Architecture and mathematics: Soap bubbles and soap films

Abstract

Plateau’s problem consists in taking a generic curve in three-space and finding a surface with the least possible area bounded by that curve. The empirical solution may be obtained by dipping a tridimensional model of the curve into soapy water, resulting in a form called a minimal surface. When a soap bubble is blown, the soapy surface stretches; when blowing ceases, the film tends toward equilibrium. Frei Otto used soap film models to design his tensile-structures, developing a technique to obtain a precise photogrammetric evaluation of soap film models and another method to simulate peaks in a membrane of soap films. H.A. Schwarz solved Plateau’s problem for a non-plane boundary by developing the periodic minimal surface. Infinite periodic minimal surfaces, combinations of saddle polygons or surfaces, are more stable. Such a surface has been adapted as a play sculpture in the Brooklyn Museum, where children can actually enter into the labyrinthic structure of periodic minimal surfaces.