Week 17: Sierpinski in 3D Building Toys

My Building partner and our Menger Sponge

This week break out your blocks (or whatever building toy you enjoy). We are building a Sierpinski cube (Menger Sponge) or Sierpinski tetrahedron. I would also encourage learners to create their own shape and expand on it to create a self-similar sculpture or fractal (think what each iteration would look like).

Here are a few options for building:

1.) Use this link for a paper model (good for a short class or quick project).

2.) Use toothpicks and gumdrops, cardboard, paper, aluminum foil or other handy building tools in the house.

3.) Use lego (I try not to show learners pictures of the tool they are going to use. I think it’s important to figure it out and discover.)

4.) Try Lux blox – this took us quite a while for the third iteration, but it was fun. We found that for the first three sides we needed to build inward to “figure it out.” My daughter built the last two sides while I build inward. It was a lot of fun.

3 iterations

5. Goobi toys are great and my kids and I have built many fractals with them as well. Below is the Sierpinski tetrahedron.

Week 13: Clay Möbius Strips

There are lots of amazing paper Möbius strips that are fun. You can cut down the middle, twist multiple times, make a Möbius paper chain, and try it with various materials. For a basic paper tutorial, I found a good one here.

Rather than creating the classic paper strips, this week learners will be creating Möbius strips with clay. Using a polymer or air-dry clay, encourage the creation of these wonderful mathematical shapes with a sculpting medium. A clay extruder can come in handy, but isn’t necessary.

I have had students make pendants, infinity signs, and amazing patterns with their projects. For advanced sculpting, learners can create a paper strip first, and then sculpt the same curves.

Matt Parker with Standupmaths also has a great video on these fun strips and how they can make linked hearts: