# Fibonacci spirals and Pentagons with our Zometool set

I picked another project from our Zome Geometry book for our Family Math project today. The topic that caught my eye last night was the Fiboancci spiral from Unit 7. We are still trying to figure out furniture for our living room, so we’ve got a great empty space for project like this one!

We started with a brief description of the project – interrupted by a few hiccups and the cat:

We made the first few squares and broke for a quick video. We used yarn to trace out the spiral. It was a little difficult to make the yarn bend into the proper spiral, so we just had it go straight across the squares. The kids noticed that the green Zometool struts would have accomplished the same goal. They were also surprised by how large the squares were getting.

We made it up to a Zome square with 21 long struts on a side and had a fun little discussion about the shape. My older son wondered how many more steps we could have gone if we used smalls instead of large blue struts. Turned out that it as many more squares as you’d think.

Also my younger son notice that the length of the yarn was also a Fibonacci pattern, that was a nice surprise.

Next up was a project involving pentagons. The connection to the prior project isn’t quite obvious in the beginning. The first step was a quick description of the project and a little bit of geometry:

After building a couple of steps in this project, my younger son noticed a Fibonacci-like pattern in the number of struts we were using. The interesting thing was that he saw the patter in the number only, but not in the size of the struts. Because neither kid initially saw the connection to the side lengths, it took a little bit of time to see the connection between steps, but eventually they found there way there.

We didn’t go all the way to filling the living room floor with this one, but we did build a few more stages. Talking through this shape this time, the kids notice a few more Fibonacci patterns. They were surprised to see the Fibonacci numbers show up talking about pentagons.

So, definitely a fun little project. The Fibonacci spiral piece is a nice project all by itself and it gives you a nice sense of how quickly the spiral grows. The Pentagon project doesn’t seem to be connected to the spiral project, but the Fibonacci numbers show up in an unexpected way. Fun morning.