passing on Python lore
I'm herewith archiving an email from earlier today, to the guy in charge of the Python curriculum at this company I work for (see LinkedIn profile). It refers back to this listserv, in the context of recycling what I consider a choice piece of Python lore: that generator for deriving digits of pi. -- Kirby ---------- Forwarded message --------- From: Kirby Urner <kirby@clarusway.com> Date: Wed, Jul 24, 2024 at 4:05 PM Subject: Python generators (a fun example, not by me) To: On the topic of Python generators, I just wanted to share what I consider a mysterious one, meaning I didn't write it and don't understand why it works (eyeballing the code has not yielded answers). It may have actually come to me from Guido himself if I remember how it went on edu-sig (one of the archived Python.org discussion groups on which I've been active). He and I have a long term shared interest around integrating Python into everyday math learning (we've come a long way since then). For context, I'm copying this Python generator from my Jupyter Notebook called Pi Day, which is about using Python to generate the number pi in various ways: https://nbviewer.org/github/4dsolutions/Python5/blob/master/Pi%20Day%20Fun.i... Although most of the Python is by me, I'm simply implementing algorithms discovered by others (it's about their genius, not mine), such as that famous one by Ramanujan in the middle of the page. Here's the generator I'm talking about (at the very end of the above notebook, before the flashing GIF pizza pi): """ Another generator example: converging to Pi https://mail.python.org/pipermail/edu-sig/2015-September/date.html """ def pi(): k, a, b, a1, b1 = 2, 4, 1, 12, 4 while True: p, q, k = k*k, 2*k+1, k+1 a, b, a1, b1 = a1, b1, p*a+q*a1, p*b+q*b1 d, d1 = a/b, a1/b1 while d == d1: yield int(d) a, a1 = 10*(a%b), 10*(a1%b1) d, d1 = a/b, a1/b1 if __name__ == "__main__": the_gen = pi() for _ in range(100): print(next(the_gen),end="") print() If I run that I get (I also have 3.9 as well as 3.11): Python 3.9.12 (main, Apr 5 2022, 01:53:17) Type "copyright", "credits" or "license" for more information. IPython 7.31.1 -- An enhanced Interactive Python. runfile('/Users/kirbyurner/Documents/clarusway_data_analysis/python_warm_up/pi_generator.py', wdir='/Users/kirbyurner/Documents/clarusway_data_analysis/python_warm_up') 3141592653589793238462643383279502884197169399375105820974944592307816406286208998628034825342117067 Those are the digits of pi <https://www.piday.org/million/>! Why? Pretty interesting, no? Kirby
FYI, the algorithm was created by Dik Winter, a colleague of Guido's at CWI, and was first used as an example for the ABC programming language (which Guido helped to implement, before his Python days)..Guido very early on translated it to Python (a trivial exercise - ABC also had unbounded ints)., although - of course - it wasn't "a generator" at first. Note that DIk invented a number of "spigot" algorithms for computing pi, and I don't think this one is actually his best known. More here: https://www.gavalas.dev/blog/spigot-algorithms-for-pi-in-python/ On Wed, Jul 24, 2024 at 11:03 PM kirby urner <kirby.urner@gmail.com> wrote:
I'm herewith archiving an email from earlier today, to the guy in charge of the Python curriculum at this company I work for (see LinkedIn profile). It refers back to this listserv, in the context of recycling what I consider a choice piece of Python lore: that generator for deriving digits of pi. -- Kirby
---------- Forwarded message --------- From: Kirby Urner <kirby@clarusway.com> Date: Wed, Jul 24, 2024 at 4:05 PM Subject: Python generators (a fun example, not by me) To:
On the topic of Python generators, I just wanted to share what I consider a mysterious one, meaning I didn't write it and don't understand why it works (eyeballing the code has not yielded answers).
It may have actually come to me from Guido himself if I remember how it went on edu-sig (one of the archived Python.org discussion groups on which I've been active). He and I have a long term shared interest around integrating Python into everyday math learning (we've come a long way since then).
For context, I'm copying this Python generator from my Jupyter Notebook called Pi Day, which is about using Python to generate the number pi in various ways:
https://nbviewer.org/github/4dsolutions/Python5/blob/master/Pi%20Day%20Fun.i...
Although most of the Python is by me, I'm simply implementing algorithms discovered by others (it's about their genius, not mine), such as that famous one by Ramanujan in the middle of the page.
Here's the generator I'm talking about (at the very end of the above notebook, before the flashing GIF pizza pi):
""" Another generator example: converging to Pi
https://mail.python.org/pipermail/edu-sig/2015-September/date.html
"""
def pi():
k, a, b, a1, b1 = 2, 4, 1, 12, 4 while True: p, q, k = k*k, 2*k+1, k+1 a, b, a1, b1 = a1, b1, p*a+q*a1, p*b+q*b1 d, d1 = a/b, a1/b1 while d == d1: yield int(d) a, a1 = 10*(a%b), 10*(a1%b1) d, d1 = a/b, a1/b1
if __name__ == "__main__": the_gen = pi() for _ in range(100): print(next(the_gen),end="") print()
If I run that I get (I also have 3.9 as well as 3.11):
Python 3.9.12 (main, Apr 5 2022, 01:53:17) Type "copyright", "credits" or "license" for more information.
IPython 7.31.1 -- An enhanced Interactive Python.
runfile('/Users/kirbyurner/Documents/clarusway_data_analysis/python_warm_up/pi_generator.py', wdir='/Users/kirbyurner/Documents/clarusway_data_analysis/python_warm_up') 3141592653589793238462643383279502884197169399375105820974944592307816406286208998628034825342117067
Those are the digits of pi! Why? Pretty interesting, no?
Kirby
_______________________________________________ Edu-sig mailing list -- edu-sig@python.org To unsubscribe send an email to edu-sig-leave@python.org https://mail.python.org/mailman3/lists/edu-sig.python.org/ Member address: tim.peters@gmail.com
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Tim Peters