Project (Sep 28) ---Mathematics & Art

 

This piece of artwork was created by Emily Cannon, and our group selected her works as our project. The inspiration comes from the idea of combining fractals. The necklace and earrings show the famous Sierpinski triangle, which is a typical fractal. The detailed information about Sierpinski triangle is introduced in Megan ( our project group member)'s Blog. In this post, I will focus on square fractal which inspired by Emily's another work shown in below photo. 

This pair of earrings depict two generators of fractals and the generators of their two possible combined fractals. Fractal is a never-ending pattern, and no matter how far you zoom in you will always see the same structure. With this property, I created an artwork called Fractal Rose.  

I used square instead of triangle. Two forms of artistic expression were used---Drawing and Origami. Origami, a Japanese term, is the art of paper folding. By using Origami technique I can transform a 2-D paper sheet into a 3-d paper sculpture to make my rose more vivid.

The outermost square is the initiator. The generator is to connect the mid point of each side of the initiator. Then another square is formed inside. Then we could repeat this process as many time as we can. Similarly operation for Origami. I keep folding layer by layer in the same way. I made 5 layers for my rose. 

What does this project bring to me and why is it important for us to feel the beauty of mathematics in the format of art? As Emily said, " Mathematics and art can combine to make beautiful, elegant, and meaningful pieces! The patterns created by mathematics are often quite lovely and aesthetically pleasing. Additionally, by interpreting mathematics in different forms and arrangements, we can share mathematics with a wide variety of people and learn more about the mathematics behind our art pieces. " I couldn't agree more with her. 

This is the Box fractal. I think we could use it as an in-class activity in high school when students learn the exponential function. 

I use Box Fractal to show them how fast this things can grow and how to generate an exponential function from tables. This activity could be done in small groups. The questions could be:

--How many black boxes in step n, find Nn?

--If the side length of the box in step 0 is 1, please find the side length of each box in step n, Ln?

--The area of the box in step 0 is 1 (1x1),what is the total area of black boxes in step 1, and in step 20?

Firstly, I will invite student to find the pattern of Box fractal. Then I will suggest students to make table, help them to determine independent variable and dependent variable, and encourage them to draw graph.  Finally, they can find the exponential function for this fractal, so they can find the number of boxes in any term. Through this activity students can get an overall understanding on exponential function, and help them to review the prior knowledge they learned  and the knowledge they are learning.