## Appendix A: pi='3141592653589793238462643383279502884197169399375105820974944592307816406286208998628034825342117067'#exactly 100 digits of each mathematical constant were used in this specific case. e='2718281828459045235360287471352662497757247093699959574966967627724076630353547594571382178525166427'#Both pi and e are proven to be transcendental. root2='1414213562373095048801688724209698078569671875376948073176679737990732478462107038850387534327641572'#the square root of 2 is irrational. golden='1618033988749894848204586834365638117720309179805762862135448622705260462818902449707207204189391137'#The golden ratio is an irrational number. gamma='0577215664901532860606512090082402431042159335939923598805767234884867726777664670936947063291746749'#gamma is also referred to as Eulers constant, and is thought to be transcendental. def list_function(n): first = n[:15]#for both programs, the variable first is the stored digits of the non-terminating number. power = 2 first = int(first) base = first ** (1. / power)# this is essentially a square root calculator. base2 = base# this is the variable used in the else statement. base = str(base) ref = len(base) count = 0 # count is the counter for the while loop. while count