A surface is not a membrane, a thin plastic
foil, a transition boundary, the surface of a material object, the boundary
between fluids or anything else material. It is not a Euclidean surface
as a collection or locus of points. A surface is an intrinsic form
unto itself; consisting of nothing else. It is therefor an
object rather than a collection of objects. It resides in three-dimensional
Being,
as the superimposition of pure form within
the substance of Being. A surface is an object limited in presence
and behavior by its defined nature; comprising only contiguous relative
adjacent position.
A surface may be expressed as form extending infinitely great (a) along two dimensions and infinitely small (infinitesimal or zero (0)) along the other. If a point is an object represented by (a,b and c), where a = b= c = 0, a surface may be represented by (a,b and c) where a = 0 and b = c = a.
By convention, if b and c are equated to any imaginary lines or geodesics coplanar to a surface, such lines, which may also be denoted as b and c, and set mutually orthogonal to each other, and to any line as an extension of dimension a. It follows, that dimension a and its corresponding line, represent the thickness of the surface.
If Being may be equated to any three-dimensional rigid frame of reference, such as a Cartesian frame of reference (X, Y and Z), a, b and c do not necessarily correspond to X, Y and Z, and may be oriented in any direction relative to frame X, Y and Z, providing at the junction of any set of the orthogonal vectors of the family a, b and c, falls upon and is coincident to the surface at any given location on the surface.