Mathematical Art: DIY Fibonacci Spiral and My Big News


I have BIG NEWS!! My life is changing. After leaving teaching high school math sixteen years ago to get married and focus on family, I am going back to the classroom full time in the fall. Then on top of that news I have been helping out four days a week in the school's directed learning center since someone left at the end of April. My life has been a bit different, and you can tell by the number of posts I have been doing. This will mean some changes to Crafty Moms Share, but I am not sure the extent yet. I will change my focus to more math-based posts but am hoping to still review some books, especially math focused ones and young adult ones so I can connect with my students. I will also be doing more origami, so be ready for review of origami products. 

This summer I will be exploring the things that have changed in teaching mathematics which is a lot of technology. I have to become a Google Certified Educator before I start. I also have to explore the graphing and geometry apps that are out there. When I last taught schools had computer labs and that was the main exposure kids got to computers. Smart phones weren't around yet. Life has changed. To get myself excited I started looking at classroom decor and am shocked at how expensive the good math posters are. Then one of the kids I am working with in directed learning has a final project of painting the Fibonacci spiral. I told her I wanted one for my classroom next year. Then I thought about it and realized I could easily make one myself!! Today I am going to share with you my steps and ideas for this fun decor for a math classroom, but it also makes an amazing project for a geometry class (and I may use it next year since the school is very project based and has many artistic kids)!  

First let's talk about the Fibonacci Spiral. I have discussed it previously. Leonardo Fibonacci was an Italian mathematician. He is well known for the Fibonacci Series which is a series of numbers where you add the previous two numbers and get the next number. It begins: 1, 1, 2, 3, 5, 8, 13, ... The Fibonacci Spiral takes these numbers as squares and the curve along the diagonals of the squares form the spiral. We see this spiral often in nature as well as the numbers of the Fibonacci Sequence. 

Fibonacci spiral

Now let's talk about the Golden Ratio. The Golden Ratio is called phi and is approximately 1.618. It is an irrational number and thus the decimal does not end or repeat. The Golden Ratio is pleasing to the human eye. We see it in nature as well as it is used in art. The Golden Ratio is found when the longer part of a line segment is compared to the entire line segment, and it equals the longer part over the shorter part.

Now how are the Golden Ratio and Fibonacci Sequence related? Well, if you take two consecutive numbers in the Fibonacci Sequence and divide the larger by the smaller, the further you go in the sequence the closer you get to the Golden Ratio! (You can see Phi to 100,000 decimal places here.) The further you go with the Fibonacci Spiral the closer it will be to the Golden Rectangle (sides whose proportions are in the Golden Ratio). Often the two spirals are called the same. We see them in nature. One of the most common is the conch shell.

Golden spiral on a shell
Golden Spiral on a Shell photo by Suyothami, CC BY-SA 4.0, via Wikimedia Commons

Now onto our project! The goal is to make a painting of the Fibonacci Spiral. I want to see the squares that make the Fibonacci Sequence and the spiral. The rest of the painting is up to you. Start with a canvas (I am using a 16" x 20"). I drew a scaled plan of the squares so I could envision it. I used an on-line drawing program to sketch the curve but it isn't pretty.

Then I made up actual paper squares up until the 8.5" square. I started with 1/4-inch squares for my two ones. You can download my printable templates here. I laid these squares on the canvas and decided to tilt my spiral.

Then I traced the small ones and used a ruler to draw the bigger ones all in pencil!

I have my squares going off my canvas. If I redo this I would start in a different place and change the angle. More on that later. 

Once I got the squares drawn I went over them with a fine point Sharpie marker so the ink would show through the paint.

Then I erased the pencil marks as much as I could. The next step is painting. You can paint it however you want. If I made a smaller spiral, I would consider doing a beach setting. I didn't want it to be about the painting, so I just chose some colors and gave it texture with the brush.

Sorry I didn't take a picture of the painting before I added my spiral. After discussing it with my resident artist, Hazel, I used a Sharpie pen to draw the spiral. I think next time I will try black paint!

There are two parts of the spiral I am not happy with. The first is the top middle part. It should have gone off the canvas to get the curve correct. The other one is the end. It really would have gone off the canvas on the side and not the bottom. I do think I will try making another of these to hang in my classroom next year! I also may have the kids make them in class! I may use centimeters instead of inches next time to try to get a more condensed spiral. 

I also typed up a draft of this as a project to use with a class. I would consider adding it to a sequence unit.


Looking for more to do with the Fibonacci Spiral and Fibonacci Sequence? Check out this round-up I put together for you! (I will be updating this with more when I get permission from bloggers to share!)

1) Finding Pi with Math (Fibonacci) Sun Catchers from <OurFamilyCode/>

2) Fibonacci Sequence in Nature Posters from Wise Owl Factory

3) Leonardo Fibonacci with Printable Project

Books That Feature or Include Fibonacci Sequence

4) It's a Numberful World by Eddie Woo (12-17 year-olds)

5) Mesmerizing Math by Jonathan Litton (7-10 year-olds)

6) Danny Chung Sums It Up by Maisie Chan (Middle grade novel)

7) Fibonacci in Nature Collection of Picture Books (preschool - grade 4)