Summing Fibonacci numbers

In this recipe, we will sum the even-valued terms in the Fibonacci sequence whose values do not exceed four million. The Fibonacci series is a sequence of integers starting with zero, where each number is the sum of the previous two; except, of course, the first two numbers zero and one.

Note

For more information, read the Wikipedia article about Fibonacci numbers at http://en.wikipedia.org/wiki/Fibonacci_number .

This recipe uses a formula based on the golden ratio, which is an irrational number with special properties comparable to pi. It we will use the sqrt, log, arange, astype, and sum functions.

How to do it...

The first thing to do is calculate the golden ratio (http://en.wikipedia.org/wiki/Golden_ratio), also called the golden section or golden mean.

1. Calculate the golden ratio.

   We will be using the sqrt function to calculate the square root of five:

   phi = (1 + numpy.sqrt(5))/2
   print "Phi", phi

   This prints the golden mean:

   Phi 1.61803398875
   

2. Find the index below...