Convex and Concave information

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...

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...

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

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...

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...

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...

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...

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...

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

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

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

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...

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

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...

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...

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

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...

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...

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...

staircase given to M. C. Escher by Prof. Schouten and which was an inspiration for Escher's Convex and Concave. This illusion is also seen in another Escher's...