Plateau's laws describe the structure of soap film

Soap film

Soap films are thin layers of liquid surrounded by air. For example, if two soap bubbles enters in contact, they merged and a thin film is created in between. Thus, foams are composed of a network of films connected by Plateau borders...

s. These laws were formulated in the 19th century by the Belgian physicist Joseph Plateau from his experimental observations.

Plateau's laws state:

1. Soap films are made of entire smooth surfaces.
2. The average curvature of a portion of a soap film is everywhere constant on any point on the same piece of soap film.
3. Soap films always meet in threes along an edge called a Plateau border, and they do so at an angle of cos⁻¹(−1/2)  =  120 degrees.
4. These Plateau borders meet in fours at a vertex, and they do so at an angle of cos⁻¹(−1/3) ≈ 109.47 degrees (the tetrahedral angle).

Configurations other than those of Plateau's laws are unstable and the film will quickly tend to rearrange itself to conform to these laws.

That these laws hold for minimal surface

Minimal surface

In mathematics, a minimal surface is a surface with a mean curvature of zero.These include, but are not limited to, surfaces of minimum area subject to various constraints....

s was proved mathematically using methods of geometric measure theory

Geometric measure theory

In mathematics, geometric measure theory is the study of the geometric properties of the measures of sets , including such things as arc lengths and areas. It uses measure theory to generalize differential geometry to surfaces with mild singularities called rectifiable sets...

 by Jean Taylor.

External links

• Mathworld.wolfram.com