Ebenen

Ebenen is the German plural of Ebene and can refer to several related concepts in geography, mathematics, and information technology. In everyday language Ebenen often means plains or flat lands, while in technical contexts it denotes flat surfaces or layers.

In geography and geomorphology, Ebenen describe broad, flat or gently rolling regions with low relief. They emerge from sediment deposition, tectonic processes, or river activity and are important for agriculture, climate, and settlement patterns. Notable European examples include large lowland zones such as the North German Plain and the Central European Plain.

In mathematics, Ebenen denote planes in Euclidean space. A plane is a two-dimensional surface that extends without bound. It can be described by a linear equation ax + by + cz = d, with normal vector n = (a, b, c). Through a given point p0, the plane consists of all points p satisfying n · (p − p0) = 0. Planes intersect along lines and can be parallel if their normal vectors are proportional. Through the origin, the plane ax + by + cz = 0 is a subspace of R^3; in general a plane need not pass through the origin.

In computing and graphics, Ebenen are layers or sheets used to organize content, such as map layers in geographic information systems or image editing layers. Layers can be reordered, shown or hidden, and combined to create complex visuals.

Overall, Ebenen share the core idea of a flat, two-dimensional surface or organizational layer, with domain-specific definitions and uses.