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.
Plateau's laws state:
- Soap films are made of entire smooth surfaces.
- The average curvature of a portion of a soap film is everywhere constant on any point on the same piece of soap film.
- 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.
- 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 surfaces was proved mathematically using methods of geometric measure theory by Jean Taylor.[1][2]
See also
Notes
- ^ Jean E. Taylor. "The Structure of Singularities in Soap-Bubble-Like and Soap-Film-Like Minimal Surfaces". Annals of Mathematics, 2nd Ser., Vol. 103, No. 3. May, 1976, pp. 489–539.
- ^ Frederick J. Almgren Jr and Jean E. Taylor, “The geometry of soap films and soap bubbles”, Scientific American, vol. 235, pp. 82–93, July 1976.
External links
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