Project Euler Problem 2, some Python solutions

euler2.py

"""Sum of all even fibonacci numbers below 4000000
http://projecteuler.net/index.php?section=problems&id=2"""

#Brute force
def fibs_up_to(t, a=1, b=2):
  while a < t:
    yield a
    a, b = b, a + b

sum(n for n in fibs_up_to(4000000) if n % 2 == 0)

#Only generating even fibs (every third)
def even_fibs_up_to(t):
  a, b = 2, 3
  while a < t:
    yield a
    a, b = a + 2 * b, 2 * a + 3 * b

sum(n for n in even_fibs_up_to(4000000))

#Only deal with the even fibs
def even_fibs_up_to(t):
  a, b = 2, 8
  while a < t:
    yield a
    a, b = b, a + 4 * b

sum(n for n in even_fibs_up_to(4000000))

#Golden ratio used for generating even fibs
def even_fibs_up_to(t):
  phi = (1 + sqrt(5)) / 2
  phi3 = phi ** 3
  a = 2
  while a < t:
    yield a
    a = round(a * phi3)

sum(n for n in even_fibs_up_to(4000000))