Centrumpunt

Centrumpunt is a term used in geometry to denote the center point of a geometric figure, commonly equated with the centroid or barycenter in many contexts. The word combines centrum (center) and punt (point) and appears in some European-language texts and translations. It is not a standard English mathematical term in core references, but it is encountered in educational materials and discussions of geometry terminology.

For a two-dimensional lamina of uniform density, the centrumpunt coincides with the centroid. In a triangle, the centrumpunt is the intersection of the medians. For a general polygon or irregular shape, it can be found by decomposing the figure into simpler parts (such as triangles) and combining their centroids by area, or by applying the first moments of area in a continuous setting. In discrete or computational contexts, the centrumpunt is determined by weighting points by their mass or area and averaging their coordinates accordingly.

The centrumpunt should be distinguished from centers defined by equal distances to vertices (circumcenter) or to sides (incenter). It is primarily a balancing point: a location at which the shape would balance if made of a uniform material. Accordingly, it is used as a reference point in design, computer graphics, architecture, and geographic information systems to analyze symmetry, mass distribution, and layout.

Related concepts include centroid, barycenter, geometric center, and center of mass.