# -*- coding: utf-8 -*-
"""
Created on Sat Dec 12 19:03:48 2020
A simple python program to illustrate:
    an 'executable' or 'runable' complete python program
    importing a 'module' to extend the capacity of basic python
    basic program output using 'print()'
    example of a typical 'for loop', a method to do repeated calculations

@author: neil
"""

# using the (very inefficient) Euler series for estimating PI
# PI**2 /6 = 1+1/2^2 + 1/3^2 + 1/4^2 ....

# by convention most imports of modules should be at the begining of a program
import numpy as np

# also good programming practise puts any variables that the user might want to change as a header section
terms = 20                   # how many terms of the series are we going to use?

ourpi = 1                    # ourpi is the '~pi' given by increasing terms in Euler series
for n in range(2,terms):     # example 'for' loop, the 'range()' function returns a list of numbers (start,stop)
    ourpi += 1/(n**2)        # each time through the loop, add an extra terms based on 'n' (which is incremented)
    print(n,np.sqrt(6*ourpi))# 'print' is a complex function, but at its simplest it just prints readable numbers

print(np.sqrt(6*ourpi), "our estimate of pi after",n+1,"terms in series")   
print(np.pi,"an accurate value for pi")