Convex or convexity may refer to:
Science and technology
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Convex lens
A lens is a transmissive optical device which focuses or disperses a light beam by means of refraction. A simple lens consists of a single piece of transparent material, while a compound lens consists of several simple lenses (''elements''), ...
, in optics
Mathematics
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Convex set
In geometry, a subset of a Euclidean space, or more generally an affine space over the reals, is convex if, given any two points in the subset, the subset contains the whole line segment that joins them. Equivalently, a convex set or a convex ...
, containing the whole line segment that joins points
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Convex polygon
In geometry, a convex polygon is a polygon that is the boundary of a convex set. This means that the line segment between two points of the polygon is contained in the union of the interior and the boundary of the polygon. In particular, it is a ...
, a polygon which encloses a convex set of points
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Convex polytope, a polytope with a convex set of points
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Convex metric space, a generalization of the convexity notion in abstract metric spaces
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Convex function
In mathematics, a real-valued function is called convex if the line segment between any two points on the graph of the function lies above the graph between the two points. Equivalently, a function is convex if its epigraph (the set of poin ...
, when the line segment between any two points on the graph of the function lies above or on the graph
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Convex conjugate
In mathematics and mathematical optimization, the convex conjugate of a function is a generalization of the Legendre transformation which applies to non-convex functions. It is also known as Legendre–Fenchel transformation, Fenchel transformatio ...
, of a function
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Convexity (algebraic geometry), a restrictive technical condition for
algebraic varieties
Algebraic varieties are the central objects of study in algebraic geometry, a sub-field of mathematics. Classically, an algebraic variety is defined as the set of solutions of a system of polynomial equations over the real or complex number
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originally introduced to analyze Kontsevich