konveksseid

Konveksseid is an Estonian grammatical form—the plural partitive of the adjective konveks (convex). It is used when describing multiple convex shapes or objects, for example konveksseid kujundeid meaning convex shapes. In mathematics, the underlying concept is convexity, which is referred to in Estonian as konveksus.

A set S in a real vector space is called convex if for any two points x and y in S and any t in the closed interval [0, 1], the point (1 − t)x + ty also lies in S. This means that the line segment joining any two points of S is entirely contained in S. Convexity can also be described using convex combinations: S is convex whenever every finite convex combination of its points remains in S.

Key properties include that the intersection of any family of convex sets is convex, and every set has a convex hull—the smallest convex set containing it. Convex sets are closed under convex combinations: if you take any finite set of points in a convex set and form a weighted average with nonnegative weights summing to one, the result stays in the set. Typical convex shapes include line segments, circles, ellipses, and polygons without indentations. Shapes with dents or reentrant angles, such as crescent moons or star-shaped polygons with inward points, are not convex.

Konveksus and convexity have broad applications in optimization, economics, computational geometry, and computer graphics. They provide foundational tools for understanding feasible regions in linear programming, for deriving efficient algorithms, and for analyzing geometric properties of shapes and functions.