Summing the Fibonacci Sequence

The golden ratio.
An image from nature (by Sustainable San Mateo). The golden ratio approximately (this is a topic for discussion) appears in here and is closely related to the Fibonacci sequence.

Consider the following problem (Project Euler, 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.

Solving this problem by using a programming language is relatively easy and requires only looping through the sequence. How can you tackle this problem without the need for a computer? Spoiler alert: there is only one final step in which we will use a calculator.

(more…)

Read More

Project Euler using Scala: Problem #1

In this last post I gave a short introduction to Scala. In this article, I will show you the strength of Scala for solving one of the mathematical problems posted on Project Euler. The problem description is as follows:

Multiples of 3 and 5

If we list all the natural numbers below 10 that are multiples of 3 or 5, we get 3, 5, 6 and 9. The sum of these multiples is 23. Find the sum of all the multiples of 3 or 5 below 1000.

I will first show you a naive approach and then I will show you a better approach.

(more…)

Read More