Convex and Concave is a lithograph print by the Dutch artist M. C. Escher, first printed in March 1955. It depicts an ornate architectural structure with...

a concave function is one for which the function value at any convex combination of elements in the domain is greater than or equal to that convex combination...

while a concave function's graph is shaped like a cap ∩ {\displaystyle \cap } . A twice-differentiable function of a single variable is convex if and only...

with a curved reflecting surface. The surface may be either convex (bulging outward) or concave (recessed inward). Most curved mirrors have surfaces that...

non-convex sets. A set that is not convex is called a non-convex set. A polygon that is not a convex polygon is sometimes called a concave polygon, and some...

of the other surface. A lens with one convex and one concave side is convex-concave or meniscus. Convex-concave lenses are most commonly used in corrective...

boundary of the polygon does not cross itself. All convex polygons are simple. Concave: Non-convex and simple. There is at least one interior angle greater...

In convex analysis, a non-negative function f : Rn → R+ is logarithmically concave (or log-concave for short) if its domain is a convex set, and if it...

A simple polygon that is not convex is called concave, non-convex or reentrant. A concave polygon will always have at least one reflex interior angle—that...

over convex sets (or, equivalently, maximizing concave functions over convex sets). Many classes of convex optimization problems admit polynomial-time algorithms...

quasiconvex function that is neither convex nor continuous. Convex function Concave function Logarithmically concave function Pseudoconvexity in the sense...

mirror Concave function, the negative of a convex function Concave polygon, a polygon which is not convex Concave set The concavity of a function, determined...

and angles are equal. It is possible to go past these limiting cases, creating concave or nonconvex pyritohedra. The endo-dodecahedron is concave and...

very similar to convex and concave functions. For this reason, an optimization problem which concerns optimizing a convex or concave function can also...

In geometry, the convex hull, convex envelope or convex closure of a shape is the smallest convex set that contains it. The convex hull may be defined...

constructed from the centers and crossing points of any two intersecting circles. Kites as described here may be either convex or concave, although some sources...

or crossed). Simple quadrilaterals are either convex or concave. The interior angles of a simple (and planar) quadrilateral ABCD add up to 360 degrees...

requires correction. A good set of gauges will offer both convex and concave sections, and allow for their application in awkward locations. Every leaf has...

particular the subfields of convex analysis and optimization, a proper convex function is an extended real-valued convex function with a non-empty domain...

water and glass. Water-based fluids like sap, honey, and milk also have a concave meniscus in glass or other wettable containers. Conversely, a convex meniscus...

given vertex and the two adjacent vertices). Every non-degenerate triangle is strictly convex. Convex curve – Type of plane curve Concave polygon – Simple...

mixture of convex and concave circular arc edges. Three given angles θ 1 {\displaystyle \theta _{1}} , θ 2 {\displaystyle \theta _{2}} , and θ 3 {\displaystyle...

two forms: concave angles and convex angles. Concave angles have slightly concave sides and open to the medial (inner) area of the tusk. Convex angles have...

for convex and concave real-valued functions, defined on an interval of the real line. It generalizes the discrete form of Jensen's inequality, and generalizes...

which self-intersect in a repetitive way. Concave polyhedra of a particular kind which alternate convex and concave or saddle vertices in a repetitive way...

Schur, Schur-convex functions are used in the study of majorization. A function f is 'Schur-concave' if its negative, −f, is Schur-convex. Every function...

carnivals and fairs. Instead of a normal plane mirror that reflects a perfect mirror image, distorting mirrors are curved mirrors, often using convex and concave...

columns and decorative pilasters. Ancient Egyptian architecture used fluting in many buildings; most often the flutes are convex rather than concave, so the...

that keeps separate lists of convex and concave vertices will run in O(n2) time. This method is known as ear clipping and sometimes ear trimming. An efficient...

either convex (bending outward) or concave (bending inward). The intersection of three disks forms a circular triangle whose sides are all convex. An example...