
Re: Compute pi to base 12 using Python?
In article [EMAIL PROTECTED], Dan Bishop [EMAIL PROTECTED] wrote: But there's no reason other than tradition why you should arrange them into groups of 10. Well, it is traditional for people to have 10 fingers :-) Other fun things to think about are negative bases. For example, 3(10) = 111(-2). That's 1*(-2)^2 + 1*(-2)^1 + 1*(-2)^0 = 4 - 2 + 1. I can't think of any use for negative bases, but they are a fun game to play with (if you're into that sort of stuff). Non-integer bases are fun too. -- http://mail.python.org/mailman/listinfo/python-list
Re: Compute pi to base 12 using Python?
Dick Moores wrote: Dan Bishop wrote at 04:07 4/13/2005: ... For a floating-point number x, the representation with d decimal places count be found by taking the representation of int(round(x * radix ** d)) and inserting a . d places from the right. But I'm sorry, but I can't follow you. I do have the first 1 or so places of pi base 10 (http://mathwithmrherte.com/pi_digits.htm), but could you show me what to do with, say, just 3.14159? First, decide how many decimal places to use for the conversion. Five decimal digits is equivalent to 5*log(10)/log(12) = 4.63 base-12 digits, so use 4 digits. Next, multiply by 12**4, obtaining the value 65144.01024, and round to the nearest integer, 65144. Convert this to base 12, obtaining 31848. But this is 12**4 times the number we really want, so divide this by 12**4 (i.e., shift the radix point left 4 places), for a final result of 3.1848. -- http://mail.python.org/mailman/listinfo/python-list
Re: Compute pi to base 12 using Python?
Roy Smith wrote: In article [EMAIL PROTECTED], Dan Bishop [EMAIL PROTECTED] wrote: But there's no reason other than tradition why you should arrange them into groups of 10. Well, it is traditional for people to have 10 fingers :-) Other fun things to think about are negative bases. For example, 3(10) = 111(-2). That's 1*(-2)^2 + 1*(-2)^1 + 1*(-2)^0 = 4 - 2 + 1. I can't think of any use for negative bases, but they are a fun game to play with (if you're into that sort of stuff). Non-integer bases are fun too. If you think those are fun, try base (1j - 1) --Scott David Daniels [EMAIL PROTECTED] -- http://mail.python.org/mailman/listinfo/python-list
Re: Compute pi to base 12 using Python?
Scott David Daniels [EMAIL PROTECTED] wrote: If you think those are fun, try base (1j - 1) Get real. I can't imagine using anything so complex. -- http://mail.python.org/mailman/listinfo/python-list
Re: Compute pi to base 12 using Python?
On 13 Apr 2005 12:06:26 -0400, Roy Smith [EMAIL PROTECTED] wrote: Scott David Daniels [EMAIL PROTECTED] wrote: If you think those are fun, try base (1j - 1) Get real. I can't imagine using anything so complex. +1 QOTW -- Kristian kristian.zoerhoff(AT)gmail.com zoerhoff(AT)freeshell.org -- http://mail.python.org/mailman/listinfo/python-list
Re: Compute pi to base 12 using Python?
Scott David Daniels wrote: Roy Smith wrote: In article [EMAIL PROTECTED], Dan Bishop [EMAIL PROTECTED] wrote: But there's no reason other than tradition why you should arrange them into groups of 10. Well, it is traditional for people to have 10 fingers :-) Other fun things to think about are negative bases. For example, 3(10) = 111(-2). That's 1*(-2)^2 + 1*(-2)^1 + 1*(-2)^0 = 4 - 2 + 1. I can't think of any use for negative bases, but they are a fun game to play with (if you're into that sort of stuff). Non-integer bases are fun too. Pi has an interesting representation in bases between 0 and 1, exclusive. There are a finite number of digits after the radix point, but an infinite number _before_ it. If you think those are fun, try base (1j - 1) I think Knuth wrote something about complex bases back in the year 10002000100010001. -- http://mail.python.org/mailman/listinfo/python-list
Re: Compute pi to base 12 using Python?
On 2005-04-13, Dan Bishop [EMAIL PROTECTED] wrote: Pi has an interesting representation in bases between 0 and 1, exclusive. There are a finite number of digits after the radix point, but an infinite number _before_ it. You really oughtn't make me think so hard right after lunch. -- Grant Edwards grante Yow! I'd like some JUNK at FOOD... and then I want to visi.combe ALONE -- -- http://mail.python.org/mailman/listinfo/python-list
Re: Compute pi to base 12 using Python?
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
Re: Compute pi to base 12 using Python?
Bengt Richter wrote at 14:52 4/13/2005: 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! It sure does. When I ran it my jaw dropped. I had 7,947 CORRECT digits in 2 minutes 0 seconds (by my stopwatch)! Now on to base 12. Thanks! Dick Moores [EMAIL PROTECTED] -- http://mail.python.org/mailman/listinfo/python-list
Re: Compute pi to base 12 using Python?
On 13 Apr 2005 12:06:26 -0400, [EMAIL PROTECTED] (Roy Smith) wrote: Scott David Daniels [EMAIL PROTECTED] wrote: If you think those are fun, try base (1j - 1) Get real. I can't imagine using anything so complex. Well said. :-) Dan -- http://mail.python.org/mailman/listinfo/python-list
Re: Compute pi to base 12 using Python?
On Wed, 13 Apr 2005 03:27:06 -0700, Dick Moores [EMAIL PROTECTED] wrote: I'm just trying to help an artist acquaintance who needs (I just learned) the first 3003 digits of pi to the base 12. Now you've got me curious. Why would an artist want the first 3003 digits of pi to the base 12? Dan -- http://mail.python.org/mailman/listinfo/python-list
Re: Compute pi to base 12 using Python?
Dan wrote at 18:02 4/13/2005: On Wed, 13 Apr 2005 03:27:06 -0700, Dick Moores [EMAIL PROTECTED] wrote: I'm just trying to help an artist acquaintance who needs (I just learned) the first 3003 digits of pi to the base 12. Now you've got me curious. Why would an artist want the first 3003 digits of pi to the base 12? He says, Do you know how I can get base12 pi? Because the chromatic scale is base12. c c# d d# e f f# g g# a a# b Dick -- http://mail.python.org/mailman/listinfo/python-list
Re: Compute pi to base 12 using Python?
Dick Moores [EMAIL PROTECTED] writes: 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? Using the GNU bc utility: $ bc -l bc 1.06 Copyright 1991-1994, 1997, 1998, 2000 Free Software Foundation, Inc. This is free software with ABSOLUTELY NO WARRANTY. For details type `warranty'. scale = 3000# number of output places wanted obase = 12 # output base print 4 * a(1) # pi = 4*arctan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quit $ The arctan calculation takes about 20 sec on an Athlon of around 2 ghz. -- http://mail.python.org/mailman/listinfo/python-list
Re: Compute pi to base 12 using Python?
Hi All-- Dick Moores wrote: Dan wrote at 18:02 4/13/2005: On Wed, 13 Apr 2005 03:27:06 -0700, Dick Moores [EMAIL PROTECTED] wrote: I'm just trying to help an artist acquaintance who needs (I just learned) the first 3003 digits of pi to the base 12. Now you've got me curious. Why would an artist want the first 3003 digits of pi to the base 12? He says, Do you know how I can get base12 pi? Because the chromatic scale is base12. c c# d d# e f f# g g# a a# b Oooh. Wanta hear it. Metta, Ivan -- Ivan Van Laningham God N Locomotive Works http://www.andi-holmes.com/ http://www.foretec.com/python/workshops/1998-11/proceedings.html Army Signal Corps: Cu Chi, Class of '70 Author: Teach Yourself Python in 24 Hours -- http://mail.python.org/mailman/listinfo/python-list
Re: Compute pi to base 12 using Python?
Paul Rubin wrote at 18:20 4/13/2005: Dick Moores [EMAIL PROTECTED] writes: 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? Using the GNU bc utility: $ bc -l bc 1.06 Copyright 1991-1994, 1997, 1998, 2000 Free Software Foundation, Inc. This is free software with ABSOLUTELY NO WARRANTY. For details type `warranty'. scale = 3000# number of output places wanted obase = 12 # output base print 4 * a(1) # pi = 4*arctan(1) I don't believe GNU bc is available for Windows, is it? Thanks, Dick Moores [EMAIL PROTECTED] -- http://mail.python.org/mailman/listinfo/python-list
Re: Compute pi to base 12 using Python?
Dick Moores [EMAIL PROTECTED] writes: I don't believe GNU bc is available for Windows, is it? I don't know. It probably works ok under Cygwin at least. -- http://mail.python.org/mailman/listinfo/python-list
Re: Compute pi to base 12 using Python?
Dick Moores wrote: Dan wrote at 18:02 4/13/2005: On Wed, 13 Apr 2005 03:27:06 -0700, Dick Moores [EMAIL PROTECTED] wrote: I'm just trying to help an artist acquaintance who needs (I just learned) the first 3003 digits of pi to the base 12. Now you've got me curious. Why would an artist want the first 3003 digits of pi to the base 12? He says, Do you know how I can get base12 pi? Because the chromatic scale is base12. c c# d d# e f f# g g# a a# b Dick So it's, like, the guy is going to play pi? So why does the melody have 3003 notes? regards Steve -- Steve Holden+1 703 861 4237 +1 800 494 3119 Holden Web LLC http://www.holdenweb.com/ Python Web Programming http://pydish.holdenweb.com/ -- http://mail.python.org/mailman/listinfo/python-list
Re: Compute pi to base 12 using Python?
Dan wrote: On 13 Apr 2005 12:06:26 -0400, [EMAIL PROTECTED] (Roy Smith) wrote: Scott David Daniels [EMAIL PROTECTED] wrote: If you think those are fun, try base (1j - 1) Get real. I can't imagine using anything so complex. Well said. :-) Oh, no, now we're sunk three-holes-in-the-ground-ly y'rs - steve -- Steve Holden+1 703 861 4237 +1 800 494 3119 Holden Web LLC http://www.holdenweb.com/ Python Web Programming http://pydish.holdenweb.com/ -- http://mail.python.org/mailman/listinfo/python-list
Re: Compute pi to base 12 using Python?
In article [EMAIL PROTECTED], Dick Moores [EMAIL PROTECTED] wrote: Dan wrote at 18:02 4/13/2005: On Wed, 13 Apr 2005 03:27:06 -0700, Dick Moores [EMAIL PROTECTED] wrote: I'm just trying to help an artist acquaintance who needs (I just learned) the first 3003 digits of pi to the base 12. Now you've got me curious. Why would an artist want the first 3003 digits of pi to the base 12? He says, Do you know how I can get base12 pi? Because the chromatic scale is base12. c c# d d# e f f# g g# a a# b Dick Does your artist friend have any idea what base 12 means? The chromatic scale is based on one twelfth powers of two, i.e., if the frequency of a note in the scale is f(n), then the frequency of the next note is given by f(n+1) = f(n) * 2^(1/12) so by the time you go all 12 notes in an octave you have doubled the frequency. There is nothing here involving base 12 or pi. -- Doug Schwarz dmschwarzurgrad,rochester,edu Make obvious changes to get real email address. -- http://mail.python.org/mailman/listinfo/python-list
Re: Compute pi to base 12 using Python?
Doug Schwarz wrote at 20:14 4/13/2005: In article [EMAIL PROTECTED], Dick Moores [EMAIL PROTECTED] wrote: Dan wrote at 18:02 4/13/2005: On Wed, 13 Apr 2005 03:27:06 -0700, Dick Moores [EMAIL PROTECTED] wrote: I'm just trying to help an artist acquaintance who needs (I just learned) the first 3003 digits of pi to the base 12. Now you've got me curious. Why would an artist want the first 3003 digits of pi to the base 12? He says, Do you know how I can get base12 pi? Because the chromatic scale is base12. c c# d d# e f f# g g# a a# b Dick Does your artist friend have any idea what base 12 means? The chromatic scale is based on one twelfth powers of two, i.e., if the frequency of a note in the scale is f(n), then the frequency of the next note is given by f(n+1) = f(n) * 2^(1/12) so by the time you go all 12 notes in an octave you have doubled the frequency. There is nothing here involving base 12 or pi. He's a friend of a friend. I don't know what he knows, but I'll forward this to MY friend. Thanks. Dick -- Doug Schwarz dmschwarzurgrad,rochester,edu Make obvious changes to get real email address. -- http://mail.python.org/mailman/listinfo/python-list -- http://mail.python.org/mailman/listinfo/python-list
Re: Compute pi to base 12 using Python?
On Thu, 14 Apr 2005 03:14:51 GMT, Doug Schwarz [EMAIL PROTECTED] wrote: In article [EMAIL PROTECTED], Dick Moores [EMAIL PROTECTED] wrote: Dan wrote at 18:02 4/13/2005: On Wed, 13 Apr 2005 03:27:06 -0700, Dick Moores [EMAIL PROTECTED] wrote: I'm just trying to help an artist acquaintance who needs (I just learned) the first 3003 digits of pi to the base 12. Now you've got me curious. Why would an artist want the first 3003 digits of pi to the base 12? He says, Do you know how I can get base12 pi? Because the chromatic scale is base12. c c# d d# e f f# g g# a a# b Dick Does your artist friend have any idea what base 12 means? Maybe he wants to play sounds of pi and has found base 10 digits don't hit all the notes, and he may not be as dumb as you think ;-) The chromatic scale is based on one twelfth powers of two, i.e., if the frequency of a note in the scale is f(n), then the frequency of the next note is given by f(n+1) = f(n) * 2^(1/12) so by the time you go all 12 notes in an octave you have doubled the frequency. There is nothing here involving base 12 or pi. I expect something interesting and imaginative ;-) It might also be interesting to keep a running sum of the base 12 values and use sum % 88 to select piano keys, to let it walk intervals outside of a single octave ;-) I found using different base digits to draw end-to-end vectors selected from equal vectors equally spaced in all base directions for a random walk picture was interesting. I also changed the color according to various criteria such as digit run length ending on the current digit. Maybe the artist could scale that up and put it on the wall as backdrop to the music ;-) It would be easy to generate postscript for it, that could be scaled up and printed wall size. Or pdf. I'm tempted to play with my pdf plotting toy and maybe make it work ;-) I'm kind of curious what the ear could pick up about pi from hearing the sequence as notes. Or intervals, or grouped to make chords even. Anyone have an easy python midi interface for windows to play on the sound card? I could generate a .wav file to play tones, but midi would be much more compact ;-) Regards, Bengt Richter -- http://mail.python.org/mailman/listinfo/python-list
Re: Compute pi to base 12 using Python?
On Thu, 14 Apr 2005 11:05:17 +1000, John Machin [EMAIL PROTECTED] wrote: On Wed, 13 Apr 2005 08:28:29 -0400, Roy Smith [EMAIL PROTECTED] wrote: In article [EMAIL PROTECTED], Dan Bishop [EMAIL PROTECTED] wrote: But there's no reason other than tradition why you should arrange them into groups of 10. Well, it is traditional for people to have 10 fingers :-) According to anthropology archives, there was once a tribe called OS/360 system programmers who would cut off their thumbs and great toes in order that they might better count in hexadecimal. I suspect using four dates back to the nixie tribe, who practiced bi-quinary. And they would cut off little toes and fingers rather, because then the thumb was more significant and it was easier to remember it as 5 (or 0 if hidden) with the rest counting octally ;-) Regards, Bengt Richter -- http://mail.python.org/mailman/listinfo/python-list
Re: Compute pi to base 12 using Python?
On 13 Apr 2005 18:20:06 -0700, Paul Rubin http://[EMAIL PROTECTED] wrote:
Dick Moores [EMAIL PROTECTED] writes:
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?
Using the GNU bc utility:
$ bc -l
bc 1.06
Copyright 1991-1994, 1997, 1998, 2000 Free Software Foundation, Inc.
This is free software with ABSOLUTELY NO WARRANTY.
For details type `warranty'.
scale = 3000# number of output places wanted
obase = 12 # output base
print 4 * a(1) # pi = 4*arctan(1)
3.184809493B918664573A6211BB151551A05729290A7809A492742140A60A55256A\
0661A03753A3AA54805646880181A3683083272BBBA0A370B12265529A828903B4B2\
56B8403759A71626B8A54687621849B849A8225616B442796A31737B229B23914898\
53943B8763725616447236B027A421AA17A38B52A18A838B01514A51144A23315A30\
09A8906B61B8B48A62253A88A50A43BA0944572315933664476B3AABB77583975120\
683526B75B462060BB03B432551913772729A2147553531793848A0402B999B50585\
35374465A68806716644039539A8431935198527B9399B112990ABB0383B10764542\
4577A51601B3624A88B7A676A3992912121A213887B92873946A61332242217AA735\
4115357744939112602BA4B18A3269222B528487747839994AB223B65B876269\
5422822669BA00A586097842A51750362073B5A768363B21BB1A97A4A19444774939\
9804922175A068A46739461990A2065BB0A30BBAB7024A585B1A84428195489784A0\
7A331A7B0A1574565B373B05B03A5A80A13AB87857734679985558A5373178A7B282\
71992A3894A5776085083B9B238B2220542462888641A2BAB8B3083AB49659172A31\
2B78518654494A068662586A181835A64440B2970A12281397589881536720890580\
1032881449223841428763329617531239B9A657405584014534390B587625606BB8\
0923795944B43757A431B039556282978A6A49590553490BA1844947175637A90824\
7B50127722464441380A852B0847B5813019BB70A67663B426565434069884476132\
193344BA55A2128A03838974606B851B2979321A408067225A5AA4B3464A1A174735\
95333909AB9127079655B3164B68B9B28A9B818A220A025AB0934203995B7A62A7AA\
739355340539BA3182905B193905603A43B660B9426A92294697144A896A5B233935\
8BB2B7294BB89635B071A6351211360B820B1882AB8433B54757B87A373284B1BA18\
2A10326476B369A4A6365B58B8018994BB152556765475A704BB94B6B2A39458971A\
8B90512786B5029404818644323552916170B3ABB7363496427B088B68725A685700\
40617949289077B278069A09B559324B8A66828B40549B0296065B2300330592569A\
7B76B92BA1293585B6A9B604567A0901362856373B4B56897946256B4172B1B50474\
351364749A33996A81BA8847347A8411B850B79A03018291672AA0945656A159AA6A\
A0A845531A592005B8A34366B882257107B190969A846474836A9800750778920BA7\
97297A2791101B0685A86BB704B9BAA17B055293679843B35215B0A8B1182B611953\
B080AA5431B219907A8448A81B1A9493245676B88013B47033524085959415862101\
4216619553246570601967448B470174B9244892444817453865A4003B5AA7176451\
AAB90681A949786154AA040477382BA69371041710B8728458A23979252B25423675\
3A44A1900AA283536A227648812525743868B410A567794663359A6726A528678332\
8135114789B7645505B047848020A730A9557B206776AA56A19682744107901306B2\
9008808619866B4911A05264B872A46B5376383932699531B449195640B62A636228\
30886247A47B3957169861239358041AA281333622AA15912B0A636047A489BB0726\
282A78B96671B27305A9652496B9B999011A7BA36898891665B1A6009058978850A2\
1B01A158A1473B84A192B8672542A2A7056581995207A436A5B3BA2824637A3112AB\
B57176468206A071200A327B3216425148100786502AA21236ABB35499277670A126\
9730583403B1922A483856007301983989159BB688A58B602339806B63002A339A50\
B0BA533B84827793913081070A32595A101803A9A20234691B1A0B623274B69B0B44\
688195169461059543A252BB05208720BA13118266A872B26B9B584959B44B
quit
$
The arctan calculation takes about 20 sec on an Athlon of around 2 ghz.
That's cool. I will have to find out about bc. Thanks ;-)
Interesting to note, it also took about 20 sec on my _old_ machine:
from time import clock
def foo():
...t0 = clock()
...open('pi12by60.txt','w').write(
... ''.join(c+'\n'[:(i+1)%60==0] for i,c in enumerate(pidigits(12,
3003)))+'\n')
...print clock()-t0
...
foo()
22.3866400935
That's on a 300Mhz Pentium II using the Lambert Meertens algorithm for pi ;-)
Regards,
Bengt Richter
--
http://mail.python.org/mailman/listinfo/python-list
