Plateau's laws

Plateau’s laws describe the natural structure of soap films and bubbles. They state that soap films form minimal surfaces, meeting in ways that minimize energy: films meet in threes at 120° angles along edges, and these edges meet in fours at the vertices at approximately 109.5°, similar to the angles in a regular tetrahedron. These rules help explain the efficient, stable arrangements of soap films, which naturally optimize surface area and energy. Overall, Plateau’s laws reveal how soap films self-organize into geometric patterns that reflect underlying physical principles of minimal surface area and energy minimization.