Medelpunkt

Medelpunkt is a Swedish term meaning “mean point” or “center point,” used in mathematics and related fields to describe a central or balancing position. The concept is primarily defined as an average position of points or masses.

In geometry, medelpunkt most commonly refers to the midpoint of a line segment: for endpoints A(x1, y1) and B(x2, y2), the medelpunkt M has coordinates ((x1 + x2)/2, (y1 + y2)/2). In three-dimensional space, the same idea yields M = ((x1 + x2)/2, (y1 + y2)/2, (z1 + z2)/2). More generally, medelpunkt can denote the centroid, the center of mass for a shape or system with mass distribution.

For a triangle with vertices A, B, C, the centroid is the intersection point of the medians and has coordinates ((xA + xB + xC)/3, (yA + yB + yC)/3). For a polygon, the centroid can be computed by a area-weighted sum of its vertices using a standard formula, which generalizes the notion of a center of mass for uniform density.

In physics and engineering, medelpunkt often refers to the center of mass (barycenter) of a system of particles with given masses mi at positions ri, given by R = (sum mi ri) / (sum mi).

The term is used across disciplines to describe a central or balancing point. It is related to, but distinct from, terms such as mittenpunkt or mittpunkt (midpoint), centroid, and barycenter, depending on context.