evenfibonacci.py

#!/usr/bin/env python3


"""
projetceuler.net

Problem 2

Each new term in the Fibonacci sequence is generated by adding the previous two terms. By starting with 1 and 2, the first 10 terms will be:

1, 2, 3, 5, 8, 13, 21, 34, 55, 89, ...

By considering the terms in the Fibonacci sequence whose values do not exceed four million, find the sum of the even-valued terms.


fibonacci function based on Binet's Fibonacci Number Formula

     (1 + sqrt(5))n - (1 - sqrt(5))n
Fn = -------------------------------
             2n sqrt(5)

"""
import math
import datetime

sqrt = math.sqrt

t = 0
n = 0
while int(((1+sqrt(5))**n-(1-sqrt(5))**n)/(2**n*sqrt(5))) < 4000000:
    if int(((1+sqrt(5))**n-(1-sqrt(5))**n)/(2**n*sqrt(5))) % 2  == 0:
#       print( "Even",n,int(((1+sqrt(5))**n-(1-sqrt(5))**n)/(2**n*sqrt(5))))
       t = t + int(((1+sqrt(5))**n-(1-sqrt(5))**n)/(2**n*sqrt(5)))
    n = n + 1

print( "Binet's Fibonacci Number Formula: ",t)

# Solution using phi thecodeaddict.wordpress.com/tag/golden-ratio

from math import sqrt

limit, current, sum = 4000000, 2, 0
phi3 = ((1+sqrt(5))/2)**3

while sum < limit:
        sum += current
        current = round(phi3*current)

print ("Answer using Phi golden ratio",sum)


evenSum, a, b = 0, 1, 2
while a < 4000000:
	if b % 2 == 0:
		evenSum += b
	a, b = b, a+b
print("Answer using Even Sum = ", evenSum)