PYTHON ASSIGNMENT

To make this project easier, you can utilize the Fraction module which will have a much higher resolution then using floating point types. So, use the following import command:

from Fraction import *

Additionally, we will use the Decimal data type which has more precision than floats:

from decimal import *

Next, we will need some module-level variables for calculations:

Pi out to 50 digits:

pi50 = Decimal("3.14159265358979323846264338327950288419716939937510")

Number of iterations to perform:

iterations = 1000000

Create an iterator class to calculate the value of pi using the Leibniz series:

class LeibnizPiIterator:

• __init__() signature:

def __init__(self):

• For this method, simply use a pass command. All of the setup will occur in __iter__.

• __iter__() signature:

def __iter__(self):

• This method initializes the values we will need for the iterator
• Create an instance variable called self.fraction and assign to it a Fraction object with a numerator of 0 and denominator of 1. This will represent the running total for the series.
• Create an instance variable called self.n and assign 1 to it. This will represent the denominator to be used in the next iteration (see documentation above).
• Create an instance variable called self.add_next and assign to it True. This is a Boolean value indicating if the next iteration will be an add or subtract.
• Return self

• __next__() signature:

def __next__(self):

• This method is where the work is done for each iteration.
• If self.add_next is True then the next value is to be added to self.fraction. Otherwise, subtract it.
• The next value is a new Fraction object with the value 4 / self.n
• After updating self.fraction do the following:
  • Change the value of self.add_next to its opposite.
  • Add 2 to self.n
  • Return self.fraction.value

Test the Iterator:

• Set iterations to 100,000 (dont use the thousands separator)
• Create a new LeibnizPiIterator object and loop through it iterations times.
  • You can implement using a for loop or while loop.
• Report the result of the final value to the terminal
• Then calculate the difference between the final value from the iterator and pi50 and report that value to the terminal as well.
• Change the iterations variable to 10,000,000 and re-run the test (it will take much more time, maybe get a coffee!)

Sample Output:

pi after 100000 iterations: 3.14158265358985315979006807645440766789826367641700

Difference: 0.00000999999994007867257530682509500000000000000000

pi after 10000000 iterations: 3.14159255358913974898979182536369204750639121844740 Difference: 0.00000010000065348947285155791581080000000000000000