Note: The actual pi-calculating part of this I derived from freely available source code. Everything after the "if __name__ == '__main__':" line is my own work though. I also had to modify the algorithm provided so that it would print only 2000 digits instead of an infinite number. (Google just couldn't handle that!)

from __future__ import division import copy import sys from types import IntType,FloatType,LongType,ListType,TupleType,InstanceType,ClassType # set error output to stdout instead #__errout = sys.stderr __errout = sys.stdout # # Define class contfrac # Continued Fraction object version 1 # class contfrac: def __init__(self,numerator,denominator=0,limit=256,epsilon=2e-9): self.classname="contfracv1" # if called by A=contfrac(3.1416) if denominator==0: if type(numerator)==IntType or type(numerator)==LongType: self.num=numerator self.den=1 self.cf=[numerator] elif type(numerator)==FloatType: self.cf = decimal2contfrac(numerator,limit,epsilon) (self.num,self.den) = contfrac2rational(self.cf) elif type(numerator)==ListType: self.cf=copy.copy(numerator) self.num,self.den=contfrac2rational(numerator) elif is_contfrac(numerator): self.num=numerator.num self.den=numerator.den self.cf=copy.copy(numerator.cf) else: # if all else fails its the devil's number self.num=666 self.den=1 self.cf=[666] # if called by A=(2,3) else: self.cf = rational2contfrac(long(numerator),long(denominator)) (self.num,self.den) = contfrac2rational(self.cf) def __len__(self): return len(self.cf) def lid(cfobj): return lazy_identity(cfobj) # # Define class lazy_identity # Lazy connector for contfrac objects # class lazy_identity: def __init__(self,cf): self.classname="lazy_identity" self.cfobj=cf self.n=0 self.a=0 self.b=1 self.c=1 self.d=0 def egest(self,debugflag=False): # First check if we can egest # if we can then egest a digit # otherwise loop until we can if debugflag : print >> __errout,"a=%d,b=%d,c=%d,d=%d" % (self.a,self.b,self.c,self.d) while 1 : if self.c == 0 and self.d == 0 : break if self.c <> 0 and self.d <> 0 and (self.a//self.c) == (self.b//self.d) : if debugflag : print >> __errout,"We can egest" break # Now we must ingest one term from cfobj if debugflag : print >> __errout,"n=%d len(cfobj)=%d" % (self.n,len(self.cfobj)) if self.n < len(self.cfobj) : p=self.cfobj.cf[self.n] if debugflag : print >> __errout,"term ingested is ",p self.n=self.n+1 # Now calculate the new a,b,c,d self.a,self.b,self.c,self.d=self.b,self.a+self.b*p,self.d,self.c+self.d*p else : if debugflag : print >> __errout,"term ingested is INF" self.n=self.n+1 self.a,self.b,self.c,self.d=self.b,self.b,self.d,self.d if debugflag : print >> __errout,"after ingestion a=%d,b=%d,c=%d,d=%d" % (self.a,self.b,self.c,self.d) # out of the while loop if self.c== 0 and self.d == 0 : if debugflag : print >> __errout,"egest the number INF" return 'INF' else: q=self.a//self.c if debugflag : print >> __errout,"egest the number ",q # Now calculate the new a,b,c,d self.a,self.b,self.c,self.d=self.c,self.d,self.a-self.c*q,self.b-self.d*q if debugflag : print >> __errout,"after egestion a=%d,b=%d,c=%d,d=%d" % (self.a,self.b,self.c,self.d) return q # # Define class lazy_rcf_4onpi # Lazy connector for 4/pi in regular continued fractions format # [(1,1),(3,4),(5,9),(7,16),(9,25),(11,36),...] # (2n+1,(n+1)^2) # class lazy_rcf_4onpi: def __init__(self): self.classname="lazy_rcf_4onpi" self.n=0 def egest(self,debugflag=False): a= self.n * 2 + 1 b= (self.n + 1) * (self.n + 1) self.n = self.n + 1 return (a,b) # # Define class lazy_rcf2cf # Lazy connector for turning regular continued fractions # into standardize continued fractions # class lazy_rcf2cf: def __init__(self,rcf): self.classname="lazy_rcf2cf" self.cfobj=rcf self.a=0 self.b=1 self.c=1 self.d=0 def egest(self,debugflag=False): # First check if we can egest # if we can then egest a digit # otherwise loop until we can if debugflag : print >> __errout,"a=%d,b=%d,c=%d,d=%d" % (self.a,self.b,self.c,self.d) while 1 : if self.c == 0 and self.d == 0 : break if self.c <> 0 and self.d <> 0 and (self.a//self.c) == (self.b//self.d) : if debugflag : print >> __errout,"We can egest" break # Now we must ingest one term from cfobj (p,q)=self.cfobj.egest() if debugflag : print >> __errout,"term ingested is ",p # Now calculate the new a,b,c,d self.a,self.b,self.c,self.d=self.b*q,self.a+self.b*p,self.d*q,self.c+self.d*p if debugflag : print >> __errout,"after ingestion a=%d,b=%d,c=%d,d=%d" % (self.a,self.b,self.c,self.d) # out of the while loop if self.c== 0 and self.d == 0 : if debugflag : print >> __errout,"egest the number INF" return 'INF' else: q=self.a//self.c if debugflag : print >> __errout,"egest the number ",q # Now calculate the new a,b,c,d self.a,self.b,self.c,self.d=self.c,self.d,self.a-self.c*q,self.b-self.d*q if debugflag : print >> __errout,"after egestion a=%d,b=%d,c=%d,d=%d" % (self.a,self.b,self.c,self.d) return q # # Define class lazy_decimal # Lazy connector for contfrac objects # class lazy_decimal: def __init__(self,lazycf): self.classname="lazy_decimal" self.cfobj=lazycf self.a=0 self.b=1 self.c=1 self.d=0 def egest(self,debugflag=False): # First check if we can egest # if we can then egest a digit # otherwise loop until we can if debugflag : print >> __errout,"a=%d,b=%d,c=%d,d=%d" % (self.a,self.b,self.c,self.d) while 1 : if self.c == 0 and self.d == 0 : break if self.c <> 0 and self.d <> 0 and (self.a//self.c) == (self.b//self.d) : if debugflag : print >> __errout,"We can egest" break # Now we must ingest one term from cfobj p=self.cfobj.egest() if p == 'INF' : if debugflag : print >> __errout,"term ingested is INF" self.a,self.b,self.c,self.d=self.b,self.b,self.d,self.d else : if debugflag : print >> __errout,"term ingested is ",p # Now calculate the new a,b,c,d self.a,self.b,self.c,self.d=self.b,self.a+self.b*p,self.d,self.c+self.d*p if debugflag : print >> __errout,"after ingestion a=%d,b=%d,c=%d,d=%d" % (self.a,self.b,self.c,self.d) # out of the while loop if self.c== 0 and self.d == 0 : if debugflag : print >> __errout,"egest the number INF" return 'INF' else: r=self.a//self.c if debugflag : print >> __errout,"egest the number ",r # Now calculate the new a,b,c,d self.a,self.b,self.c,self.d=self.c,self.d,self.a-self.c*r,self.b-self.d*r if debugflag : print >> __errout,"after egestion a=%d,b=%d,c=%d,d=%d" % (self.a,self.b,self.c,self.d) # Now calculate the egestion of r2=0 and s2=10 # new_a = c * s2 # new_b = d * s2 # new_c = a - c * r2 # new_d = b - d * r2 self.a,self.b,self.c,self.d=self.c*10,self.d*10,self.a,self.b if debugflag : print >> __errout,"after renormalisation a=%d,b=%d,c=%d,d=%d" % (self.a,self.b,self.c,self.d) return r # # Define class lazy_base # Lazy base for lazy operators # class lazy_base: def egest(self,debugflag=False): # First check if we can egest # if we can then egest a term # otherwise loop until we can if debugflag : print >> __errout,"a=%d,b=%d,c=%d,d=%di,e=%d,f=%d,g=%d,h=%d" % (self.a,self.b,self.c,self.d,self.e,self.f,self.g,self.h) while 1 : self.count= self.count + 1 if self.e == 0 and self.f == 0 and self.g == 0 and self.h == 0 : # We need to return INF break if self.e <> 0 : Zoo= self.a // self.e else: Zoo='INF' if self.g <> 0 : Zoi= self.c // self.g else: Zoi='INF' if self.f <> 0 : Zio= self.b // self.f else: Zio='INF' if self.h <> 0 : Zii= self.d // self.h else: Zii='INF' if debugflag : print >> __errout,"Zoo=",Zoo," Zoi=",Zoi," Zio=",Zio," Zii=",Zii if Zoo <> 'INF' and Zoo == Zoi and Zoi == Zio and Zio == Zii : if debugflag : print >> __errout,"We can egest" break # Now we must decide which lazy input to ingest from if Zio == 'INF' or Zoo == 'INF' : alpha='INF' else: alpha=abs(Zio - Zoo) if Zoi == 'INF' or Zoo == 'INF' : beta='INF' else: beta=abs(Zoi - Zoo) if debugflag : print >> __errout,"alpha=",alpha," beta=",beta if alpha=='INF' and beta=='INF' : if self.count % 2 == 0 : target='X' else: target='Y' elif alpha=='INF' and beta<>'INF' : target='X' elif beta=='INF' and alpha<>'INF' : target='Y' elif alpha > beta : target='X' else : target='Y' # Now we must ingest one term from cfobj if target=='X' : p=self.X.egest() if p == 'INF' : if debugflag : print >> __errout,"term X ingested is INF" self.a,self.b,self.c,self.d,self.e,self.f,self.g,self.h=self.b,self.b,self.d,self.d,self.f,self.f,self.h,self.h else : if debugflag : print >> __errout,"term X ingested is ",p # Now calc the new a b c d e f g h self.a,self.b,self.c,self.d,self.e,self.f,self.g,self.h=self.b,self.a + self.b*p,self.d,self.c + self.d * p,self.f,self.e + self.f * p,self.h,self.g + self.h*p else : p=self.Y.egest() if p == 'INF' : if debugflag : print >> __errout,"term Y ingested is INF" self.a,self.b,self.c,self.d,self.e,self.f,self.g,self.h=self.c,self.d,self.c,self.d,self.g,self.h,self.g,self.h else : if debugflag : print >> __errout,"term Y ingested is ",p # Now calc the new a b c d e f g h self.a,self.b,self.c,self.d,self.e,self.f,self.g,self.h=self.c,self.d,self.a+self.c*p,self.b+self.d*p,self.g,self.h,self.e+self.g*p,self.f+self.h*p # After ingestion if debugflag : print >> __errout,"after ingestion a=%d,b=%d,c=%d,d=%d,e=%d,f=%d,g=%d,h=%d" % (self.a,self.b,self.c,self.d,self.e,self.f,self.g,self.h) # out of the while loop if self.e == 0 and self.f == 0 and self.g == 0 and self.h == 0 : if debugflag : print >> __errout,"egest the number INF" return 'INF' else: if debugflag : print >> __errout,"egest the number ",Zoo # Now calculate the new a,b,c,d,e,f,g,h self.a,self.b,self.c,self.d,self.e,self.f,self.g,self.h=self.e,self.f,self.g,self.h,self.a-self.e*Zoo,self.b-self.f*Zoo,self.c-self.g*Zoo,self.d-self.h*Zoo if debugflag : print >> __errout,"after egestion a=%d,b=%d,c=%d,d=%d,e=%d,f=%d,g=%d,h=%d" % (self.a,self.b,self.c,self.d,self.e,self.f,self.g,self.h) return Zoo # # Define class lazy_add # Lazy addition for lazy objects # class lazy_add(lazy_base): def __init__(self,XX,YY): self.classname="lazy_add" self.count=0 self.X=XX self.Y=YY self.a=0 self.b=1 self.c=1 self.d=0 self.e=1 self.f=0 self.g=0 self.h=0 # # Define class lazy_sub # Lazy subtraction for lazy objects # class lazy_sub(lazy_base): def __init__(self,XX,YY): self.classname="lazy_sub" self.count=0 self.X=XX self.Y=YY self.a=0 self.b=1 self.c=-1 self.d=0 self.e=1 self.f=0 self.g=0 self.h=0 # # Define class lazy_mul # Lazy multiplication for lazy objects # class lazy_mul(lazy_base): def __init__(self,XX,YY): self.classname="lazy_mul" self.count=0 self.X=XX self.Y=YY self.a=0 self.b=0 self.c=0 self.d=1 self.e=1 self.f=0 self.g=0 self.h=0 # # Define class lazy_div # Lazy division for lazy objects # class lazy_div(lazy_base): def __init__(self,XX,YY): self.classname="lazy_div" self.count=0 self.X=XX self.Y=YY self.a=0 self.b=1 self.c=0 self.d=0 self.e=0 self.f=0 self.g=1 self.h=0 if __name__ == '__main__': #print "=======================================" #print "Pi = 4 div 4/pi" #print " " #print "V = lazy_rcf2cf of lazy_rcf_4onpi" #print "A = lazy_decimal of ( lazy(4) lazy_div V )" #print "Now display value of A one digit at a time" iterationstoprocess = 2000; print "<html><head><title>Pi to " + str(iterationstoprocess) + " Digits - Calculated on Google's Servers</title><meta name='verify-v1' content='tTwo+ldRpu5Av4Y6e8+yKYklXw6ONxe/voThlLDpKJ4=' /><meta name='description' content='Pi - The mathematical infinite'/><meta name='keywords' content='appengine, pi, maths, mathematics, number, google, calculate, python, script, development, programming'/></head><body>" print "<h1><b>Pi to " + str(iterationstoprocess) + " Digits - Calculated on Google's Servers</b></h1> <b><img src='http://tbn0.google.com/images?q=tbn:YBhz2zk-tTqexM:http://bp0.blogger.com/_UU-faylKkn4/RfeVnBJTszI/AAAAAAAAAKs/H0x3_4Z_NDY/s320/pi.jpg' style='float: left;'/>Welcome to the Pi page! If you enjoyed this app, tell me what you'd like to see next by emailing me at <a href='mailto:ignis.animi@gmail.com'>ignis.animi@gmail.com</a> and if you'd like to really give me a kick, drop by at <a href='http://davids-pics.blogspot.com/?utm_campaign=appengine'>my website</a>. :) Just remember to leave a comment ;)</b> <br />" print "Pi is one of the most important mathematical constants, approximately equal to 3.14159. It represents the ratio of any circle's circumference to its diameter in Euclidean geometry, which is the same as the ratio of a circle's area to the square of its radius. Many formulas from mathematics, science, and engineering involve pi.<br/><br/>It is an irrational number, which means that it cannot be expressed as a fraction m/n, where m and n are integers. Consequently its decimal representation never ends or repeats. Beyond being irrational, it is a transcendental number, which means that no finite sequence of algebraic operations on integers (powers, roots, sums, etc.) could ever produce it. Throughout the history of mathematics, much effort has been made to determine pi more accurately and understand its nature; fascination with the number has even carried over into culture at large.<br/><br/>Below is listed the value of Pi to " + str(iterationstoprocess) + " decimal places. This number has been calculate for you on-the-fly by a Python script running on Google AppEngine servers. (for more info, see bottom of page)<br/><hr/><br/>" #print '<script type="text/javascript"> </script> <script type="text/javascript" src="http://pagead2.googlesyndication.com/pagead/show_ads.js"> </script><br />' #print '<div style="float: right;"><script type="text/javascript"> </script> <script type="text/javascript" src="http://pagead2.googlesyndication.com/pagead/show_ads.js"> </script></div>' print '<div style="float: right;"><script type="text/javascript"> </script> <script type="text/javascript" src="http://pagead2.googlesyndication.com/pagead/show_ads.js"> </script></div>' rpi=lazy_rcf_4onpi() V=lazy_rcf2cf(rpi) A=lazy_decimal(lazy_div(lid(contfrac(4)),V)) iterations = 0; while iterations < iterationstoprocess: digit=A.egest() sys.stdout.write(str(digit)) if iterations == 0: sys.stdout.write(".") #if this is the 3, print a . after it as requested! :) sys.stdout.flush() iterations = iterations + 1 if iterations % 50 == 0: print " "; print '<hr/><script type="text/javascript"> </script> <script type="text/javascript" src="http://pagead2.googlesyndication.com/pagead/show_ads.js"> </script>' print "<p style='margin-top:10px; margin-bottom:0; padding-bottom:0; text-align:center; line-height:0'><a href='http://feeds.feedburner.com/~r/DavidsNaturePhotos/~6/1'><img src='http://feeds.feedburner.com/DavidsNaturePhotos.1.gif' alt='David's Images of Nature Gallery' style='border:0'></a></p><p style='margin-top:5px; padding-top:0; font-size:x-small; text-align:center'><a href='http://www.feedburner.com/fb/a/headlineanimator/install?id=874615&w=1' onclick='window.open(this.href, 'haHowto', 'width=520,height=600,toolbar=no,address=no,resizable=yes,scrollbars'); return false' target='_blank'>↑ Grab this Headline Animator</a></p>" print "<br/><br/>" print "<b><h1>How I made this App</h1><br/>" print "Some of you are probably wondering "Why one earth did this fella make a pi program?" It's simple really. I got excited about Google AppEngine, and before I knew what was happening, a program sprang up before my eyes. This really encouraged me to see how quick and simple it was to build a basic Web app with AppEngine, even when I didn't know Python at all! :) So I hope you can learn from this, just email me if you want to see the source code, but I wouldn't look if I were you....... ugly! ;)" print "</b>" print "<b><h1>What Now?</h1><br/>" print "Upcoming features:<br/><ul><li>Cached requests<br/>(slows the 'quota exceeded' message)</li><li>Incremental Calculations with cache<br/>Calculates more and more digits every time you reload!</li></ul>" print "</b>" print " <br/><script type='text/javascript'> var gaJsHost = (('https:' == document.location.protocol) ? 'https://ssl.' : 'http://www.'); document.write(unescape('%3Cscript src='' + gaJsHost + 'google-analytics.com/ga.js' type='text/javascript'%3E%3C/script%3E')); </script> <script type='text/javascript'> var pageTracker = _gat._getTracker('UA-4077681-1'); pageTracker._initData(); pageTracker._trackPageview(); </script></body></html>";