# Class notes from week 2
#
# Examples of simple for-loops in Python

import math

#--------------------------------------------------------------------
# This program adds up the first n whole numbers starting from 1.
# To run it, you have to give it the value of n as a parameter.
# For example, calling addFirst(10) will add up the first 10 numbers
# and then return the result, addFirst(100) will add up the first 100
# numbers, and so on.

def addFirst(n):
    total = 0
    for i in range(1, n+1):
        # the line below will get executed n times, each time with a
        # different value of i, starting from 1, 2, 3, ... and
        # continuing up to and including n (but NOT n+1):
        total = total + i
    # print out the final result when the for-loop finishes
    print "The sum of the numbers from 1 to", n, "is", total

#--------------------------------------------------------------------
# This program computes an approximation for pi using the rather
# amazing fact that
#
#   pi = 4/1 - 4/3 + 4/5 - 4/7 + 4/9 - 4/11 + ...
#
# if you add up an infinite number of terms.  If you have less
# patience, you can just add up n terms.  The program asks the
# user for n and then computes the approximation, comparing it
# to the value for pi built into Python's math library.

def approx():
    n = input("Enter number of terms to add up: ")

    # initialize the variables
    total = 0
    numerator = 4
    denominator = 1
    sign = +1

    # perform the loop n times, once for each term to add up
    for i in range(n):
        # show the intermediate values of total as we go
        print "   total is now", total
        # compute next term and add it to the running total
        term = sign * float(numerator) / float(denominator)
        total = total + term
        # update denominator and sign for next loop cycle
        denominator = denominator + 2
        sign = -sign

    print "Pi is approximately", total
    print "Value of math.pi is", math.pi

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