(* :Author: Christopher Moretti *) 
(* :Summary: This package contains the command 
    PiByRelativelyPrime,which estimates pi by estimating the probability that 2 integers 
have no common factor. *) 
(* :History: Version 1.0 by Christopher Moretti, 1997 *) 

PiByRelativelyPrime[n_,ran_]:= 
 Block[ {i}, 
  i=0; 
  Do[ 
  If[ GCD[Random[Integer,{-ran,ran}],Random[Integer,{-ran,ran}]]==1, i=i+1];,{ 
        j,1,n}]; 
  Print["Out of ",n," random pairs of integers, ",i, 
      " were relatively prime."]; 
  Print["The percentage of relatively prime pairs is approximately ", 
      N[100 i/n]]; 
  Print["The approximation to Pi is ",N[Sqrt[6n/i],20]] 
  ];