Initiating the Investigation of Soap Films

We see a little square soap film form inside a cube.

When one thinks of soap bubbles, math is certainly not the first thing that comes to mind. Rather, people tend to think about children blowing bubbles outside on a sunny summer day and watching them until they pop high up in the sky. However, those of us that study math know that soap bubbles have played a huge role in studying minimal surfaces; thus, I am interested in studying it myself. For the third week of research, I began investigating the soap films that are formed by platonic solids.

First, the recipe that I used to make the soap solution is as follows:

• 2.5 gallons of water
• 1/2 cup of Dawn soap
• 1 tablespoon of Glycerin

Second, I used Zometools to build the shapes that I want to submerge into the soap solution. For my first time examining soap films, I built the platonic solids along with a few other simple shapes. Before I immersed the shapes into the mixture, I attempted to predict the shape, but I soon discovered that the shape that the soap films form are usually unexpected.

A chart of my predictions and the actual results.

Octahedron

Triangular Prism

Tetrahedron

I was unable to finish investigating the soap films in one day, so I let the solution sit for two days, which apparently enhances the bubbles. When I continued, I dipped the dodecahedron and I thought it was odd how the soap films formed at first. After attempting it a second time and letting it sit longer, I was actually able to watch the soap films minimize.

In the video above, we can see the soap film minimize on the dodecahedron. It seems that leaving the soap solution out for a couple of day slows down the soap film from minimizing as it took a minute and thirty seconds to minimize here.

While I was observing the soap films, I thought of many questions. As a math major, my main question is what is the mathematics behind soap films? As the summer progresses, I hope to find answers to my own questions.