Thursday, April 22, 2010
Tuesday, April 13, 2010
Kids love to create the bubbles made by dipping a circular frame into a soap solution and then blowing on the film. A circle is a geometric figure confined to a plane. In other words, a circle is flat, two-dimensional. When dipped, a circular frame creates a disk-shaped soap film. What happens if 3-dimensional shapes are dipped in a soap solution?
In the picture below, Joshua dips his skewed variation of a cube. Unfortunately (or fortunately) you can’t see the soap films in the photo. [To see the films, you will have to make the shapes and dip them!]
Multiple soap films intersect in whatever way minimizes the energy of all of the films taken together. This causes the films to pull together into the patterns seen in the dipped edge frames.
Perhaps the most unusual and unexpected shape is made by first dipping a cube edge-frame (blue cube) and then quickly dipping it a second time to capture a bubble in the center. The bubble in the center forms a smaller cube (red cube) with its 8 vertices connected to the vertices of the larger cube (green lines). The trapezoidal planes formed by a blue base line, the opposite red line, and the two green edges are beautiful to behold.
Wrinkle in Time by Madeleine L'Engle is a very popular science fantasy book read by millions of upper elementary school children. The main plot device is a tessaract, the edge-frame projection onto 3-dimensional space of a 4-dimensional The cube within a cube is that 3-space projection.
In a later post I will refer back to the soap frames as we learn about the numerical relationship between the number of edges E, vertices V, and faces F in any edge-frame model.
What's the shape of the bubbles produced by blowing on the shape-frames? Try this activity and find out!