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An example of a concave polygon. A simple polygon that is not convex is called concave, [1] non-convex [2] or reentrant. [3] A concave polygon will always have at least one reflex interior angle—that is, an angle with a measure that is between 180 degrees and 360 degrees exclusive. [4]
Concave: Non-convex and simple. There is at least one interior angle greater than 180°. Star-shaped: the whole interior is visible from at least one point, without crossing any edge. The polygon must be simple, and may be convex or concave. All convex polygons are star-shaped. Self-intersecting: the boundary of the polygon crosses itself.
The sum of two concave functions is itself concave and so is the pointwise minimum of two concave functions, i.e. the set of concave functions on a given domain form a semifield. Near a strict local maximum in the interior of the domain of a function, the function must be concave; as a partial converse, if the derivative of a strictly concave ...
For the graph of a function f of differentiability class C 2 (its first derivative f', and its second derivative f'', exist and are continuous), the condition f'' = 0 can also be used to find an inflection point since a point of f'' = 0 must be passed to change f'' from a positive value (concave upward) to a negative value (concave downward) or ...
Concave or concavity may refer to: Science and technology. Concave lens; Concave mirror; Mathematics. Concave function, the negative of a convex function;
A: The bottom of a concave meniscus. B: The top of a convex meniscus. In physics (particularly fluid statics), the meniscus (pl.: menisci, from Greek 'crescent') is the curve in the upper surface of a liquid close to the surface of the container or another object, produced by surface tension.
A concave mirror with light rays Center of curvature. In geometry, the center of curvature of a curve is a point located at a distance from the curve equal to the radius of curvature lying on the curve normal vector. It is the point at infinity if the curvature is zero. The osculating circle to the curve is centered at the centre of curvature.
The dimensionless circular radii 1/2C coincides with capillary bridge radii of curvature. The positive sign '+' represents generatrix profile of concave bridge and negative '-', oblate. For the convex capillary bridges, the circular generatrix is retained until the boundary of definition domain is reached while stretching.