Plateau's problem

Plateau's problem is a question in mathematics and the calculus of variations that asks how to find the simplest surface that spans a given boundary. Imagine a soap film stretched across a wireframe shape; the film naturally takes on the shape with the least surface area while maintaining the boundary. Plateau's problem seeks to determine the mathematical conditions for such minimal surfaces, which can have applications in physics, engineering, and materials science. It challenges our understanding of geometry and efficiency in how surfaces behave under constraints.