Vlakken

Vakken is the Dutch plural form of vlak, a term used in geometry and everyday language to refer to flat surfaces or planes. In Dutch, a vlak can denote a flat, two‑dimensional surface that extends in particular directions, and the plural vlakken is used when describing multiple such surfaces, such as the faces of a polyhedron or the surfaces of a geometric model.

In mathematics, a plane (een vlak) is a special type of vlak: a flat, two‑dimensional surface that extends infinitely in all directions within a space. A plane in three‑dimensional space can be defined by a point and a normal vector, or by the linear equation ax+by+cz+d=0. Coordinate planes, such as the xy‑plane, xz‑plane, and yz‑plane, are common examples of planes.

More general surfaces, often called oppervlakken in Dutch, are two‑dimensional manifolds that may be curved within a higher‑dimensional space. Unlike planes, these surfaces can bend and twist and have curvature. The tangent plane at a point on such a surface provides a local flat approximation and is central to differential geometry.

Vlakken and oppervlakken are fundamental in fields such as geometry, computer graphics, architecture, and geospatial sciences. They are used to model shapes, compute areas and volumes, and simulate physical processes on surfaces. Related concepts include polyhedron faces, meshes, and geodesics, all of which describe or navigate two‑dimensional structures embedded in space.