Konkávak

Konkávak is a term used in geometry to describe a type of curve or shape. A shape is considered konkáv if it caves inward, meaning that if you draw a line segment between any two points on the boundary of the shape, at least one point on that line segment will lie outside the shape. Alternatively, a konkáv shape is one that is not convex.

A convex shape, in contrast, has the property that any line segment connecting two points on its boundary lies entirely within or on the boundary of the shape. Think of a circle or a square; these are convex. A star shape, however, is konkáv because the points where the inner angles meet cause the boundary to cave inward.

In mathematics, the term "konkáv" is often used in the context of functions. A function is konkáv if the line segment connecting any two points on its graph lies below or on the graph. This is sometimes referred to as being "concave down." The opposite is a convex function, which is "concave up."

The concept of konkávity is important in various fields, including calculus, optimization, and computer graphics. Understanding whether a shape or function is konkáv or convex can significantly affect the methods used to analyze and manipulate it. For instance, in optimization problems, finding the minimum of a convex function is generally easier than finding the minimum of a konkáv function. The term originates from the Latin word "concavus," meaning hollow or arched inward.