In mathematics, a surface (in ordinary space) is a part of space with no thickness: a sheet of paper (possibly folded or twisted), the infinitely thin skin of a fruit… The area of a surface, by contrast, is a measure of its size. It is a quantity that can, for example, be expressed in m2. The area of a region of the plane is relatively easy to define using the notion of an integral. However, the area of an arbitrary surface in space is more difficult to define rigorously, even though ordinary intuition suffices in simple cases.