“Euler calculated without apparent effort, as men breathe, or as eagles sustain themselves in the wind.” ~ François Arago
The only sound apparent was the silvery, creek-like trickle of the fish tank.
And of course the scratch of graphite on paper, the rubbery pass of the eraser, the occasional puff of breath clearing the work area, and the rapid tap of keyboard keys.
I began again.
0, 1, 1, 2, 3, 5, 8, 13, 21, 34…
Do you recognize this sequence of numbers?
Your eye knows and loves them well, even if your brain is drawing a blank.
If you have every admired the spiral perfection of a stunning seashell, these numbers have whispered to you. Did you think that was the ocean calling when you placed the shell to your ear?
Wrong. It was the surreptitious mathematics that lies beneath so much of the beauty we adore.
This sequence of numbers is known as the Fibonacci sequence and it is often found in nature and art.
The Fibonacci sequence is also what I found myself obsessing over last night between the hours of 11pm and 3am.
It all started with me reading a blog called coding and writing with a stethoscope. This is a great blog that I have discovered recently and I highly recommend it.
In the post, the author mentioned a website called ProjectEuler.net.
I was immediately intrigued because Euler was one of the greatest mathematicians of all time.
Project Euler turned out to be a site with 511 math problems! The best part is these problems are designed for you to write a computer program to solve them!
I was over the moon when I discovered this. In my previous post, If You Build It, I discuss the importance of working on projects and building things from scratch with code.
Now I have a repository of over 500 problems that I can use for practice!
It gets better. Each time you solve a problem, you gain access to a discussion thread where others have posted their solutions. This gives you the opportunity to compare solutions and discover new skills.
Which brings me back to Fibonacci.
Yesterday I spent almost all night attempting to solve problem number 2. Here is the problem statement:
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.
Early this morning, I did solve this problem. The sense of accomplishment I felt when my solution was verified is hard to capture in words. It was a swelling of the heart, a puffing-out of the chest.