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In mathematics, the modulus of convexity and the characteristic of convexity are measures of "how convex" the unit ball in a Banach space is. In some sense, the modulus of convexity has the same relationship to the ε-δ definition of uniform convexity as the modulus of continuity does to the ε-δ definition of continuity.
In geometry, a polyhedral compound is a figure that is composed of several polyhedra sharing a common centre. They are the three-dimensional analogs of polygonal compounds such as the hexagram. The outer vertices of a compound can be connected to form a convex polyhedron called its convex hull. A compound is a faceting of its convex hull ...
Convex polygon, a polygon which encloses a convex set of points; Convex polytope, a polytope with a convex set of points; Convex metric space, a generalization of the convexity notion in abstract metric spaces; Convex function, when the line segment between any two points on the graph of the function lies above or on the graph
A dodecahedron is a convex body.. In mathematics, a convex body in -dimensional Euclidean space is a compact convex set with non-empty interior.Some authors do not require a non-empty interior, merely that the set is non-empty.
In complex geometry and analysis, the notion of convexity and its generalizations play an important role in understanding function behavior. Examples of classes of functions with a rich structure are, in addition to the convex functions, the subharmonic functions and the plurisubharmonic functions.
The term convex is often referred to as convex down or concave upward, and the term concave is often referred as concave down or convex upward. [ 3 ] [ 4 ] [ 5 ] If the term "convex" is used without an "up" or "down" keyword, then it refers strictly to a cup shaped graph ∪ {\displaystyle \cup } .
The polytopes of rank 2 (2-polytopes) are called polygons.Regular polygons are equilateral and cyclic.A p-gonal regular polygon is represented by Schläfli symbol {p}.. Many sources only consider convex polygons, but star polygons, like the pentagram, when considered, can also be regular.
The definition of a convex polyomino is different from the usual definition of convexity, but is similar to the definition used for the orthogonal convex hull. A polyomino is said to be vertically or column convex if its intersection with any vertical line is convex (in other words, each column has no holes).