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Soap bubbles

A soap bubble is a thin film of soap water, which is covered with air to form a hollow ball with a iridescent surface. Soap bubbles usually break themselves or come into contact with other objects, lasting only a few seconds. They are usually used for children's entertainment, but also for artistic performances. The accumulation of multiple bubbles produces foam.

When light hits a bubble, it appears to change color. Unlike those seen in rainbows, which are caused by differential refraction, the color seen in soap bubbles is caused by the interference of light reflected from the front and back of the thin soap film. Depending on the thickness of the film, different colors interfere with each other long and cancel.

Soap bubbles are physical examples of complex mathematical problems with minimal surfaces. They will assume a shape containing the minimum surface area of a given volume. The soap film can more appropriately describe a real minimum surface, the pressure of the soap film inside and outside is equal, so the average curvature of the surface is zero. A soap bubble is a closed soap film: it is a surface with constant average curvature due to the difference of external and internal pressure.

Although it has been known since 1884 that a spherical soap bubble is the minimum area method to seal a given volume of air (HA Schwarz theorem), it was not until 2000 that two combined soap bubbles can provide the best sealing effect. A method of closing two different sizes of air of a given volume with a minimum surface area. This is called the double bubble conjecture.

Because of these characteristics, soap bubble film has been used in practical problem solving applications. Frei Otto, a structural engineer, uses a soap bubble film to determine the geometry of the sheet with the smallest surface area, which is scattered between multiple points, and transforms the geometry into a revolutionary stretched roof structure. A famous example is his West Germany Pavilion at World Expo 67 in Montreal.