When most of us think of the word “surface” we often envision our own world—the thin outer crust of soil and rock we walk and live on. In engineering, the term means the outer part (or the skin with a thickness of zero) of a body. In science it can apply to a plethora of objects, from geologic structures to micrometer-sized particles.

In mathematics, “surface” also has numerous meanings. The most common denotes a two-dimensional topological space or three-dimensional Euclidean space. A surface in mathematics can be complicated and complex, such as in certain fractals, or extremely simple, such as in a plane.