Plateau's Laws

Plateau's laws describe the structure of soap films. These laws were formulated in the 19th century by the Belgian physicist Joseph Plateau from his experimental observations. Many patterns in nature are based on foams obeying these laws.

Plateau's laws state:

1. Soap films are made of entire smooth surfaces.
2. The mean 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 arccos(−1/2) = 120 degrees.
4. These Plateau borders meet in fours at a vertex, and they do so at an angle of arccos(−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 surfaces was proved mathematically using methods of geometric measure theory by Jean Taylor.