Math 163 - Calculating Infinity Project

infiniteseries.py

import math

print("\n\n")
print("Welcome to Dr. Reid's Magical Approximation Program! \n\n")
print("This program computes approximations of Pi. \n\n")
print("Sources for formulas/approximations:")
print(" * http://mathworld.wolfram.com/PiApproximations.html")
print(" * http://mathworld.wolfram.com/PiFormulas.html\n\n")



# ======================
# Pi Approximations

# --------------------
# Archimedes
pi_approx = 22/7

print('Archimedes\' Approximation:')
print('Computed Value of Pi: %.16F'%(pi_approx))
print('Error: %.2E'%( math.fabs(math.pi - pi_approx)/math.pi ))
print("\n")

# --------------------
# de Jerphanion
pi_approx = math.log(10691/462)

print('de Jerphanion\'s Approximation:')
print('Computed Value of Pi: %.16F'%(pi_approx))
print('Error: %.2E'%( math.fabs(math.pi - pi_approx)/math.pi ))
print("\n")



# =======================
# Pi Formulas

# --------------------
# Ramanujan's Method

# This expression converges extremely quickly - 8 decimal places for each term.
Nterms = 1

one_over_pi = 0
a = ((2*math.sqrt(2))/(9801))
for k in range(Nterms):
    # Be careful selecting a value of k, these numbers will blow up fast
    num = math.factorial(4*k)*(1103+26390*k)
    denom = math.pow(math.factorial(k),4) * math.pow(396,4*k)
    one_over_pi += a*(num/denom)
pi_approx = 1/one_over_pi

print('Ramanujan\'s Formula:')
print('Computed Value of Pi: %.16F'%(pi_approx))
print('Error: %.2E'%( math.fabs(math.pi - pi_approx)/math.pi ))
print("\n")