suprafata

Suprafata, or suprafata with diacritics, is a Romanian term that broadly means the surface or outer face of an object. In everyday language it refers to the external boundary or the topmost layer of a thing, such as the surface of a table or the surface of land. In mathematical and scientific contexts, it denotes a two-dimensional locus or a two-dimensional object embedded in a higher-dimensional space, and it is closely linked to the notion of surface area.

In geometry and differential geometry, a surface is a two-dimensional manifold that can be curved and embedded in three-dimensional space. A surface can be described locally by parametric equations r(u,v) and studied through its tangent planes, normal vectors, and curvature. Regularity conditions are imposed to ensure smoothness, enabling the use of tools such as first and second fundamental forms, surface integrals, and curvature measures.

Surface area measures the two-dimensional extent of a surface. For a parametric surface r(u,v) defined on a domain D, the area is A = ∬D |r_u × r_v| du dv. Common examples include the area of a plane (A = base × height), a sphere (A = 4πr^2), a cube (A = 6a^2), and a cylinder (A = 2πr(h + r)). Units are square units, typically square meters (m^2) in physical contexts.

In Romanian usage, suprafata can refer to the physical surface of an object or, in mathematical language, to the surface itself, while the word aria is often used for the numerical measure of that surface, i.e., the area.