Plateau's laws describe the shape and configuration of soap films as follows: • Soap films are made of entire (unbroken) smooth surfaces. • The
mean 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 arccos(−) = 120°. • These Plateau borders meet in fours at a vertex, at the
tetrahedral angle of arccos(−) ≈ 109.47°. 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 by
Jean Taylor using
geometric measure theory. ==See also==