Plateau's laws

Plateau's Rules describe the structure of soap films in foams. These rules were formulated in the 19th century by the Belgian physicist Joseph Plateau from his experimental observations.

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Plateau's rules state:

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

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

These rules were proved mathematically using the methods of geometric measure theory by Jean Taylor^[1]

Notes

1. ^ Jean E. Taylor. The Structure of Singularities in Soap-Bubble-Like and Soap-Film-Like Minimal Surfaces. The Annals of Mathematics, 2nd Ser., Vol. 103, No. 3. May, 1976), pp. 489-539.