Konkáv

Konkáv is the Hungarian term for the geometric notion of concave. It describes shapes, surfaces, and functions that curve inward, in contrast to konvex (convex). In geometry, a plane or solid figure is konkáv if there exists a line segment joining two points of the figure that leaves the figure at least partially. For simple polygons, this occurs when at least one interior angle exceeds 180 degrees, or when a diagonal lies outside the polygon. In contrast, a convex figure has all such line segments contained inside.

In mathematics, the term konkáv also applies to functions defined on a convex domain. A function f is konkáv if, for all x and y in its domain and all t in [0,1], f(t x + (1−t) y) ≥ t f(x) + (1−t) f(y). Equivalently, the graph of a konkáv function lies above the line segment (chord) connecting any two points on the graph. Concave and convex functions are central in optimization theory.

In optics and engineering, konkáv surfaces bend inward: a konkáv mirror or a konkáv lens converges light. In computational geometry, the term konkáv may appear in reference to non-convex sets and to concepts such as the concave hull, the tightest concave enclosing shape of a point set.

Examples include bowls, dented surfaces, and any indented polygon. See also konvex and concavities.