A minimal surface can refer to one of two kinds of entities: a natural minimal surface or a mathematical minimal surface.
The natural minimal surface is that of a soap film stretched within a framework, and it has helical edges which can be observed if the framework is 1/2 inch plexiglass tubes.
A mathematical minimal surface, is defined as a surface with mean curvature of zero, and by contrast with a natural minimal surface, has straight edges, and can only approximate the true minimal surface that occurs throughout nature, that of the soap film. Examples of a mathematical minimal are catenoids and helicoids.
Minimal surfaces have become an area of intense mathematical and scientific study over the past 15 years, specifically in the areas of molecular engineering and materials science, due to their anticipated nanotechnology applications.
