Zometool and minimal surfaces

Two weeks ago my older son was in a program over at Merrimack college and I happened to chat with Dana Rowland, who is the co-chair of the math department. She showed me a neat minimal surface project you can do with soap bubbles.

A few days later Paula Beardell Krieg sent me this link pointing to a minimal surface project with Zometool pieces:

Minimal surfaces were in the air! Today we tried out a little project:

I started by having each of the boys build two shapes from the Zometool set. Here’s their description of the shapes that they built – it was funny to me that the each built a prism but described it in totally different ways:

Next we dipped the shapes one at a time. The octahedron was first – “it looked like something from the 4th dimension”:

The second shape was the prism that my younger son built – “and there’s an archway . . . interesting”:

Now the smushed and stretched cube – “whoa – it is like a smushed hypercube . . . . except that it is a hyper square.”:

Now came the last of the original shapes – the tetrahedron – “. . . who knew that bubbles could find the center of a tetrahedron?” and then an amazing suprise . . . :

Finally, the boys wanted to try a cube. The boys expected to see a shape similar to a hyper cube, but instead we got a shape that was similar to what we saw with the “smushed” cube. Eventually, though, we did get the shape they were expecting to see. That led to the conjecture that for platonic solids if “you catch a bubble” you’ll get the original shape on the inside.

So, a fun (and pretty easy) project. They boys played with it for about 15 minutes after we turned off the camera. Definitely a neat little project for kids!