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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]
This is a list of two-dimensional geometric shapes in Euclidean and other geometries. For mathematical objects in more dimensions, see list of mathematical shapes. For a broader scope, see list of shapes.
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 ...
In mathematics, a real-valued function is called convex if the line segment between any two distinct points on the graph of the function lies above or on the graph between the two points. Equivalently, a function is convex if its epigraph (the set of points on or above the graph of the function) is a convex set .
Such shapes include polygons, which may be concave, shapes with holes, and collections of such shapes (i.e. the regions need not be connected). The corresponding problem that the theorem solves is known as the fold-and-cut problem , which asks what shapes can be obtained by the so-called fold-and-cut method.
Circular triangles with a mixture of convex and concave edges. A circular triangle is a triangle with circular arc edges. The edges of a circular triangle may be either convex (bending outward) or concave (bending inward). [c] The intersection of three disks forms a circular triangle whose sides are all convex.