konkavitet

Konkavitet is the property of concavity as it is used in several fields to describe inward curvature of a shape, surface, or function. The term is the counterpart to convexitet, which denotes outward bending. In mathematics and related disciplines, konkavitet characterizes the way a boundary or graph bends toward the interior of a region.

In geometry, a set or shape is konkav if it is not convex. For polygons, this means there exists at least one line segment joining two points of the polygon that leaves the polygon’s interior. A concave polygon has indentations or interior angles greater than 180 degrees. By contrast, convex shapes have no such indentations.

In calculus and analysis, konkavitet describes the curvature of graphs and functions. A real-valued function on an interval is concave if the line segment between any two points of its graph lies on or below the graph; equivalently, the second derivative is non-positive (f'' ≤ 0) on that interval. If f'' ≥ 0, the function is convex.

Outside pure mathematics, konkavitet appears in optics, with concave lenses and mirrors that curve inward and converge light, and in design and engineering where inward curvature affects fit, contact, or stress distribution. In anatomy and biomechanics, concave surfaces describe inward-curved bone or joint surfaces, often interacting with convex counterparts.

Summary: konkavitet describes inward bending relative to a reference region, scale, or axis. It is defined by geometric properties, curvature, or functional behavior, and is understood in relation to convexity. Context determines whether concavity is considered advantageous or problematic, depending on goals such as focal properties, stability, or fit.