Joy Hsiao

High School Math Teacher and Origami Club Adviser
Brooklyn Technical High School
Brooklyn, NY

I have always enjoyed making origami as a child, but it wasn't until four years ago, when I started an origami club at school, that I got serious about origami and made several complex pieces. My motivation has always been my students. They make me want to learn more and know more so that I can be a better teacher. This is true in the mathematics that I teach as well as the origami that I create. Only the best for my students!

Menger Sponge Fractal - Level III
Menger Sponge Fractal - Level III
card stock paper and color paper

After learning how to make a Level II Menger Sponge at an origami workshop, I wanted to challenge myself to make a higher level Menger Sponge. The Menger Sponge is a 3-D analogue of the so called Sierpinski Carpet. The Sierpinski Carpet and the Sierpinski Triangle are both well known examples of fractals. A Menger Sponge has to be built as one piece, from beginning to end, rather than assembled from individual cubic units. Similarly, each color paper had to be applied along the way to the white card stock "core" as the construction expanded. As a result, it became especially interesting and challenging to monitor the developing construction. Constant checking was necessary to see where the square holes would be and which color should be applied to which surface. Mistakes were made along the way. I felt the full fractal effect. I had to think fractal, see fractal, and it was a lot of fun!

Menger Sponge Fractal - Level IV
Menger Sponge Fractal - Level IV
Card stock paper and color paper

The process of making a Menger Sponge is meditative and addictive (no kidding!) Students from both Bard High School Early College in Queens and Brooklyn Technical High School contributed to the making of this level IV Menger Sponge which at this time, is one-fourth done.

NYC Metrocard PHiZZ unit Buckyball
NYC Metrocard PHiZZ unit Buckyball
90 Metrocards (NYC subway and bus fare cards)

Brooklyn Technical High School has over 5,000 students. This spring my Origami Club collected and recycled student Metrocards with the help of the Green Leaf Recycling Club at our school. This Buckyball is a product of this collaboration. It unites my love for mathematics and origami. The large student body certainly helped make it possible to acquire all of the necessary construction materials. We actually could obtain 90 green-colored Metrocards in one day! The technical aspect of our school is also reflected in the design of the truncated icosahedron.