platvlak

Platvlak is the Dutch term for a plane surface in geometry, referring to a flat, two-dimensional surface that extends without bound in its own plane. In Euclidean space, a platvlak is a plane. It has zero curvature and can be embedded in three-dimensional space as the set of points satisfying a linear equation ax + by + cz + d = 0, where [a,b,c] is a nonzero normal vector.

Geometric properties: any two points determine a line; any three non-collinear points determine the plane; two planes are either parallel or intersect along a line; the distance from a point to a plane is |ax0+by0+cz0+d| / sqrt(a^2+b^2+c^2). The XY, YZ, and XZ planes are common examples (z=0, x=0, y=0) in R^3.

Applications: platvlakken are foundational in geometry, physics, engineering and computer graphics. In CAD and 3D modeling, they serve as flat surfaces or surface primitives, used for clipping, shading, and intersection computations. In analytic geometry, they provide a simple setting to study linear equations and vector normals.

Etymology: the term comes from Dutch, combining plat (flat) and vlak (surface).