irrational_number_estimator.sagews

n = input("How many decimals of e would you like to approximate?")

sum = 0
desired_e = N(e, digits = n + 1)
term_number = 0

while sum != desired_e:
    sum += 1/factorial(term_number)
    term_number += 1

print "NOTE: The code will approximate to the " + str(n) + " digits you requested, but it will show " + str(n+1) + " digits to prevent rounding errors."
print "-----------------------------------------------------------------------"
print "Estimated value of e: " + str(N(sum, digits = n + 1))
print "-----------------------------------------------------------------------"
print "Actual value of e:    " + str(desired_e)
print "-----------------------------------------------------------------------"
print "Difference:           " + str((N(desired_e - sum, digits = 2)))
print "-----------------------------------------------------------------------"

How many decimals of e would you like to approximate?

NOTE: The code will approximate to the 20 digits you requested, but it will show 21 digits to prevent rounding errors. ----------------------------------------------------------------------- Estimated value of e: 2.71828182845904523536 ----------------------------------------------------------------------- Actual value of e: 2.71828182845904523536 ----------------------------------------------------------------------- Difference: 0.00 -----------------------------------------------------------------------

n_2 = input("How many decimals of sqrt(2) would you like to approximate?")

sum_2 = 0
desired_2 = N(sqrt(2), digits = n_2 + 1)
term_number_2 = 0

while sum_2 != desired_2:
    sum_2 += (factorial(2*(term_number_2)+1))/((2^(3*(term_number_2)+1))*(factorial(term_number_2))^2)
    term_number_2 += 1

print "NOTE: The code will approximate to the " + str(n_2) + " digits you requested, but it will show " + str(n_2+1) + " digits to prevent rounding errors."
print "-----------------------------------------------------------------------"
print "Estimated value of 2: " + str(N(sum_2, digits = n_2 + 1))
print "-----------------------------------------------------------------------"
print "Actual value of 2:    " + str(desired_2)
print "-----------------------------------------------------------------------"
print "Difference:           " + str((N(desired_2 - sum_2, digits = 2)))
print "-----------------------------------------------------------------------"

How many decimals of sqrt(2) would you like to approximate?

NOTE: The code will approximate to the 20 digits you requested, but it will show 21 digits to prevent rounding errors. ----------------------------------------------------------------------- Estimated value of 2: 1.41421356237309504880 ----------------------------------------------------------------------- Actual value of 2: 1.41421356237309504880 ----------------------------------------------------------------------- Difference: 0.00 -----------------------------------------------------------------------

n_pi = input("How many decimals of pi would you like to approximate?")

sum_pi = 0
desired_pi = N(pi, digits = n_pi + 1)
term_number_pi = 0

while sum_pi != desired_pi:
    sum_pi += (1/(16^term_number_pi))*((4/(8*(term_number_pi)+1))-(2/(8*(term_number_pi)+4))-(1/(8*(term_number_pi)+5))-(1/(8*(term_number_pi)+6)))
    term_number_pi += 1

print "NOTE: The code will approximate to the " + str(n_pi) + " digits you requested, but it will show " + str(n_pi+1) + " digits to prevent rounding errors."
print "-----------------------------------------------------------------------"
print "Estimated value of pi: " + str(N(sum_pi, digits = n_pi + 1))
print "-----------------------------------------------------------------------"
print "Actual value of pi:    " + str(desired_pi)
print "-----------------------------------------------------------------------"
print "Difference:            " + str((N(desired_pi - sum_pi, digits = 2)))
print "-----------------------------------------------------------------------"

How many decimals of pi would you like to approximate?

NOTE: The code will approximate to the 20 digits you requested, but it will show 21 digits to prevent rounding errors. ----------------------------------------------------------------------- Estimated value of pi: 3.14159265358979323846 ----------------------------------------------------------------------- Actual value of pi: 3.14159265358979323846 ----------------------------------------------------------------------- Difference: 0.00 -----------------------------------------------------------------------