from __future__ import division from math import sqrt goldenarray=[1]; goldenmean=(sqrt(5)-1)/2; N_max=input("Choose the maximum power of N (at least 2) for time-out purposes:"); N=2; i=1; while (N==2 or goldenarray[N]==recursive[N]) and N<N_max: N+=1; while i<=N: goldenarray.append(goldenmean*goldenarray[i-1]); i+=1; i=N-1; recursive=goldenarray; while i<=N: recursive[i]=recursive[i-2]-recursive[i-1]; i+=1; print "The power at which round off error occurs is "+str(N)+".\nthe value of the non-recursive approximation, which is more wrong, is "+str(goldenarray[N])+",\nwhile the value of the more accurate recursive approximation is "+str(recursive[N]); # we suspect the recursive formula to be more accurate because the error in it is additive rather than multiplicative and the errors in all the different numbers are likely to self-correct somewhat, while the multiplicative errors will not.
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