Fibonacci and the Good Kind of Math



Did you hear that? That was me locking the door so you can’t leave. I want to talk about math and I know how (most of) you feel about that particular topic. But trust me. This is the good kind of math, the useful kind, the kind that won’t hurt your brain. Do you trust me, right?

I didn’t think so. That’s why I locked the door.

So while you’re stuck in here, you might as well sit back and let me ramble about Fibonacci and the number sequence that he discovered. Leonardo Pisano, aka Fibonacci (that was his nickname), was born in the late 1100’s in the Republic of Pisa, which is now part of Italy. His dad was a diplomat and so Fibonacci was raised in foreign lands. Specifically he grew up in North Africa and the Near East were mathematics was a flourishing subject of study. When he got back to Italy he wrote a number of books about math that convinced Europeans that math was pretty cool stuff. What he is best known for is the number sequence that goes:

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55,… and so on.

Btw, number sequences have a starting point but they don’t have ending points. They go on to infinity. They also have “rules”. Any set sequence of numbers has a “rule” that you use to get the next number in the sequence. Fibonacci’s “rule” is very simple:

Take the last two numbers in the sequence… add them together… and get the next number. 

So you start with 0, 1. Add those numbers and you get:

0, 1, 1

Take the last two numbers (1 and 1), add them together and you get

0, 1, 1, 2

Take the last two numbers (1 and 2), add them together and you get

0, 1, 1, 2, 3

And like that on out to infinity. Its very easy to get the next number in the Fibonacci sequence.

So what?

That is a very good question. So freaking what? Fibonacci didn’t invent this sequence, he discovered it. He discovered that these numbers, the numbers that you get by adding the last two together to get the next, are the numbers that we find in nature all the time. These numbers are the blueprint for how (almost all) living things grow.

Take the pineapple for example:

pineapple fibonacci

Cool right? And its not just pineapples.

image from The Fibonacci Sequence


Its all sorts of stuff, living stuff. Fibonacci numbers are numbers behind the beauty of Mother Nature. The iconic image of Fibonacci numbers in nature is the Fibonacci spiral. Its made up of square blocks (blocks that are as tall as they are wide), arranged in order by Fibonacci number.


That spiral is everywhere.





Cool, but so what?

Again with the good question! What awesome students you all are. Once Fibonacci pointed this out to those nerdy intellectuals in Italy, they realized that this sequence/spiral/shape is what the human eye finds appealing. These are the numbers and the shapes that we have been seeing all our lives and its what we find to be naturally beautiful. Artists have been making good use of this knowledge ever since.


(There is also a line of thought that goes these numbers, the Fibonacci numbers, are proof that the world is not an accidental place, but a thoughtful creation. These numbers in nature over and over again, are the footprints of our Creator, of God. Thus the Fibonacci Spiral is often called the Golden Spiral or the Divine Spiral. I’ll let you ponder that on your own.)

You know who else can use Fibonacci numbers to make their stuff look good? People who play with yarn. 

Ahh. That’s what.

from Lismi Knits. Check out her article on Fibonacci in knitting.

Anytime you want a set of non-identical stripes to look good in your knitting, use Fibonacci numbers. 

A Fibonacci Striped scarf by Deborah Cooke


You can also use Fibonacci numbers to get a nice shape, one that has the right visual proportions.

The Fibonacci Drops Shawl by Lindsay Lewchuk


And for those few that sat through this whole math lecture, enjoyed it, and never even got up to see if the door was really locked, you can just crochet the Fibonacci Spiral.

The Nautilus Shell by Marina


You know, for funsies!



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52 Comments on "Fibonacci and the Good Kind of Math"

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This is the “fun” kind of math- not the critical figuring-the-bills kind of math, but the what-can-I-do-with-it kind of math. I’ve seen some knit patterns that are loosely based on this sequence for their stripes and it does lend a pleasing air to them. What will you think of next? On another front, can they take plastic bottles and bags and recycle them into soft, lovely yarn? Isn’t it the same sort of material the synthetic yarn is made of in the first place? How is that for another kind of math? (plastic + recycling= yarn?) I do the shortcut… Read more »

Love this! You’re awesome!


I am familiar with this truism in math having studied it some eons ago. I was an accountant in my previous life so did a lot a math studying at one time. But I never would have thought to apply this to the yarny arts. Oh my you never cease to teach me something new and amazing! Love it.

Okay, I was good and didn’t even sneak a peek at the door after you locked it. And you were good because you didn’t lie and try and make my head explode by stuffing it with impossible to understand algebraic mathematical equations. Lol! This is the kind of math I appreciate… know, the kind that actually makes sense? Unlike algebra where the teacher gives you three letters and expects you to, in some bizarre fashion that I never understood, turn them into numbers. And not just ANY numbers…..oh, nonono! You’ve got to come up with the numbers that he randomly… Read more »

I had heard about it but never understood it before. How neat is that? Thank you