felszín

Felszín, in Hungarian, generally means surface and is used across disciplines to denote a two-dimensional extent or boundary. The term covers both the mathematical concept of a two-dimensional manifold embedded in a higher-dimensional space and the outer layer of a body, such as the Earth’s surface. In everyday language and science, felszín often refers to the visible or accessible interface between different media.

In mathematics, a felszín is typically a two-dimensional differentiable manifold, commonly embedded in three-dimensional Euclidean space. It can be described parametrically by a map r(u,v) from an open subset of R^2 into R^3, with partial derivatives ru and rv spanning the tangent plane at each regular point. A regular surface is locally homeomorphic to the plane, so every small patch resembles a flat region even if the global shape is curved. Surfaces may be orientable or nonorientable and may possess boundaries.

Curvature and global properties are central to the study of felszínek (plural) in differential geometry. The Gaussian curvature K is intrinsic to the surface, while the mean curvature H describes how the surface bends in the ambient space. Common examples include the plane (K = 0), the sphere (K > 0), and the saddle surface (K < 0). Surfaces can be classified topologically by genus and by whether they are compact or have boundary. Special families include minimal surfaces, where H = 0.

Outside pure geometry, felszín also denotes surfaces in applied contexts: the Earth’s topography modeled by digital elevation models, the interface between materials, or the surfaces used in computer graphics and architectural design.