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.