konkav

Konkav is a term used in several languages to describe surfaces or shapes that bend inward, rather than outward. It is the counterpart of convex. The word is related to the Latin concavus and appears in technical contexts such as geometry, optics, and calculus, where the English equivalent is concave.

In geometry, konkav describes a shape in which some interior angles exceed 180 degrees, or, equivalently, a line segment joining two points of the shape may lie outside the shape. A konkav polygon contrasts with a convex polygon, whose interior region contains all line segments between its points.

In optics, konkav surfaces curve inward. A concave mirror has an inward-curving reflecting surface and can converge light to a focal point under appropriate conditions. A concave lens diverges light, spreading rays away from a virtual focal point on the same side as the object.

In mathematics, a concave function curves downward. For a twice-differentiable function, f''(x) < 0 on an interval implies concavity on that interval. Concavity is a key concept in optimization and economic theory, reflecting diminishing returns or benefits as inputs rise.

Related concepts include convexity, curvature, concavity, and the convex hull. While the term konkav is used in several languages to describe inward-curving geometry, the underlying ideas align with the standard mathematical notion of concavity across disciplines.