Konveksliini

Konveksliini is a mathematical concept referring to a line segment that connects two points on the boundary of a convex set. A convex set is a set of points where for any two points within the set, the line segment connecting them is entirely contained within the set. Therefore, any line segment connecting two points on the boundary of a convex set is also a konveksliini. The properties of konveksliini are directly tied to the convexity of the set it belongs to. For instance, if a set is strictly convex, then any konveksliini connecting two distinct boundary points will lie entirely within the interior of the set, except for its endpoints. This distinguishes konveksliini from chords in non-convex shapes, where a connecting line segment might pass outside the shape. The concept is fundamental in areas of mathematics such as convex geometry, optimization, and functional analysis.