Exploring Pi with a Fractal & Pi Activity Round-Up


I really wanted to do something with pi for artwork in my classroom plus would love a good pi activity. I struggled with this one. I have seen the pi skyline like this one over at What Do We Do All Day? It is fun but not quite what I am looking for. There are different pi artworks if you google "pi art" but most is based on the digits of pi. To be honest I do not believe in having kids memorize the digits of pi, so much of the artwork is not my thing. As I was searching for ideas, I came across this YouTube video that intrigued me. I decided to make the "fractal" that has an area of pi! It is a spin from the Sierpinski Carpet, Menger Sponge, and the Wallis Sieve. Now fractals are supposed to be infinite, but I cannot draw them this way. I am working on taking this fractal to the third level. If you were able to go on infinitely the area of this picture would be pi. 

To make this fractal you want to start with a 2x2 square. I used graph paper to ease the process. My graph paper has 20 squares per inch. I made my square 210 x 210 squares or 10.5-inches. 

With each quarter you divide the four squares into ninths. You will remove (or color black) the middle ninth of each of them. 

For the next stage you take the remaining squares and divide them into 25 squares and remove the middle square. I didn't take a picture of stage 2. I started stage 3 while creating stage 2. Stage 3 will take the remaining squares and removing divide them into 49 squares. For my graph paper this is each small square. I will then remove the center square. I have not completed stage 3 yet. 

I will work on completing my fractal this week. I had the idea of putting this fractal over a piece of paper and using a razor to cut out all the black squares from both layers to get a full Wallis Sieve Fractal. I think it will be too hard to cut all the little squares though. 

As you can see in my area calculations, the area is headed towards pi. The further you take the stages the closer it will get to pi. The Wallis Sieve is really one quarter of my fractal. It has an area of pi over 4. This is why my fractal starts with a square of area 4. The other shape with an area of pi is a circle with radius 1 unit. I definitely will consider having kids make their own of this fractal to have a visual of pi. 

If this fractal is not for you, I have a round-up of activities and printables to explore pi! You can also check out some of my past pi posts that include printables to use in classes!

1) Pi Skyline from Our Family Code

2) Pilish: How to Write Pi Poems from Our Family Code

3) Finding Pi with Math Suncatchers from Our Family Code

4) Pi Bracelets and Bookmarks from Team Cartwright

5) Pi Necklace Coding Activity from Our Family Code

1) Pi Coloring Page from J.Daniel4's Mom

2) Free Pi Day Activity Pack from Homeschool of 1

3) First 100 Digits of Pi Color Wheel Activity from Our Family Code

4) Pi Day Printables from Wise Owl Factory

5) Pi Inspired Spring Tree from Mama Smiles

What do you do for pi in your classroom or at your home?