The Fibonacci Sequence

Of late, I’ve been trying to get to the base of how algorithms and mathematics works in general. I’ve wanted to do this for a while because I have an inane fear of Mathematics, and I wanted to face it.

This was also an effort to deep dive into the fundamentals of Computer Science, a topic dear to my heart, but something I’ve ignored for a while. I chanced upon Teach Yourself CS, a good roadmap for getting started with brushing up your CS fundamentals.

As a part of this roadmap, I’ve been solving programs on Project Euler, Hacker Rank and other competitive coding websites. And almost all programs will have a challenge that includes the Fibonacci Sequence.

For ex : Here is Project Euler’s 2nd Program

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.

and here’s how I solved it

    i = 0
    j = 1
    sum = 0
    num = 0
    while (num < 4000000):    
         num = i + j    
         i = j    
         j = num    
         if num % 2 == 0:        
         sum = sum + num    
    print("Final Sum is")
    print(sum)

If you can overlook my use of the while loop and my amateur Python skills, this looks like a good start. However while working on this program, I went on a rabbit hole, trying to read more about Fibonacci Sequence.

That’s when I stumbled upon the different applications for the sequence. One fun use case is Planning Poker, where participants in a Scrum meeting are given the sequence cards for estimation.

But what enchanted me was the fact that the sequence appears in biological settings as well. For ex: Some flowers are pentagonal because of the arrangement of spirals.

And it also extends into genealogy as well. Bees for that matter.

• If an egg is laid by an unmated female, it hatches a male or drone bee.
• If, however, an egg was fertilized by a male, it hatches a female.

And thus, if one were to trace the ancestory of any male bee, he has 1 parent bee, 2 grandparents, 3 great grand parents and so on.

While learning all these facts about how mathematics and nature are interlocked, I was reminded of Rene Descartes quote

In my opinion, everything happens in nature in a mathematical way.

Indeed.