Cubes of soapwater.

A small frame of metal string and a cup with soapwater - that is the secret of the worlds cheapest and probably most facinating toy.
For children as for adults, it looks as shear magic when the one perfect bubble after the other leaves the frame, floating away, showing all the colors of a shimmering rainbow.
The facination is of course that perfection comes from such simple means.

Two bubbles some times connect, and actually form the structure that encapsulates the two chamber volume with the least possible surface.
Scientists have tried for long, to compute different structures like toruses and rings, but had to - eventually - accept that the two-bubble IS the smallest area of them all. So in an instance, the soap surface has solved an extremely complex mathematical problem perfectly.

MANY different bubble figures are possible, but as I have devoted these pages to cubes, then a soap cube is an interesting subject.

First make your soap solution:
* 2/3 cup Joy dishwashing soap
* 1 gallon water
* 2 to 3 tablespoons of glycerine (available at the pharmacy or chemical supply house.)

Dip a cube frame in soap solution, and lift it up.
The soap membrane properties do that it form surfaces with the smallest area for a given volume. The soap will now fill the six outer surfaces with sides, but it will also - against expectations - form an 'hourglass' like shape inside the cube. innermost is a small 'square soap membrane' - well approximately - as the corner angles are not 90 deg but 109.47 deg. which mean that its sides are bend slightly outwards.
Not a solution one would guess.

I think it slightly resembles a 4D cube figure - don't you?"
Click here for more about Cubes in the 4'th Dimension.

The secret to the bubble 'soap membrane' is laziness - least possible stress. (What a wonderfull concept) Exactly as a rubber band stretched between two points will always select the shortest - line. Because in this position it is the most relaxed.
The soap film does the same trick, but in 3 dimensions.
Chemically the reason is that soap consist of long chainlike molecules, whose one end is attracted to water while the other end is attracted to fat.
This is precicely what we utilize daily: The soap attach to fat so that it may be dissolved in water.
But the soap molecules have the added property that, when they are part of a watery solution, they will align in even longer chains, head against tail, so that they form structures that we will otherwise only find in rubber and other elastic materials.
This elastic soap film is governed by one physical force - the surface tension.
This is the same force that works on the surface of a water drop, and which is actually holding it together.

The primary property of the surface tension is, that it is the same in all directions, along the surface.
If we imagine that the surface had taken a shape where the area was NOT minimal, then there would be points on it where the surface tension did not pull equally in all directions, this would be in contradiction to its nature and it would immediately start to align the forces, seeking towards a smaller area.

So it is two properties in cooperation
Elasticity and surface tension that makes the properties of the soap membrane.