Fibonacci Numbers

Fibonacci numbers are another fantastically mathmagical pattern. And don’t you just love to say fib-oh-nach-ee? It feels great rolling off the tongue! What are Fibonacci numbers? Well, one of the great things about Fibonacci numbers is that it is a really simple adding pattern. It goes like this. Start with 0. (This is somewhat under debate. Some people start with 1. Either way will work!) Add the next consecutive number, which is 1.   0 + 1 = 1 so the next number is 1. Your sequence now looks like this: 0,1.

Next add 1 + 1 = 2. Now your sequence is 0,1,1, 2. Now add 1 + 2 = 3. Your sequence is now 0,1,1,2,3. Getting the idea? Keep going until you get tired of adding! (Not sure when that would happen! Adding is easy and fun!).

So the Fibonacci pattern or sequence is:

0,1,1,2,3,5,8,13,21,34, 55, 89 and so on.

Aside from being easy to generate what’s so mathmagical about Fibonacci numbers and why the heck are they called Fibonacci numbers?!

Well, the pattern was first explained to Western mathematicians by Leonardo Fibonacci in his book written in the middle ages. It’s been around for a while. That’s why we call them Fibonacci numbers. He sort of “discovered” them for us.  The mathmagical part comes in where we find Fibonacci numbers. Have you watched Donald in Mathmagic Land yet? Well, in the movie they talk about the Golden ratio. This is a proportion that is found in nature and in architecture. The proportion creates beauty. And that proportion is the Fibonacci sequence! If you divide consecutive Fibonacci numbers you will always get the Golden ratio. Try it! Start with the big numbers. If you divide 89 by 55, you get 1.61. If you divide 55 by 34, you get 1.61. If you divide 34 by 21, you get 1.61. And so on. You can look up the Golden ratio and explore more or try creating the spiral below. It’s fun and you as you draw you will really get a feel for the Fibonacci sequence and the Golden ratio!

Just like other patterns, like fractals and color patterns, once you start looking, it’s really easy to find the Fibonacci sequence everywhere. How many examples of the Fibonacci pattern can you find today?

Drawing a Fibonacci spiral:

You will need one inch graph paper*, a pencil, a ruler and some coloring items.  (*Any size graph paper will work but I had the most fun with the inch graph paper. Plus, I found that even if I started really, really tiny on really tiny graph paper I could only get my Fibonacci square up to 13 because it wouldn’t fit on the paper. That’s why I think one inch works great. If you want to make your spiral huge, which would be super fun, cut out one inch graph paper sheets and tape them together. You could make a huge, gorgeous spiral! If you make one, send me a picture!)

First, draw a one inch square in the upper center of your graph paper, like this:

Fibonacci 1

Next, draw another 1 inch square right next to it. Remember, we are drawing the Fibonacci pattern which starts 1, 1.

After that draw a 2 inch square above the two one inch squares. Keep going until you can’t draw anymore.

Fibonacci 2 Fibonacci 3

Now you get to draw the spiral. You can use a compass if you wish but I just drew free hand. I drew an arc corner to corner in each box, starting with the middle 1 inch square. It’s not perfect but I think it still turned out pretty great!

Fibonacci 4

Here’s another one that I drew on smaller grid paper. As you can see, I wasn’t able to make it much bigger than the first one.

fibonacci 5

Fibonacci 6Time to color! I decided to color mine like rainbow. I’m rather partial to rainbows. They’re pretty mathfairy-ish, if you think about it. How are you going to color yours? Like I said
above, send us your beautiful artwork!

 

seashell

 

Oh, and here’s real seashell spiral from the beach. The pattern in this real seashell is a Fibonacci sequence, too. More evidence of the mathmagicalness of the world around us.

Have fun with math every day!